**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Clock Conversion
time_limit_ms: 1000
memory_limit_mb: 256
Description: Given the time in 24-hour format, output the equivalent time in 12-hour format.

- 24-hour format divides the day into 24 hours from $$$00$$$ to $$$23$$$, each of which has 60 minutes from $$$00$$$ to $$$59$$$.
- 12-hour format divides the day into two halves: the first half is $$$\mathrm{AM}$$$, and the second half is $$$\mathrm{PM}$$$. In each half, the hours are numbered in the order $$$12, 01, 02, 03, \dots, 11$$$. Each hour has 60 minutes numbered from $$$00$$$ to $$$59$$$.

Input: The first line contains a single integer $$$t$$$ ($$$1 \leq t \leq 1440$$$) — the number of test cases.

The only line of each test case contains a string $$$s$$$ of length $$$5$$$ with format hh:mm representing a valid time in the 24-hour format. hh represents the hour from $$$00$$$ to $$$23$$$, and mm represents the minute from $$$00$$$ to $$$59$$$.

The input will always be a valid time in 24-hour format.

Output: For each test case, output two strings separated by a space ("hh:mm AM" or "hh:mm PM"), which are the 12-hour equivalent to the time provided in the test case (without quotes).

You should output the time exactly as indicated; in particular, you should not remove leading zeroes.

Examples:
input:
11
09:41
18:06
12:14
00:59
00:00
14:34
01:01
19:07
11:59
12:00
21:37
output:
09:41 AM
06:06 PM
12:14 PM
12:59 AM
12:00 AM
02:34 PM
01:01 AM
07:07 PM
11:59 AM
12:00 PM
09:37 PM

Note:

Buggy Code:
import java.util.*;
import java.io.*;

public class Main {

    public static void main(String[] args) throws IOException {
        BufferedReader f = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter out = new PrintWriter(System.out);
        StringTokenizer st;
        int t = Integer.parseInt(f.readLine());
        while (t-- > 0) {
            String s = f.readLine();
            String[] arr = s.split(":");
            if (Integer.parseInt(arr[0]) < 12) {
                if (Integer.parseInt(arr[0]) == 0) {
                    out.println("12" + ":" + arr[1] + " AM");
                } else {
                    out.println(arr[0] + ":" + arr[1] + " AM");
                }
            } else {
                if (Integer.parseInt(arr[0]) == 12) {
                    out.println("12" + ":" + arr[1] + " PM");
                } else {
                    out.println("0" + (Integer.parseInt(arr[0]) - 12) + ":" + arr[1] + " PM");
                }
            }

        }
        f.close();
        out.close();
    }
}

**Instructions:**
- Focus on edge cases or scenarios that maximize the failure probability in faulty solutions.
- Due to the output length limit, you should generate a **small-scale** test input that is **complete and valid**.
- Output the test input directly, not code to generate it.

**Output format:**
```plaintext
{test input}
```

Think step by step.

Response:
```plaintext
3
00:00
12:00
23:59
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Clock Conversion
time_limit_ms: 1000
memory_limit_mb: 256
Description: Given the time in 24-hour format, output the equivalent time in 12-hour format.

- 24-hour format divides the day into 24 hours from $$$00$$$ to $$$23$$$, each of which has 60 minutes from $$$00$$$ to $$$59$$$.
- 12-hour format divides the day into two halves: the first half is $$$\mathrm{AM}$$$, and the second half is $$$\mathrm{PM}$$$. In each half, the hours are numbered in the order $$$12, 01, 02, 03, \dots, 11$$$. Each hour has 60 minutes numbered from $$$00$$$ to $$$59$$$.

Input: The first line contains a single integer $$$t$$$ ($$$1 \leq t \leq 1440$$$) — the number of test cases.

The only line of each test case contains a string $$$s$$$ of length $$$5$$$ with format hh:mm representing a valid time in the 24-hour format. hh represents the hour from $$$00$$$ to $$$23$$$, and mm represents the minute from $$$00$$$ to $$$59$$$.

The input will always be a valid time in 24-hour format.

Output: For each test case, output two strings separated by a space ("hh:mm AM" or "hh:mm PM"), which are the 12-hour equivalent to the time provided in the test case (without quotes).

You should output the time exactly as indicated; in particular, you should not remove leading zeroes.

Examples:
input:
11
09:41
18:06
12:14
00:59
00:00
14:34
01:01
19:07
11:59
12:00
21:37
output:
09:41 AM
06:06 PM
12:14 PM
12:59 AM
12:00 AM
02:34 PM
01:01 AM
07:07 PM
11:59 AM
12:00 PM
09:37 PM

Note:

Buggy Code:
#include<bits/stdc++.h>
using namespace std;
string convert(string &s){
    string st="";
    st+=s[0];
    st+=s[1];
    int a=stoi(st);
    if(a==12){
      for(int i=2;i<5;i++){
        st+=s[i];
    }
    st+=" ";
    st+="PM";
    }
    else if(a==00){
        st="12";
        for(int i=2;i<5;i++){
        st+=s[i];
    }
    st+=" ";
    st+="AM";
    }
    else if(a>12){
      a= a-12;
      if(a<10){
        st="0"+to_string(a);
        for(int i=2;i<5;i++){
        st+=s[i];
    }
     st+=" ";
    st+="PM";
      }
      else if(a>10){
        st=to_string(a);
        for(int i=2;i<5;i++){
        st+=s[i];
    }
     st+=" ";
    st+="PM";
      }

    }
  else{
    for(int i=2;i<5;i++){
        st+=s[i];
    }
     st+=" ";
    st+="AM";
  }

    return st;
}
int main(){
    int t;
    cin>>t;
    while(t--){
        string s;
        cin>>s;
        string st;
        st=convert(s);
        cout<<st<<endl;
    }
    return 0;
}

**Instructions:**
- Focus on edge cases or scenarios that maximize the failure probability in faulty solutions.
- Due to the output length limit, you should generate a **small-scale** test input that is **complete and valid**.
- Output the test input directly, not code to generate it.

**Output format:**
```plaintext
{test input}
```

Think step by step.

Response:
To generate a challenging test input that exposes the bug in the given buggy code, we need to focus on edge cases and scenarios that are likely to cause issues. Here are the steps to identify and create such a test input:

1. **Edge Cases for AM/PM Conversion:**
   - Midnight (00:00) should be converted to 12:00 AM.
   - Noon (12:00) should be converted to 12:00 PM.
   - Just before midnight (23:59) should be converted to 11:59 PM.
   - Just after midnight (00:01) should be converted to 12:01 AM.
   - Just before noon (11:59) should be converted to 11:59 AM.
   - Just after noon (12:01) should be converted to 12:01 PM.

2. **Edge Cases for Leading Zeros:**
   - Times with leading zeros in the hour (e.g., 01:00, 09:00) should be correctly converted to 01:00 AM and 09:00 AM.
   - Times with leading zeros in the minute (e.g., 00:01, 12:09) should be correctly converted to 12:01 AM and 12:09 PM.

3. **General Cases:**
   - Times that are exactly 12 hours apart (e.g., 06:00 and 18:00) should be converted to 06:00 AM and 06:00 PM.

Given these considerations, here is a small-scale test input that includes all the necessary edge cases:

```plaintext
10
00:00
00:01
01:00
09:00
11:59
12:00
12:01
18:00
23:59
12:34
```

This test input will help identify issues with the conversion logic, especially around midnight, noon, and leading zeros.


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Clock Conversion
time_limit_ms: 1000
memory_limit_mb: 256
Description: Given the time in 24-hour format, output the equivalent time in 12-hour format.

- 24-hour format divides the day into 24 hours from $$$00$$$ to $$$23$$$, each of which has 60 minutes from $$$00$$$ to $$$59$$$.
- 12-hour format divides the day into two halves: the first half is $$$\mathrm{AM}$$$, and the second half is $$$\mathrm{PM}$$$. In each half, the hours are numbered in the order $$$12, 01, 02, 03, \dots, 11$$$. Each hour has 60 minutes numbered from $$$00$$$ to $$$59$$$.

Input: The first line contains a single integer $$$t$$$ ($$$1 \leq t \leq 1440$$$) — the number of test cases.

The only line of each test case contains a string $$$s$$$ of length $$$5$$$ with format hh:mm representing a valid time in the 24-hour format. hh represents the hour from $$$00$$$ to $$$23$$$, and mm represents the minute from $$$00$$$ to $$$59$$$.

The input will always be a valid time in 24-hour format.

Output: For each test case, output two strings separated by a space ("hh:mm AM" or "hh:mm PM"), which are the 12-hour equivalent to the time provided in the test case (without quotes).

You should output the time exactly as indicated; in particular, you should not remove leading zeroes.

Examples:
input:
11
09:41
18:06
12:14
00:59
00:00
14:34
01:01
19:07
11:59
12:00
21:37
output:
09:41 AM
06:06 PM
12:14 PM
12:59 AM
12:00 AM
02:34 PM
01:01 AM
07:07 PM
11:59 AM
12:00 PM
09:37 PM

Note:

Buggy Code:
#include<iostream>
#include <bits/stdc++.h>
using namespace std;
int main(){
int t;
cin>>t;
for(int i=0;i<t;i++){
     string s,s1;
     cin>>s;
    s1+=s[0];
    s1+=s[1];
    int k=stoi(s1);

    if(k>12){
        k=k-12;
        string s3;
        s3+='0';
         string s4= to_string(k);
         s3+=s4;
         s3+=s[2];
         s3+=s[3];
         s3+=s[4];
         s3+=" ";
         s3+="PM";
         cout<<s3;
         cout<<endl;

    }
    else if(k<=12 && k!=0){
        s+=" ";
        if(k==12){
           s+="PM";
        }
        else{
         s+="AM";
        }
         cout<<s;
         cout<<endl;
    }
    else {
        k+=12;
        string s3 = to_string(k);
         s3+=s[2];
         s3+=s[3];
         s3+=s[4];
         s3+=" ";
         s3+="AM";
         cout<<s3;
         cout<<endl;
    }
}
return 0;
}

**Instructions:**
- Focus on edge cases or scenarios that maximize the failure probability in faulty solutions.
- Due to the output length limit, you should generate a **small-scale** test input that is **complete and valid**.
- Output the test input directly, not code to generate it.

**Output format:**
```plaintext
{test input}
```

Think step by step.

Response:
```plaintext
3
00:00
12:00
23:59
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Clock Conversion
time_limit_ms: 1000
memory_limit_mb: 256
Description: Given the time in 24-hour format, output the equivalent time in 12-hour format.

- 24-hour format divides the day into 24 hours from $$$00$$$ to $$$23$$$, each of which has 60 minutes from $$$00$$$ to $$$59$$$.
- 12-hour format divides the day into two halves: the first half is $$$\mathrm{AM}$$$, and the second half is $$$\mathrm{PM}$$$. In each half, the hours are numbered in the order $$$12, 01, 02, 03, \dots, 11$$$. Each hour has 60 minutes numbered from $$$00$$$ to $$$59$$$.

Input: The first line contains a single integer $$$t$$$ ($$$1 \leq t \leq 1440$$$) — the number of test cases.

The only line of each test case contains a string $$$s$$$ of length $$$5$$$ with format hh:mm representing a valid time in the 24-hour format. hh represents the hour from $$$00$$$ to $$$23$$$, and mm represents the minute from $$$00$$$ to $$$59$$$.

The input will always be a valid time in 24-hour format.

Output: For each test case, output two strings separated by a space ("hh:mm AM" or "hh:mm PM"), which are the 12-hour equivalent to the time provided in the test case (without quotes).

You should output the time exactly as indicated; in particular, you should not remove leading zeroes.

Examples:
input:
11
09:41
18:06
12:14
00:59
00:00
14:34
01:01
19:07
11:59
12:00
21:37
output:
09:41 AM
06:06 PM
12:14 PM
12:59 AM
12:00 AM
02:34 PM
01:01 AM
07:07 PM
11:59 AM
12:00 PM
09:37 PM

Note:

Buggy Code:
# C
num = int(input())

for i in range(num):
    s = input().split(":")
    a = int(s[0])
    if (a == 0):
        print(f"12:{s[1]} AM")
    elif (a < 12):
        print(':'.join(s), "AM")
    elif (a == 12):
        print(':'.join(s), "PM")
    else:
        print(f"0{a-12}:{s[1]} PM")

**Instructions:**
- Focus on edge cases or scenarios that maximize the failure probability in faulty solutions.
- Due to the output length limit, you should generate a **small-scale** test input that is **complete and valid**.
- Output the test input directly, not code to generate it.

**Output format:**
```plaintext
{test input}
```

Think step by step.

Response:
To expose the bug in the provided code, we need to focus on edge cases that might cause the code to fail. The code has issues with handling the 12-hour format correctly, especially around the transition points between AM and PM and the handling of leading zeros.

Here are the key edge cases to consider:
1. **Midnight (00:00) and Noon (12:00)**: These times should be handled specially.
2. **Hours just before and after midnight and noon** (e.g., 11:59 PM to 12:01 AM and 11:59 AM to 12:01 PM).
3. **Leading zeros in the hour and minute**.

Let's generate a small-scale test input that includes these edge cases:

```plaintext
5
00:00
00:59
11:59
12:00
12:01
```

This test input includes:
1. **00:00** - Midnight, which should be "12:00 AM".
2. **00:59** - Just before midnight, which should be "12:59 AM".
3. **11:59** - Just before noon, which should be "11:59 AM".
4. **12:00** - Noon, which should be "12:00 PM".
5. **12:01** - Just after noon, which should be "12:01 PM".

These cases will help expose any issues with the handling of the 12-hour format and the transition between AM and PM.


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Clock Conversion
time_limit_ms: 1000
memory_limit_mb: 256
Description: Given the time in 24-hour format, output the equivalent time in 12-hour format.

- 24-hour format divides the day into 24 hours from $$$00$$$ to $$$23$$$, each of which has 60 minutes from $$$00$$$ to $$$59$$$.
- 12-hour format divides the day into two halves: the first half is $$$\mathrm{AM}$$$, and the second half is $$$\mathrm{PM}$$$. In each half, the hours are numbered in the order $$$12, 01, 02, 03, \dots, 11$$$. Each hour has 60 minutes numbered from $$$00$$$ to $$$59$$$.

Input: The first line contains a single integer $$$t$$$ ($$$1 \leq t \leq 1440$$$) — the number of test cases.

The only line of each test case contains a string $$$s$$$ of length $$$5$$$ with format hh:mm representing a valid time in the 24-hour format. hh represents the hour from $$$00$$$ to $$$23$$$, and mm represents the minute from $$$00$$$ to $$$59$$$.

The input will always be a valid time in 24-hour format.

Output: For each test case, output two strings separated by a space ("hh:mm AM" or "hh:mm PM"), which are the 12-hour equivalent to the time provided in the test case (without quotes).

You should output the time exactly as indicated; in particular, you should not remove leading zeroes.

Examples:
input:
11
09:41
18:06
12:14
00:59
00:00
14:34
01:01
19:07
11:59
12:00
21:37
output:
09:41 AM
06:06 PM
12:14 PM
12:59 AM
12:00 AM
02:34 PM
01:01 AM
07:07 PM
11:59 AM
12:00 PM
09:37 PM

Note:

Buggy Code:
x = int(input())
for i in range(x):
    x2 = input()
    hr = x2[0]+x2[1]
    min = x2[3] + x2[4]
    if hr =='00':
        print('12'+':'+min,'AM')
    if int(hr)>0 and int(hr)<12:
        print(hr+':'+min,'AM')
    if int(hr)==12:
        print(hr + ':' + min, 'PM')
    if int(hr)>12 and int(hr)<24:
        print('0'+str((int(hr)-12)) + ':' + min, 'PM')
    if hr == '24':
        print(hr + ':' + min, 'AM')

**Instructions:**
- Focus on edge cases or scenarios that maximize the failure probability in faulty solutions.
- Due to the output length limit, you should generate a **small-scale** test input that is **complete and valid**.
- Output the test input directly, not code to generate it.

**Output format:**
```plaintext
{test input}
```

Think step by step.

Response:
```plaintext
5
00:00
12:00
23:59
11:59
24:00
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Clock Conversion
time_limit_ms: 1000
memory_limit_mb: 256
Description: Given the time in 24-hour format, output the equivalent time in 12-hour format.

- 24-hour format divides the day into 24 hours from $$$00$$$ to $$$23$$$, each of which has 60 minutes from $$$00$$$ to $$$59$$$.
- 12-hour format divides the day into two halves: the first half is $$$\mathrm{AM}$$$, and the second half is $$$\mathrm{PM}$$$. In each half, the hours are numbered in the order $$$12, 01, 02, 03, \dots, 11$$$. Each hour has 60 minutes numbered from $$$00$$$ to $$$59$$$.

Input: The first line contains a single integer $$$t$$$ ($$$1 \leq t \leq 1440$$$) — the number of test cases.

The only line of each test case contains a string $$$s$$$ of length $$$5$$$ with format hh:mm representing a valid time in the 24-hour format. hh represents the hour from $$$00$$$ to $$$23$$$, and mm represents the minute from $$$00$$$ to $$$59$$$.

The input will always be a valid time in 24-hour format.

Output: For each test case, output two strings separated by a space ("hh:mm AM" or "hh:mm PM"), which are the 12-hour equivalent to the time provided in the test case (without quotes).

You should output the time exactly as indicated; in particular, you should not remove leading zeroes.

Examples:
input:
11
09:41
18:06
12:14
00:59
00:00
14:34
01:01
19:07
11:59
12:00
21:37
output:
09:41 AM
06:06 PM
12:14 PM
12:59 AM
12:00 AM
02:34 PM
01:01 AM
07:07 PM
11:59 AM
12:00 PM
09:37 PM

Note:

Buggy Code:
import java.util.*;
public class Clock
{
    public static void main(String args[])
    {
        Scanner sc=new Scanner(System.in);
        int t=Integer.parseInt(sc.nextLine()); // number of test cases
        String arr[]=new String[t];
        for(int i=1;i<=t;i++)
        {
            String s=sc.nextLine();
            String w=s.charAt(0)+""+s.charAt(1);
            int l=Integer.parseInt(w);
            String news="";
            if(l==0)
                news="12"+s.substring(2,5)+" "+"AM";
            else if((l>=1)&&(l<=11))
                news=s+" "+"AM";
            else if(l==12)
                news=s+" "+"PM";
            else
                news="0"+String.valueOf(l-12)+s.substring(2,5)+" "+"PM";

            arr[i-1]=news;

        }
        for(int j=0;j<t;j++)
            System.out.println(arr[j]);
    }
}

**Instructions:**
- Focus on edge cases or scenarios that maximize the failure probability in faulty solutions.
- Due to the output length limit, you should generate a **small-scale** test input that is **complete and valid**.
- Output the test input directly, not code to generate it.

**Output format:**
```plaintext
{test input}
```

Think step by step.

Response:
To generate a challenging test input that exposes the bug in the provided buggy code, we need to focus on edge cases and scenarios that are likely to cause issues. The main issues in the buggy code are:

1. Handling the conversion from 24-hour to 12-hour format, especially for times like "00:00", "12:00", and "23:59".
2. Correctly formatting the hour when it needs to be adjusted (e.g., "13:00" should be "01:00 PM").

Let's consider the following test cases:

1. "00:00" - This should convert to "12:00 AM".
2. "00:59" - This should convert to "12:59 AM".
3. "12:00" - This should convert to "12:00 PM".
4. "12:59" - This should convert to "12:59 PM".
5. "23:59" - This should convert to "11:59 PM".
6. "13:00" - This should convert to "01:00 PM".
7. "21:37" - This should convert to "09:37 PM".

These test cases cover the edge cases and the transition points between AM and PM.

Here is the test input:

```plaintext
7
00:00
00:59
12:00
12:59
23:59
13:00
21:37
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Clock Conversion
time_limit_ms: 1000
memory_limit_mb: 256
Description: Given the time in 24-hour format, output the equivalent time in 12-hour format.

- 24-hour format divides the day into 24 hours from $$$00$$$ to $$$23$$$, each of which has 60 minutes from $$$00$$$ to $$$59$$$.
- 12-hour format divides the day into two halves: the first half is $$$\mathrm{AM}$$$, and the second half is $$$\mathrm{PM}$$$. In each half, the hours are numbered in the order $$$12, 01, 02, 03, \dots, 11$$$. Each hour has 60 minutes numbered from $$$00$$$ to $$$59$$$.

Input: The first line contains a single integer $$$t$$$ ($$$1 \leq t \leq 1440$$$) — the number of test cases.

The only line of each test case contains a string $$$s$$$ of length $$$5$$$ with format hh:mm representing a valid time in the 24-hour format. hh represents the hour from $$$00$$$ to $$$23$$$, and mm represents the minute from $$$00$$$ to $$$59$$$.

The input will always be a valid time in 24-hour format.

Output: For each test case, output two strings separated by a space ("hh:mm AM" or "hh:mm PM"), which are the 12-hour equivalent to the time provided in the test case (without quotes).

You should output the time exactly as indicated; in particular, you should not remove leading zeroes.

Examples:
input:
11
09:41
18:06
12:14
00:59
00:00
14:34
01:01
19:07
11:59
12:00
21:37
output:
09:41 AM
06:06 PM
12:14 PM
12:59 AM
12:00 AM
02:34 PM
01:01 AM
07:07 PM
11:59 AM
12:00 PM
09:37 PM

Note:

Buggy Code:
import java.util.*;
public class Main {
	static Scanner in=new Scanner(System.in);
	public static void main(String[] args) {
		int t=in.nextInt();
		in.nextLine();
		while(t-->0) {
			solve();
		}
	}
	public static void solve() {
		String s=in.nextLine();
		if(s.charAt(0)=='0'&&s.charAt(1)!='0'||(s.charAt(0)=='1'&&s.charAt(1)<'2')) {
			System.out.println(s+" AM");
		}
		else {
			if(s.charAt(0)=='0'&&s.charAt(1)=='0') {
				String[] tmp=s.split(":");
				System.out.println("12:"+tmp[1]+" AM");
			}
			else if(s.charAt(0)=='1'&&s.charAt(1)=='2') {
				System.out.println(s+" PM");
			}
			else {
				String[] tmp=s.split(":");
				int t=Integer.parseInt(tmp[0])-12;
				System.out.println("0"+t+":"+tmp[1]+" PM");
			}
		}
	}
}

**Instructions:**
- Focus on edge cases or scenarios that maximize the failure probability in faulty solutions.
- Due to the output length limit, you should generate a **small-scale** test input that is **complete and valid**.
- Output the test input directly, not code to generate it.

**Output format:**
```plaintext
{test input}
```

Think step by step.

Response:
```plaintext
3
00:00
12:00
23:59
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Clock Conversion
time_limit_ms: 1000
memory_limit_mb: 256
Description: Given the time in 24-hour format, output the equivalent time in 12-hour format.

- 24-hour format divides the day into 24 hours from $$$00$$$ to $$$23$$$, each of which has 60 minutes from $$$00$$$ to $$$59$$$.
- 12-hour format divides the day into two halves: the first half is $$$\mathrm{AM}$$$, and the second half is $$$\mathrm{PM}$$$. In each half, the hours are numbered in the order $$$12, 01, 02, 03, \dots, 11$$$. Each hour has 60 minutes numbered from $$$00$$$ to $$$59$$$.

Input: The first line contains a single integer $$$t$$$ ($$$1 \leq t \leq 1440$$$) — the number of test cases.

The only line of each test case contains a string $$$s$$$ of length $$$5$$$ with format hh:mm representing a valid time in the 24-hour format. hh represents the hour from $$$00$$$ to $$$23$$$, and mm represents the minute from $$$00$$$ to $$$59$$$.

The input will always be a valid time in 24-hour format.

Output: For each test case, output two strings separated by a space ("hh:mm AM" or "hh:mm PM"), which are the 12-hour equivalent to the time provided in the test case (without quotes).

You should output the time exactly as indicated; in particular, you should not remove leading zeroes.

Examples:
input:
11
09:41
18:06
12:14
00:59
00:00
14:34
01:01
19:07
11:59
12:00
21:37
output:
09:41 AM
06:06 PM
12:14 PM
12:59 AM
12:00 AM
02:34 PM
01:01 AM
07:07 PM
11:59 AM
12:00 PM
09:37 PM

Note:

Buggy Code:
#include <bits/stdc++.h>

using namespace std;

typedef long long ll;
typedef array<ll, 2> arr2;
typedef array<ll, 3> arr3;

const ll INF = 2e9, mod = 1e9 + 7;

void Yes() {
    cout << "Yes\n";
}

void No() {
    cout << "No\n";
}

void solve() {
    string s;
    cin >> s;

    string h = s.substr(0, 2);
    string m = s.substr(3);
    string rest = s.substr(2);
    // cout << h << "\n";
    int hh = (h[0] - '0') * 10 + (h[1] - '0');
    if (hh > 12) {
        hh -= 12;
        cout << "0" << to_string(hh) << rest << " PM" << "\n";
    } else if (h == "00") {
        cout << "12" << rest << " AM\n";
    } else if (hh < 12) {
        cout << s << " AM" << "\n";
    } else {
        cout << s << " PM\n";
    }
}

int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);

    int T = 1;
    cin >> T;
    while (T--) {
        solve();
    }

    return 0;
}

**Instructions:**
- Focus on edge cases or scenarios that maximize the failure probability in faulty solutions.
- Due to the output length limit, you should generate a **small-scale** test input that is **complete and valid**.
- Output the test input directly, not code to generate it.

**Output format:**
```plaintext
{test input}
```

Think step by step.

Response:
```plaintext
3
00:00
12:00
23:59
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Clock Conversion
time_limit_ms: 1000
memory_limit_mb: 256
Description: Given the time in 24-hour format, output the equivalent time in 12-hour format.

- 24-hour format divides the day into 24 hours from $$$00$$$ to $$$23$$$, each of which has 60 minutes from $$$00$$$ to $$$59$$$.
- 12-hour format divides the day into two halves: the first half is $$$\mathrm{AM}$$$, and the second half is $$$\mathrm{PM}$$$. In each half, the hours are numbered in the order $$$12, 01, 02, 03, \dots, 11$$$. Each hour has 60 minutes numbered from $$$00$$$ to $$$59$$$.

Input: The first line contains a single integer $$$t$$$ ($$$1 \leq t \leq 1440$$$) — the number of test cases.

The only line of each test case contains a string $$$s$$$ of length $$$5$$$ with format hh:mm representing a valid time in the 24-hour format. hh represents the hour from $$$00$$$ to $$$23$$$, and mm represents the minute from $$$00$$$ to $$$59$$$.

The input will always be a valid time in 24-hour format.

Output: For each test case, output two strings separated by a space ("hh:mm AM" or "hh:mm PM"), which are the 12-hour equivalent to the time provided in the test case (without quotes).

You should output the time exactly as indicated; in particular, you should not remove leading zeroes.

Examples:
input:
11
09:41
18:06
12:14
00:59
00:00
14:34
01:01
19:07
11:59
12:00
21:37
output:
09:41 AM
06:06 PM
12:14 PM
12:59 AM
12:00 AM
02:34 PM
01:01 AM
07:07 PM
11:59 AM
12:00 PM
09:37 PM

Note:

Buggy Code:
#include <bits/stdc++.h>
using namespace std;

int main(){
ios_base::sync_with_stdio(0);
    cin.tie(0);cout.tie(0);
   long long n;
   string s;
   cin>>n;
   while(n--){
    cin>>s;
    string m=" AM";
    long long h=(s[0]-'0')*10+(s[1]-'0');
    if(h>=12)m=" PM";
    if(h==0)h=12;
    if(h>12)h-=12;
    if(h>10)
    cout<<h<<s[2]<<s[3]<<s[4]<<m<<endl;
    else
    cout<<0<<h<<s[2]<<s[3]<<s[4]<<m<<endl;
   }
    return 0;
}

**Instructions:**
- Focus on edge cases or scenarios that maximize the failure probability in faulty solutions.
- Due to the output length limit, you should generate a **small-scale** test input that is **complete and valid**.
- Output the test input directly, not code to generate it.

**Output format:**
```plaintext
{test input}
```

Think step by step.

Response:
To generate a challenging test input that exposes the bug in the provided buggy code, we need to focus on edge cases and scenarios that are likely to cause issues. Here are the key points to consider:

1. **Midnight (00:00)**: This should convert to "12:00 AM".
2. **Noon (12:00)**: This should convert to "12:00 PM".
3. **Just before midnight (23:59)**: This should convert to "11:59 PM".
4. **Just after midnight (00:01)**: This should convert to "12:01 AM".
5. **Just before noon (11:59)**: This should convert to "11:59 AM".
6. **Just after noon (12:01)**: This should convert to "12:01 PM".
7. **Edge cases for AM and PM conversion**:
   - 11:00 AM
   - 11:59 AM
   - 12:00 PM
   - 12:59 PM
   - 01:00 AM
   - 01:59 AM
   - 11:00 PM
   - 11:59 PM
8. **General cases**:
   - 09:41 AM
   - 18:06 PM
   - 00:59 AM
   - 21:37 PM

Based on these considerations, let's construct a small-scale test input that includes these edge cases:

```plaintext
8
00:00
12:00
23:59
00:01
11:59
12:01
01:00
21:37
```

This test input includes the critical edge cases and a few general cases to ensure the code handles them correctly.


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Clock Conversion
time_limit_ms: 1000
memory_limit_mb: 256
Description: Given the time in 24-hour format, output the equivalent time in 12-hour format.

- 24-hour format divides the day into 24 hours from $$$00$$$ to $$$23$$$, each of which has 60 minutes from $$$00$$$ to $$$59$$$.
- 12-hour format divides the day into two halves: the first half is $$$\mathrm{AM}$$$, and the second half is $$$\mathrm{PM}$$$. In each half, the hours are numbered in the order $$$12, 01, 02, 03, \dots, 11$$$. Each hour has 60 minutes numbered from $$$00$$$ to $$$59$$$.

Input: The first line contains a single integer $$$t$$$ ($$$1 \leq t \leq 1440$$$) — the number of test cases.

The only line of each test case contains a string $$$s$$$ of length $$$5$$$ with format hh:mm representing a valid time in the 24-hour format. hh represents the hour from $$$00$$$ to $$$23$$$, and mm represents the minute from $$$00$$$ to $$$59$$$.

The input will always be a valid time in 24-hour format.

Output: For each test case, output two strings separated by a space ("hh:mm AM" or "hh:mm PM"), which are the 12-hour equivalent to the time provided in the test case (without quotes).

You should output the time exactly as indicated; in particular, you should not remove leading zeroes.

Examples:
input:
11
09:41
18:06
12:14
00:59
00:00
14:34
01:01
19:07
11:59
12:00
21:37
output:
09:41 AM
06:06 PM
12:14 PM
12:59 AM
12:00 AM
02:34 PM
01:01 AM
07:07 PM
11:59 AM
12:00 PM
09:37 PM

Note:

Buggy Code:
import math
import sys
tests = int(sys.stdin.readline().strip())
for i in range(tests):
    time = sys.stdin.readline().strip().split(':')
    #print(time)
    if time[0] == '12':
        print('12'+':'+time[1] + ' ' + 'PM')
    if time[0] == '00':
        print('12' + ':' + time[1] + ' ' + 'AM')
    if int(time[0]) < 10 and int(time[0]) != 00 :
        print('0'+str(int(time[0])) + ':' + str(time[1]) + ' ' + 'AM')
    if int(time[0]) == 10 or int(time[0]) == 11:
        print(str(int(time[0])) + ':' + str(time[1]) + ' ' + 'AM')

    if int(time[0]) > 12:
        print('0'+str(int(time[0])-12) + ':' + time[1] + ' ' + 'PM')

**Instructions:**
- Focus on edge cases or scenarios that maximize the failure probability in faulty solutions.
- Due to the output length limit, you should generate a **small-scale** test input that is **complete and valid**.
- Output the test input directly, not code to generate it.

**Output format:**
```plaintext
{test input}
```

Think step by step.

Response:
```plaintext
3
09:41
12:14
21:37
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Clock Conversion
time_limit_ms: 1000
memory_limit_mb: 256
Description: Given the time in 24-hour format, output the equivalent time in 12-hour format.

- 24-hour format divides the day into 24 hours from $$$00$$$ to $$$23$$$, each of which has 60 minutes from $$$00$$$ to $$$59$$$.
- 12-hour format divides the day into two halves: the first half is $$$\mathrm{AM}$$$, and the second half is $$$\mathrm{PM}$$$. In each half, the hours are numbered in the order $$$12, 01, 02, 03, \dots, 11$$$. Each hour has 60 minutes numbered from $$$00$$$ to $$$59$$$.

Input: The first line contains a single integer $$$t$$$ ($$$1 \leq t \leq 1440$$$) — the number of test cases.

The only line of each test case contains a string $$$s$$$ of length $$$5$$$ with format hh:mm representing a valid time in the 24-hour format. hh represents the hour from $$$00$$$ to $$$23$$$, and mm represents the minute from $$$00$$$ to $$$59$$$.

The input will always be a valid time in 24-hour format.

Output: For each test case, output two strings separated by a space ("hh:mm AM" or "hh:mm PM"), which are the 12-hour equivalent to the time provided in the test case (without quotes).

You should output the time exactly as indicated; in particular, you should not remove leading zeroes.

Examples:
input:
11
09:41
18:06
12:14
00:59
00:00
14:34
01:01
19:07
11:59
12:00
21:37
output:
09:41 AM
06:06 PM
12:14 PM
12:59 AM
12:00 AM
02:34 PM
01:01 AM
07:07 PM
11:59 AM
12:00 PM
09:37 PM

Note:

Buggy Code:
for _ in range(int(input())):
    l=['12','00','01','02','03','04','05','06','07','08','09','10','11']
    s=input()
    x=s[:2]
    ans=''
    if int(x)<=12 and int(x)!=0:
        ans+=x
    elif int(x)==0:
        ans+='12'
    else:
        ans+=l[(int(x)+1)%12]
    ans+=':'
    ans+=s[3:]
    if int(x)>=12:
        ans+=' PM'
    else:
        ans+=' AM'
    print(ans)

**Instructions:**
- Focus on edge cases or scenarios that maximize the failure probability in faulty solutions.
- Due to the output length limit, you should generate a **small-scale** test input that is **complete and valid**.
- Output the test input directly, not code to generate it.

**Output format:**
```plaintext
{test input}
```

Think step by step.

Response:
```plaintext
3
00:00
12:00
23:59
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Clock Conversion
time_limit_ms: 1000
memory_limit_mb: 256
Description: Given the time in 24-hour format, output the equivalent time in 12-hour format.

- 24-hour format divides the day into 24 hours from $$$00$$$ to $$$23$$$, each of which has 60 minutes from $$$00$$$ to $$$59$$$.
- 12-hour format divides the day into two halves: the first half is $$$\mathrm{AM}$$$, and the second half is $$$\mathrm{PM}$$$. In each half, the hours are numbered in the order $$$12, 01, 02, 03, \dots, 11$$$. Each hour has 60 minutes numbered from $$$00$$$ to $$$59$$$.

Input: The first line contains a single integer $$$t$$$ ($$$1 \leq t \leq 1440$$$) — the number of test cases.

The only line of each test case contains a string $$$s$$$ of length $$$5$$$ with format hh:mm representing a valid time in the 24-hour format. hh represents the hour from $$$00$$$ to $$$23$$$, and mm represents the minute from $$$00$$$ to $$$59$$$.

The input will always be a valid time in 24-hour format.

Output: For each test case, output two strings separated by a space ("hh:mm AM" or "hh:mm PM"), which are the 12-hour equivalent to the time provided in the test case (without quotes).

You should output the time exactly as indicated; in particular, you should not remove leading zeroes.

Examples:
input:
11
09:41
18:06
12:14
00:59
00:00
14:34
01:01
19:07
11:59
12:00
21:37
output:
09:41 AM
06:06 PM
12:14 PM
12:59 AM
12:00 AM
02:34 PM
01:01 AM
07:07 PM
11:59 AM
12:00 PM
09:37 PM

Note:

Buggy Code:
import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int T = sc.nextInt();
        while(T-- >0){
            String s = sc.next();
            String res = "";
            int hours = Integer.parseInt(s.substring(0,2));
            String extra = s.substring(2);
            if(hours == 0){
                res = "12"+extra+" AM";
            }else if(hours == 12){
                res = "12"+extra+" PM";
            }
            else if(hours>12){
                res = "0"+Integer.toString(hours-12)+extra+" PM";
            }else{
                res = s+" AM";
            }
            System.out.println(res);

        }
    }
}

**Instructions:**
- Focus on edge cases or scenarios that maximize the failure probability in faulty solutions.
- Due to the output length limit, you should generate a **small-scale** test input that is **complete and valid**.
- Output the test input directly, not code to generate it.

**Output format:**
```plaintext
{test input}
```

Think step by step.

Response:
```plaintext
3
00:00
12:00
23:59
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Clock Conversion
time_limit_ms: 1000
memory_limit_mb: 256
Description: Given the time in 24-hour format, output the equivalent time in 12-hour format.

- 24-hour format divides the day into 24 hours from $$$00$$$ to $$$23$$$, each of which has 60 minutes from $$$00$$$ to $$$59$$$.
- 12-hour format divides the day into two halves: the first half is $$$\mathrm{AM}$$$, and the second half is $$$\mathrm{PM}$$$. In each half, the hours are numbered in the order $$$12, 01, 02, 03, \dots, 11$$$. Each hour has 60 minutes numbered from $$$00$$$ to $$$59$$$.

Input: The first line contains a single integer $$$t$$$ ($$$1 \leq t \leq 1440$$$) — the number of test cases.

The only line of each test case contains a string $$$s$$$ of length $$$5$$$ with format hh:mm representing a valid time in the 24-hour format. hh represents the hour from $$$00$$$ to $$$23$$$, and mm represents the minute from $$$00$$$ to $$$59$$$.

The input will always be a valid time in 24-hour format.

Output: For each test case, output two strings separated by a space ("hh:mm AM" or "hh:mm PM"), which are the 12-hour equivalent to the time provided in the test case (without quotes).

You should output the time exactly as indicated; in particular, you should not remove leading zeroes.

Examples:
input:
11
09:41
18:06
12:14
00:59
00:00
14:34
01:01
19:07
11:59
12:00
21:37
output:
09:41 AM
06:06 PM
12:14 PM
12:59 AM
12:00 AM
02:34 PM
01:01 AM
07:07 PM
11:59 AM
12:00 PM
09:37 PM

Note:

Buggy Code:
import java.util.*;

public class Main{
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);

        int T=sc.nextInt();
        sc.nextLine();

        for (int i=0;i<T;i++){

            String s = sc.nextLine();

            int n = Integer.parseInt(s.substring(0,2));

            if(n>12){
                n-=12;
                System.out.println("0"+Math.abs(n)+s.substring(2,5)+ " PM");
            } else if( n==00){
                n+=12;
                System.out.println(Math.abs(n)+s.substring(2,5)+ " AM");
            }else if(n==12){
                System.out.println(s+" PM");
            } else{
                System.out.println(s+" AM");
            }
        }

    }
}

**Instructions:**
- Focus on edge cases or scenarios that maximize the failure probability in faulty solutions.
- Due to the output length limit, you should generate a **small-scale** test input that is **complete and valid**.
- Output the test input directly, not code to generate it.

**Output format:**
```plaintext
{test input}
```

Think step by step.

Response:
```plaintext
3
00:00
12:00
23:59
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Little Nikita
time_limit_ms: 1000
memory_limit_mb: 256
Description: The little boy Nikita was given some cubes as a present. He decided to build a tower out of them.

Initially, the tower doesn't have any cubes. In one move, Nikita either puts exactly $1$ cube on top of the tower or removes exactly $1$ cube from the top of the tower. Is it possible that after $n$ moves, the resulting tower has exactly $m$ cubes?

Input: Each test contains multiple test cases. The first line of input contains a single integer $t$ ($1 \le t \le 100$) — the number of test cases. The description of the test cases follows.

The only line of each test case contains two integers $n$ and $m$ ($1 \le n, m \le 100$).

Output: For each test case, output "Yes" (without quotes) if Nikita can obtain a tower with $m$ cubes, and "No" (without quotes) otherwise.

You can output each letter in any case (lowercase or uppercase). For example, the strings "yEs", "yes", "Yes", and "YES" will be accepted as a positive answer.

Examples:
input:
3
3 3
2 4
5 3
output:
Yes
No
Yes

Note: In the first test case, Nikita can put $1$ cube on top of the tower $3$ times in a row, so the answer is "Yes".

In the second test case, Nikita can only end up with either a tower with no blocks or a tower with $2$ blocks, so the answer is "No".

Buggy Code:
#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define vi vector<int>
#define vll vector<long long>
#define vpp vector<pair<int,int>>
#define en '\n'
#define py cout<<"YES\n"
#define pn cout<<"NO\n"
#define fi  for(int i=0;i<n;i++) cin>> a[i];
#define fast ios::sync_with_stdio(false); cin.tie(0);

void solve(){
   int n,m; cin>>n>>m;
   if(m>n) pn;
   else py;
}

int main() {
    fast
    int tt;  cin>>tt;
    while(tt--){
        solve();
    }

    return 0;
}

**Instructions:**
- Focus on edge cases or scenarios that maximize the failure probability in faulty solutions.
- Due to the output length limit, you should generate a **small-scale** test input that is **complete and valid**.
- Output the test input directly, not code to generate it.

**Output format:**
```plaintext
{test input}
```

Think step by step.

Response:
```plaintext
3
1 1
2 1
4 2
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Little Nikita
time_limit_ms: 1000
memory_limit_mb: 256
Description: The little boy Nikita was given some cubes as a present. He decided to build a tower out of them.

Initially, the tower doesn't have any cubes. In one move, Nikita either puts exactly $1$ cube on top of the tower or removes exactly $1$ cube from the top of the tower. Is it possible that after $n$ moves, the resulting tower has exactly $m$ cubes?

Input: Each test contains multiple test cases. The first line of input contains a single integer $t$ ($1 \le t \le 100$) — the number of test cases. The description of the test cases follows.

The only line of each test case contains two integers $n$ and $m$ ($1 \le n, m \le 100$).

Output: For each test case, output "Yes" (without quotes) if Nikita can obtain a tower with $m$ cubes, and "No" (without quotes) otherwise.

You can output each letter in any case (lowercase or uppercase). For example, the strings "yEs", "yes", "Yes", and "YES" will be accepted as a positive answer.

Examples:
input:
3
3 3
2 4
5 3
output:
Yes
No
Yes

Note: In the first test case, Nikita can put $1$ cube on top of the tower $3$ times in a row, so the answer is "Yes".

In the second test case, Nikita can only end up with either a tower with no blocks or a tower with $2$ blocks, so the answer is "No".

Buggy Code:
#define dl double
#define el '\n'
#define ct cout
#define cn cin
#define ll long long
#include <bits/stdc++.h>
using namespace std;
const double pi = 3.14159265359;
void _Ramsis()
{
#ifndef ONLINE_JUDGE
  freopen("input.txt", "r", stdin);
  freopen("output.txt", "w", stdout);
#endif

  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);

 //! cout << fixed << setprecision(6);
}
int main()
{
  _Ramsis();

    int t;
    cn>>t;
    while(t--)
    {
      int n,m;
      cn>>n>>m;
      if (n>=m)
       {
         n-=m;
         if (n%2==0)
          ct << "YES";
       }
      else
      ct << "NO";

      ct<<el;
    }

}

**Instructions:**
- Focus on edge cases or scenarios that maximize the failure probability in faulty solutions.
- Due to the output length limit, you should generate a **small-scale** test input that is **complete and valid**.
- Output the test input directly, not code to generate it.

**Output format:**
```plaintext
{test input}
```

Think step by step.

Response:
To expose the bug in the given buggy code, we need to focus on scenarios where the logic fails. The main issue in the code is that it only checks if \( n \) is greater than or equal to \( m \) and then checks if the remaining moves are even. This logic is flawed because it doesn't consider the possibility of removing cubes and then adding them back, which can result in a tower with exactly \( m \) cubes even if \( n \) is not directly greater than or equal to \( m \).

### Steps to Generate a Challenging Test Input:
1. **Test Case 1: \( n = m \)**
   - This should always result in "Yes" because Nikita can simply add \( m \) cubes one by one.
2. **Test Case 2: \( n < m \)**
   - This should always result in "No" because it's impossible to end up with more cubes than the number of moves.
3. **Test Case 3: \( n > m \) and \( n - m \) is odd**
   - This should result in "No" because the remaining moves cannot be used to balance out to exactly \( m \) cubes.
4. **Test Case 4: \( n > m \) and \( n - m \) is even**
   - This should result in "Yes" because the remaining moves can be used to balance out to exactly \( m \) cubes.
5. **Test Case 5: \( n = 1 \) and \( m = 1 \)**
   - This is a simple case that should result in "Yes".
6. **Test Case 6: \( n = 2 \) and \( m = 1 \)**
   - This should result in "Yes" because Nikita can add a cube and then remove it, or just add a cube.
7. **Test Case 7: \( n = 3 \) and \( m = 2 \)**
   - This should result in "Yes" because Nikita can add two cubes and then remove one, or add one, remove one, and add one again.

### Challenging Test Input:
```plaintext
7
3 3
2 4
5 3
4 2
1 1
2 1
3 2
```

### Explanation:
- **Test Case 1: \( 3 \) \( 3 \)** - Nikita can add 3 cubes. Output: "Yes"
- **Test Case 2: \( 2 \) \( 4 \)** - Nikita cannot add 4 cubes in 2 moves. Output: "No"
- **Test Case 3: \( 5 \) \( 3 \)** - Nikita can add 3 cubes and then remove 2. Output: "Yes"
- **Test Case 4: \( 4 \) \( 2 \)** - Nikita can add 2 cubes and then remove 2. Output: "Yes"
- **Test Case 5: \( 1 \) \( 1 \)** - Nikita can add 1 cube. Output: "Yes"
- **Test Case 6: \( 2 \) \( 1 \)** - Nikita can add 1 cube and then remove 1, or just add 1 cube. Output: "Yes"
- **Test Case 7: \( 3 \) \( 2 \)** - Nikita can add 2 cubes and then remove 1, or add 1, remove 1, and add 1 again. Output: "Yes"

This test input should effectively expose the bug in the given buggy code.


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Little Nikita
time_limit_ms: 1000
memory_limit_mb: 256
Description: The little boy Nikita was given some cubes as a present. He decided to build a tower out of them.

Initially, the tower doesn't have any cubes. In one move, Nikita either puts exactly $1$ cube on top of the tower or removes exactly $1$ cube from the top of the tower. Is it possible that after $n$ moves, the resulting tower has exactly $m$ cubes?

Input: Each test contains multiple test cases. The first line of input contains a single integer $t$ ($1 \le t \le 100$) — the number of test cases. The description of the test cases follows.

The only line of each test case contains two integers $n$ and $m$ ($1 \le n, m \le 100$).

Output: For each test case, output "Yes" (without quotes) if Nikita can obtain a tower with $m$ cubes, and "No" (without quotes) otherwise.

You can output each letter in any case (lowercase or uppercase). For example, the strings "yEs", "yes", "Yes", and "YES" will be accepted as a positive answer.

Examples:
input:
3
3 3
2 4
5 3
output:
Yes
No
Yes

Note: In the first test case, Nikita can put $1$ cube on top of the tower $3$ times in a row, so the answer is "Yes".

In the second test case, Nikita can only end up with either a tower with no blocks or a tower with $2$ blocks, so the answer is "No".

Buggy Code:
#include <iostream>
// #include <cstring>
// #include <cmath>
using namespace std;

int main() {

    int num;
    cin>>num;

    for (int t=0; t<num; t++) {
        int n, m;

        cin>>n>>m;
        if (n>=m) cout<<"YES"<<endl;
        else cout<<"NO"<<endl;

        // cout<<dist<<endl;

        }

    return 0;
}

**Instructions:**
- Focus on edge cases or scenarios that maximize the failure probability in faulty solutions.
- Due to the output length limit, you should generate a **small-scale** test input that is **complete and valid**.
- Output the test input directly, not code to generate it.

**Output format:**
```plaintext
{test input}
```

Think step by step.

Response:
```plaintext
3
1 1
2 1
3 2
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Little Nikita
time_limit_ms: 1000
memory_limit_mb: 256
Description: The little boy Nikita was given some cubes as a present. He decided to build a tower out of them.

Initially, the tower doesn't have any cubes. In one move, Nikita either puts exactly $1$ cube on top of the tower or removes exactly $1$ cube from the top of the tower. Is it possible that after $n$ moves, the resulting tower has exactly $m$ cubes?

Input: Each test contains multiple test cases. The first line of input contains a single integer $t$ ($1 \le t \le 100$) — the number of test cases. The description of the test cases follows.

The only line of each test case contains two integers $n$ and $m$ ($1 \le n, m \le 100$).

Output: For each test case, output "Yes" (without quotes) if Nikita can obtain a tower with $m$ cubes, and "No" (without quotes) otherwise.

You can output each letter in any case (lowercase or uppercase). For example, the strings "yEs", "yes", "Yes", and "YES" will be accepted as a positive answer.

Examples:
input:
3
3 3
2 4
5 3
output:
Yes
No
Yes

Note: In the first test case, Nikita can put $1$ cube on top of the tower $3$ times in a row, so the answer is "Yes".

In the second test case, Nikita can only end up with either a tower with no blocks or a tower with $2$ blocks, so the answer is "No".

Buggy Code:
def check_out_result(count_of_steps, height_hustle):
    start_position = 0
    if height_hustle - count_of_steps <= 0 and height_hustle%2!=0 and count_of_steps%2==0 or height_hustle%2==0 and count_of_steps%2!=0 or height_hustle%2!=0 and count_of_steps%2!=0:
        return 'Yes'
    else:
        return 'NO'

test = int(input())
for _ in range(test):
    count_of_steps, height_hustle = map(int, input().split())
    print(check_out_result(count_of_steps, height_hustle))

**Instructions:**
- Focus on edge cases or scenarios that maximize the failure probability in faulty solutions.
- Due to the output length limit, you should generate a **small-scale** test input that is **complete and valid**.
- Output the test input directly, not code to generate it.

**Output format:**
```plaintext
{test input}
```

Think step by step.

Response:
```plaintext
3
1 1
2 1
3 2
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Little Nikita
time_limit_ms: 1000
memory_limit_mb: 256
Description: The little boy Nikita was given some cubes as a present. He decided to build a tower out of them.

Initially, the tower doesn't have any cubes. In one move, Nikita either puts exactly $1$ cube on top of the tower or removes exactly $1$ cube from the top of the tower. Is it possible that after $n$ moves, the resulting tower has exactly $m$ cubes?

Input: Each test contains multiple test cases. The first line of input contains a single integer $t$ ($1 \le t \le 100$) — the number of test cases. The description of the test cases follows.

The only line of each test case contains two integers $n$ and $m$ ($1 \le n, m \le 100$).

Output: For each test case, output "Yes" (without quotes) if Nikita can obtain a tower with $m$ cubes, and "No" (without quotes) otherwise.

You can output each letter in any case (lowercase or uppercase). For example, the strings "yEs", "yes", "Yes", and "YES" will be accepted as a positive answer.

Examples:
input:
3
3 3
2 4
5 3
output:
Yes
No
Yes

Note: In the first test case, Nikita can put $1$ cube on top of the tower $3$ times in a row, so the answer is "Yes".

In the second test case, Nikita can only end up with either a tower with no blocks or a tower with $2$ blocks, so the answer is "No".

Buggy Code:
def can_obtain_tower(n, m):
    if n >= m:
        return "Yes"
    else:
        return "No"

# Read input
import sys
input = sys.stdin.read
data = input().split()

# Number of test cases
t = int(data[0])

# List to store results
results = []

# Process each test case
index = 1
for _ in range(t):
    n = int(data[index])
    m = int(data[index + 1])
    index += 2
    result = can_obtain_tower(n, m)
    results.append(result)

# Output all results
for result in results:
    print(result)

**Instructions:**
- Focus on edge cases or scenarios that maximize the failure probability in faulty solutions.
- Due to the output length limit, you should generate a **small-scale** test input that is **complete and valid**.
- Output the test input directly, not code to generate it.

**Output format:**
```plaintext
{test input}
```

Think step by step.

Response:
```plaintext
3
1 2
2 1
4 2
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Little Nikita
time_limit_ms: 1000
memory_limit_mb: 256
Description: The little boy Nikita was given some cubes as a present. He decided to build a tower out of them.

Initially, the tower doesn't have any cubes. In one move, Nikita either puts exactly $1$ cube on top of the tower or removes exactly $1$ cube from the top of the tower. Is it possible that after $n$ moves, the resulting tower has exactly $m$ cubes?

Input: Each test contains multiple test cases. The first line of input contains a single integer $t$ ($1 \le t \le 100$) — the number of test cases. The description of the test cases follows.

The only line of each test case contains two integers $n$ and $m$ ($1 \le n, m \le 100$).

Output: For each test case, output "Yes" (without quotes) if Nikita can obtain a tower with $m$ cubes, and "No" (without quotes) otherwise.

You can output each letter in any case (lowercase or uppercase). For example, the strings "yEs", "yes", "Yes", and "YES" will be accepted as a positive answer.

Examples:
input:
3
3 3
2 4
5 3
output:
Yes
No
Yes

Note: In the first test case, Nikita can put $1$ cube on top of the tower $3$ times in a row, so the answer is "Yes".

In the second test case, Nikita can only end up with either a tower with no blocks or a tower with $2$ blocks, so the answer is "No".

Buggy Code:
t = int(input())

for _ in range(t):
    n,m = (int(x) for x in input().split())
    if((n%m)%2 == 1 or n < m):
        print("NO")
    else:
        print("YES")

**Instructions:**
- Focus on edge cases or scenarios that maximize the failure probability in faulty solutions.
- Due to the output length limit, you should generate a **small-scale** test input that is **complete and valid**.
- Output the test input directly, not code to generate it.

**Output format:**
```plaintext
{test input}
```

Think step by step.

Response:
```plaintext
4
1 1
2 2
3 2
4 3
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Little Nikita
time_limit_ms: 1000
memory_limit_mb: 256
Description: The little boy Nikita was given some cubes as a present. He decided to build a tower out of them.

Initially, the tower doesn't have any cubes. In one move, Nikita either puts exactly $1$ cube on top of the tower or removes exactly $1$ cube from the top of the tower. Is it possible that after $n$ moves, the resulting tower has exactly $m$ cubes?

Input: Each test contains multiple test cases. The first line of input contains a single integer $t$ ($1 \le t \le 100$) — the number of test cases. The description of the test cases follows.

The only line of each test case contains two integers $n$ and $m$ ($1 \le n, m \le 100$).

Output: For each test case, output "Yes" (without quotes) if Nikita can obtain a tower with $m$ cubes, and "No" (without quotes) otherwise.

You can output each letter in any case (lowercase or uppercase). For example, the strings "yEs", "yes", "Yes", and "YES" will be accepted as a positive answer.

Examples:
input:
3
3 3
2 4
5 3
output:
Yes
No
Yes

Note: In the first test case, Nikita can put $1$ cube on top of the tower $3$ times in a row, so the answer is "Yes".

In the second test case, Nikita can only end up with either a tower with no blocks or a tower with $2$ blocks, so the answer is "No".

Buggy Code:
import java.util.*;
public class Main{
    public static void main(String args[]) {
        Scanner sc=new Scanner(System.in);
        int n1=sc.nextInt();
        while(n1>0){
            int m=sc.nextInt();
            int n=sc.nextInt();
            if(m-n==0|| m-n>1){
                System.out.println("Yes");
            }
            else{
                System.out.println("No");
            }
            n1--;
        }
    }
}

**Instructions:**
- Focus on edge cases or scenarios that maximize the failure probability in faulty solutions.
- Due to the output length limit, you should generate a **small-scale** test input that is **complete and valid**.
- Output the test input directly, not code to generate it.

**Output format:**
```plaintext
{test input}
```

Think step by step.

Response:
```plaintext
3
1 1
2 1
3 2
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Little Nikita
time_limit_ms: 1000
memory_limit_mb: 256
Description: The little boy Nikita was given some cubes as a present. He decided to build a tower out of them.

Initially, the tower doesn't have any cubes. In one move, Nikita either puts exactly $1$ cube on top of the tower or removes exactly $1$ cube from the top of the tower. Is it possible that after $n$ moves, the resulting tower has exactly $m$ cubes?

Input: Each test contains multiple test cases. The first line of input contains a single integer $t$ ($1 \le t \le 100$) — the number of test cases. The description of the test cases follows.

The only line of each test case contains two integers $n$ and $m$ ($1 \le n, m \le 100$).

Output: For each test case, output "Yes" (without quotes) if Nikita can obtain a tower with $m$ cubes, and "No" (without quotes) otherwise.

You can output each letter in any case (lowercase or uppercase). For example, the strings "yEs", "yes", "Yes", and "YES" will be accepted as a positive answer.

Examples:
input:
3
3 3
2 4
5 3
output:
Yes
No
Yes

Note: In the first test case, Nikita can put $1$ cube on top of the tower $3$ times in a row, so the answer is "Yes".

In the second test case, Nikita can only end up with either a tower with no blocks or a tower with $2$ blocks, so the answer is "No".

Buggy Code:
import java.util.Scanner;

public class Round_948_Div_2
{

	private static void f()
	{
		Scanner sc = new Scanner(System.in);
		int t = sc.nextInt();
		while(t --> 0)
		{
			int n = sc.nextInt();
			int m = sc.nextInt();
			if(m<=n ) {
				System.out.println("YES");
			}
			else
			{
				System.out.println("NO");
			}

		}
	}

	public static void main(String[] args)
	{
		f();
	}

}

**Instructions:**
- Focus on edge cases or scenarios that maximize the failure probability in faulty solutions.
- Due to the output length limit, you should generate a **small-scale** test input that is **complete and valid**.
- Output the test input directly, not code to generate it.

**Output format:**
```plaintext
{test input}
```

Think step by step.

Response:
To generate a challenging test input that exposes the bug in the given buggy code, we need to focus on scenarios where the code's logic fails. The buggy code incorrectly checks if `m` is less than or equal to `n` and prints "YES" if true, without considering the parity (odd or even nature) of `n` and `m`.

### Key Insight:
- For Nikita to end up with exactly `m` cubes after `n` moves, the difference between `n` and `m` must be even. This is because each move either adds or removes one cube, and the net effect of an even number of moves must be even.

### Challenging Test Cases:
1. **Test Case 1:**
   - `n = 4`, `m = 2`
   - Expected output: "Yes" (since 4 - 2 = 2, which is even)
   - Buggy code output: "Yes" (correct, but not a challenge)

2. **Test Case 2:**
   - `n = 3`, `m = 2`
   - Expected output: "No" (since 3 - 2 = 1, which is odd)
   - Buggy code output: "Yes" (incorrect)

3. **Test Case 3:**
   - `n = 5`, `m = 3`
   - Expected output: "Yes" (since 5 - 3 = 2, which is even)
   - Buggy code output: "Yes" (correct, but not a challenge)

4. **Test Case 4:**
   - `n = 6`, `m = 1`
   - Expected output: "No" (since 6 - 1 = 5, which is odd)
   - Buggy code output: "Yes" (incorrect)

### Chosen Test Input:
```plaintext
4
4 2
3 2
5 3
6 1
```

This test input includes a mix of cases where the difference between `n` and `m` is even and odd, ensuring that the buggy code's incorrect logic is exposed.


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Little Nikita
time_limit_ms: 1000
memory_limit_mb: 256
Description: The little boy Nikita was given some cubes as a present. He decided to build a tower out of them.

Initially, the tower doesn't have any cubes. In one move, Nikita either puts exactly $1$ cube on top of the tower or removes exactly $1$ cube from the top of the tower. Is it possible that after $n$ moves, the resulting tower has exactly $m$ cubes?

Input: Each test contains multiple test cases. The first line of input contains a single integer $t$ ($1 \le t \le 100$) — the number of test cases. The description of the test cases follows.

The only line of each test case contains two integers $n$ and $m$ ($1 \le n, m \le 100$).

Output: For each test case, output "Yes" (without quotes) if Nikita can obtain a tower with $m$ cubes, and "No" (without quotes) otherwise.

You can output each letter in any case (lowercase or uppercase). For example, the strings "yEs", "yes", "Yes", and "YES" will be accepted as a positive answer.

Examples:
input:
3
3 3
2 4
5 3
output:
Yes
No
Yes

Note: In the first test case, Nikita can put $1$ cube on top of the tower $3$ times in a row, so the answer is "Yes".

In the second test case, Nikita can only end up with either a tower with no blocks or a tower with $2$ blocks, so the answer is "No".

Buggy Code:
#include<bits/stdc++.h>
using namespace std;

void solve(){
    int n,m;
    cin>>n>>m;
    if (n>=m)
    {
        cout<<"Yes"<<endl;
        return;
    }
    cout<<"No"<<endl;
    return;

}

int main(){
    int t = 1;
    cin>>t;
    while(t--){
        solve();
    }
    return 0;
}

**Instructions:**
- Focus on edge cases or scenarios that maximize the failure probability in faulty solutions.
- Due to the output length limit, you should generate a **small-scale** test input that is **complete and valid**.
- Output the test input directly, not code to generate it.

**Output format:**
```plaintext
{test input}
```

Think step by step.

Response:
```plaintext
1
100 101
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Little Nikita
time_limit_ms: 1000
memory_limit_mb: 256
Description: The little boy Nikita was given some cubes as a present. He decided to build a tower out of them.

Initially, the tower doesn't have any cubes. In one move, Nikita either puts exactly $1$ cube on top of the tower or removes exactly $1$ cube from the top of the tower. Is it possible that after $n$ moves, the resulting tower has exactly $m$ cubes?

Input: Each test contains multiple test cases. The first line of input contains a single integer $t$ ($1 \le t \le 100$) — the number of test cases. The description of the test cases follows.

The only line of each test case contains two integers $n$ and $m$ ($1 \le n, m \le 100$).

Output: For each test case, output "Yes" (without quotes) if Nikita can obtain a tower with $m$ cubes, and "No" (without quotes) otherwise.

You can output each letter in any case (lowercase or uppercase). For example, the strings "yEs", "yes", "Yes", and "YES" will be accepted as a positive answer.

Examples:
input:
3
3 3
2 4
5 3
output:
Yes
No
Yes

Note: In the first test case, Nikita can put $1$ cube on top of the tower $3$ times in a row, so the answer is "Yes".

In the second test case, Nikita can only end up with either a tower with no blocks or a tower with $2$ blocks, so the answer is "No".

Buggy Code:
#include <bits/stdc++.h>
using namespace std;
#define int long long
//#define ll long long
#define f(i,ac,n) for(int i=ac; i<n;i++)
#define f(j,b,n) for(int j=b; i<n;i++)
#define vi vector<int>
const int64_t inf = 0x3f3f3f3f;
const int N = 3e5+5;

void solve()
{
    int n, m;
    cin>>n>>m;
    if(n>=m) cout<<"Yes"<<endl;
    else cout<<"No"<<endl;

}

int32_t main() {

	int t; cin>>t;
	while(t--){

	   solve();
	}
	return 0;
}

**Instructions:**
- Focus on edge cases or scenarios that maximize the failure probability in faulty solutions.
- Due to the output length limit, you should generate a **small-scale** test input that is **complete and valid**.
- Output the test input directly, not code to generate it.

**Output format:**
```plaintext
{test input}
```

Think step by step.

Response:
```plaintext
3
1 1
2 1
3 2
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Little Nikita
time_limit_ms: 1000
memory_limit_mb: 256
Description: The little boy Nikita was given some cubes as a present. He decided to build a tower out of them.

Initially, the tower doesn't have any cubes. In one move, Nikita either puts exactly $1$ cube on top of the tower or removes exactly $1$ cube from the top of the tower. Is it possible that after $n$ moves, the resulting tower has exactly $m$ cubes?

Input: Each test contains multiple test cases. The first line of input contains a single integer $t$ ($1 \le t \le 100$) — the number of test cases. The description of the test cases follows.

The only line of each test case contains two integers $n$ and $m$ ($1 \le n, m \le 100$).

Output: For each test case, output "Yes" (without quotes) if Nikita can obtain a tower with $m$ cubes, and "No" (without quotes) otherwise.

You can output each letter in any case (lowercase or uppercase). For example, the strings "yEs", "yes", "Yes", and "YES" will be accepted as a positive answer.

Examples:
input:
3
3 3
2 4
5 3
output:
Yes
No
Yes

Note: In the first test case, Nikita can put $1$ cube on top of the tower $3$ times in a row, so the answer is "Yes".

In the second test case, Nikita can only end up with either a tower with no blocks or a tower with $2$ blocks, so the answer is "No".

Buggy Code:
from collections import deque

t = int(input())

cases = []

for i in range(t):

    text = list(map(int, input().split()))
    n, m = text[0], text[1]
    res = False

    if (n == m) | (n > m) & (m % 2) != 0:

        res = True

    cases.append(res)

for res in cases:

    print('Yes' if res == True else 'No')

**Instructions:**
- Focus on edge cases or scenarios that maximize the failure probability in faulty solutions.
- Due to the output length limit, you should generate a **small-scale** test input that is **complete and valid**.
- Output the test input directly, not code to generate it.

**Output format:**
```plaintext
{test input}
```

Think step by step.

Response:
```plaintext
3
1 1
2 1
3 2
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Little Nikita
time_limit_ms: 1000
memory_limit_mb: 256
Description: The little boy Nikita was given some cubes as a present. He decided to build a tower out of them.

Initially, the tower doesn't have any cubes. In one move, Nikita either puts exactly $1$ cube on top of the tower or removes exactly $1$ cube from the top of the tower. Is it possible that after $n$ moves, the resulting tower has exactly $m$ cubes?

Input: Each test contains multiple test cases. The first line of input contains a single integer $t$ ($1 \le t \le 100$) — the number of test cases. The description of the test cases follows.

The only line of each test case contains two integers $n$ and $m$ ($1 \le n, m \le 100$).

Output: For each test case, output "Yes" (without quotes) if Nikita can obtain a tower with $m$ cubes, and "No" (without quotes) otherwise.

You can output each letter in any case (lowercase or uppercase). For example, the strings "yEs", "yes", "Yes", and "YES" will be accepted as a positive answer.

Examples:
input:
3
3 3
2 4
5 3
output:
Yes
No
Yes

Note: In the first test case, Nikita can put $1$ cube on top of the tower $3$ times in a row, so the answer is "Yes".

In the second test case, Nikita can only end up with either a tower with no blocks or a tower with $2$ blocks, so the answer is "No".

Buggy Code:
tries_ammount = int(input())

all_tries = []

for i in range(tries_ammount):
    all_tries.append(input())

arr = []

for i in all_tries:
    arr.append(i.split(" "))

def solution(arr):
    if (int(arr[0]) == int(arr[1])) or (((int(arr[0]) - int(arr[1])) % 2 == 0) and (int(arr[0]) > 0 and int(arr[1]) > 0)) and (int(arr[0]) > int(arr[1]) and (int(arr[0]) % 2 == 1)):
        return True
    return False

for i in arr:
    if (solution(i) == True):
        print("Yes")
    else:
        print("No")

**Instructions:**
- Focus on edge cases or scenarios that maximize the failure probability in faulty solutions.
- Due to the output length limit, you should generate a **small-scale** test input that is **complete and valid**.
- Output the test input directly, not code to generate it.

**Output format:**
```plaintext
{test input}
```

Think step by step.

Response:
```plaintext
3
1 1
2 1
3 2
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Little Nikita
time_limit_ms: 1000
memory_limit_mb: 256
Description: The little boy Nikita was given some cubes as a present. He decided to build a tower out of them.

Initially, the tower doesn't have any cubes. In one move, Nikita either puts exactly $1$ cube on top of the tower or removes exactly $1$ cube from the top of the tower. Is it possible that after $n$ moves, the resulting tower has exactly $m$ cubes?

Input: Each test contains multiple test cases. The first line of input contains a single integer $t$ ($1 \le t \le 100$) — the number of test cases. The description of the test cases follows.

The only line of each test case contains two integers $n$ and $m$ ($1 \le n, m \le 100$).

Output: For each test case, output "Yes" (without quotes) if Nikita can obtain a tower with $m$ cubes, and "No" (without quotes) otherwise.

You can output each letter in any case (lowercase or uppercase). For example, the strings "yEs", "yes", "Yes", and "YES" will be accepted as a positive answer.

Examples:
input:
3
3 3
2 4
5 3
output:
Yes
No
Yes

Note: In the first test case, Nikita can put $1$ cube on top of the tower $3$ times in a row, so the answer is "Yes".

In the second test case, Nikita can only end up with either a tower with no blocks or a tower with $2$ blocks, so the answer is "No".

Buggy Code:
import java.util.*;
public class Main{
    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);
        int Test = sc.nextInt();
        while(Test-->0){
            int n = sc.nextInt();
            int m = sc.nextInt();
            if(n>=m){
                System.out.println("Yes");
            }
            else{
                System.out.println("No");
            }
        }
    }
}

**Instructions:**
- Focus on edge cases or scenarios that maximize the failure probability in faulty solutions.
- Due to the output length limit, you should generate a **small-scale** test input that is **complete and valid**.
- Output the test input directly, not code to generate it.

**Output format:**
```plaintext
{test input}
```

Think step by step.

Response:
```plaintext
3
1 1
2 1
3 2
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Little Nikita
time_limit_ms: 1000
memory_limit_mb: 256
Description: The little boy Nikita was given some cubes as a present. He decided to build a tower out of them.

Initially, the tower doesn't have any cubes. In one move, Nikita either puts exactly $1$ cube on top of the tower or removes exactly $1$ cube from the top of the tower. Is it possible that after $n$ moves, the resulting tower has exactly $m$ cubes?

Input: Each test contains multiple test cases. The first line of input contains a single integer $t$ ($1 \le t \le 100$) — the number of test cases. The description of the test cases follows.

The only line of each test case contains two integers $n$ and $m$ ($1 \le n, m \le 100$).

Output: For each test case, output "Yes" (without quotes) if Nikita can obtain a tower with $m$ cubes, and "No" (without quotes) otherwise.

You can output each letter in any case (lowercase or uppercase). For example, the strings "yEs", "yes", "Yes", and "YES" will be accepted as a positive answer.

Examples:
input:
3
3 3
2 4
5 3
output:
Yes
No
Yes

Note: In the first test case, Nikita can put $1$ cube on top of the tower $3$ times in a row, so the answer is "Yes".

In the second test case, Nikita can only end up with either a tower with no blocks or a tower with $2$ blocks, so the answer is "No".

Buggy Code:
import javax.naming.PartialResultException;
import java.util.*;
public class BeautifulTriplee {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int t = sc.nextInt();
        while (t --> 0) {
           int n = sc.nextInt();
           int m = sc.nextInt();
           if(n < m){
               System.out.println("no");
           }else if(((m-1)*2 ) +1 == n){
               System.out.println("yes");
           } else if (n == m) {
               System.out.println("yes");
           } else {
               System.out.println("no");
           }
        }
    }
}

**Instructions:**
- Focus on edge cases or scenarios that maximize the failure probability in faulty solutions.
- Due to the output length limit, you should generate a **small-scale** test input that is **complete and valid**.
- Output the test input directly, not code to generate it.

**Output format:**
```plaintext
{test input}
```

Think step by step.

Response:
```plaintext
4
1 1
2 1
3 2
4 2
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Little Nikita
time_limit_ms: 1000
memory_limit_mb: 256
Description: The little boy Nikita was given some cubes as a present. He decided to build a tower out of them.

Initially, the tower doesn't have any cubes. In one move, Nikita either puts exactly $1$ cube on top of the tower or removes exactly $1$ cube from the top of the tower. Is it possible that after $n$ moves, the resulting tower has exactly $m$ cubes?

Input: Each test contains multiple test cases. The first line of input contains a single integer $t$ ($1 \le t \le 100$) — the number of test cases. The description of the test cases follows.

The only line of each test case contains two integers $n$ and $m$ ($1 \le n, m \le 100$).

Output: For each test case, output "Yes" (without quotes) if Nikita can obtain a tower with $m$ cubes, and "No" (without quotes) otherwise.

You can output each letter in any case (lowercase or uppercase). For example, the strings "yEs", "yes", "Yes", and "YES" will be accepted as a positive answer.

Examples:
input:
3
3 3
2 4
5 3
output:
Yes
No
Yes

Note: In the first test case, Nikita can put $1$ cube on top of the tower $3$ times in a row, so the answer is "Yes".

In the second test case, Nikita can only end up with either a tower with no blocks or a tower with $2$ blocks, so the answer is "No".

Buggy Code:
#include <bits/stdc++.h>
#define ll long long
using namespace std;

void solve()
{
    int t;
    cin >> t;

    while (t--)
    {
        int n,m;
        cin>>n>>m;
        if(n<m)
        cout<<"No"<<endl;
        else
        cout<<"Yes"<<endl;

    }
}

int main()
{
    solve();
}

**Instructions:**
- Focus on edge cases or scenarios that maximize the failure probability in faulty solutions.
- Due to the output length limit, you should generate a **small-scale** test input that is **complete and valid**.
- Output the test input directly, not code to generate it.

**Output format:**
```plaintext
{test input}
```

Think step by step.

Response:
```plaintext
1
1 2
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Little Nikita
time_limit_ms: 1000
memory_limit_mb: 256
Description: The little boy Nikita was given some cubes as a present. He decided to build a tower out of them.

Initially, the tower doesn't have any cubes. In one move, Nikita either puts exactly $1$ cube on top of the tower or removes exactly $1$ cube from the top of the tower. Is it possible that after $n$ moves, the resulting tower has exactly $m$ cubes?

Input: Each test contains multiple test cases. The first line of input contains a single integer $t$ ($1 \le t \le 100$) — the number of test cases. The description of the test cases follows.

The only line of each test case contains two integers $n$ and $m$ ($1 \le n, m \le 100$).

Output: For each test case, output "Yes" (without quotes) if Nikita can obtain a tower with $m$ cubes, and "No" (without quotes) otherwise.

You can output each letter in any case (lowercase or uppercase). For example, the strings "yEs", "yes", "Yes", and "YES" will be accepted as a positive answer.

Examples:
input:
3
3 3
2 4
5 3
output:
Yes
No
Yes

Note: In the first test case, Nikita can put $1$ cube on top of the tower $3$ times in a row, so the answer is "Yes".

In the second test case, Nikita can only end up with either a tower with no blocks or a tower with $2$ blocks, so the answer is "No".

Buggy Code:
#include <bits/stdc++.h>

using namespace std;
#define int long long
signed main(){
    int t; cin>>t;
    while(t--){
        int n,m; cin>>n>>m;
        if(n >= m)cout<<"YES"<<endl;
        else cout<<"NO"<<endl;
    }
}

**Instructions:**
- Focus on edge cases or scenarios that maximize the failure probability in faulty solutions.
- Due to the output length limit, you should generate a **small-scale** test input that is **complete and valid**.
- Output the test input directly, not code to generate it.

**Output format:**
```plaintext
{test input}
```

Think step by step.

Response:
To generate a challenging test input that exposes the bug in the given buggy code, we need to focus on scenarios where the code's logic fails. The buggy code checks if `n` (the number of moves) is greater than or equal to `m` (the desired number of cubes) and outputs "YES" if it is, otherwise "NO". This logic is incorrect because it doesn't consider the possibility that the number of moves and the desired number of cubes might not align in a way that allows the desired tower to be built.

### Steps to Identify a Challenging Test Case:
1. **Odd and Even Moves**:
   - If `n` is even, the number of cubes can only be even.
   - If `n` is odd, the number of cubes can only be odd.
   - The buggy code doesn't account for this parity.

2. **Edge Cases**:
   - Test cases where `n` is just slightly larger than `m` but the parity doesn't match.
   - Test cases where `n` is much larger than `m` but the parity still doesn't match.

### Challenging Test Case:
- **Test Case 1**: `n = 2`, `m = 1`
  - Here, `n` is even, and `m` is odd. The buggy code will incorrectly output "YES" because `n` is greater than `m`, but it's impossible to end up with an odd number of cubes after an even number of moves.

- **Test Case 2**: `n = 3`, `m = 2`
  - Here, `n` is odd, and `m` is even. The buggy code will incorrectly output "YES" because `n` is greater than `m`, but it's impossible to end up with an even number of cubes after an odd number of moves.

### Final Test Input:
```plaintext
2
2 1
3 2
```

This test input will expose the bug in the buggy code by providing cases where the parity of `n` and `m` doesn't match, leading to incorrect outputs.


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Little Nikita
time_limit_ms: 1000
memory_limit_mb: 256
Description: The little boy Nikita was given some cubes as a present. He decided to build a tower out of them.

Initially, the tower doesn't have any cubes. In one move, Nikita either puts exactly $1$ cube on top of the tower or removes exactly $1$ cube from the top of the tower. Is it possible that after $n$ moves, the resulting tower has exactly $m$ cubes?

Input: Each test contains multiple test cases. The first line of input contains a single integer $t$ ($1 \le t \le 100$) — the number of test cases. The description of the test cases follows.

The only line of each test case contains two integers $n$ and $m$ ($1 \le n, m \le 100$).

Output: For each test case, output "Yes" (without quotes) if Nikita can obtain a tower with $m$ cubes, and "No" (without quotes) otherwise.

You can output each letter in any case (lowercase or uppercase). For example, the strings "yEs", "yes", "Yes", and "YES" will be accepted as a positive answer.

Examples:
input:
3
3 3
2 4
5 3
output:
Yes
No
Yes

Note: In the first test case, Nikita can put $1$ cube on top of the tower $3$ times in a row, so the answer is "Yes".

In the second test case, Nikita can only end up with either a tower with no blocks or a tower with $2$ blocks, so the answer is "No".

Buggy Code:
cases = int(input())

for _ in range(cases):
  entry = input().split()
  moves = int(entry[0])
  height = int(entry[1])

  if height == moves:
    print("Yes")
  elif (moves >= height) and (moves % height != 0):
    print("Yes")
  else:
    print("No")

**Instructions:**
- Focus on edge cases or scenarios that maximize the failure probability in faulty solutions.
- Due to the output length limit, you should generate a **small-scale** test input that is **complete and valid**.
- Output the test input directly, not code to generate it.

**Output format:**
```plaintext
{test input}
```

Think step by step.

Response:
```plaintext
4
1 1
2 1
3 2
4 2
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Little Nikita
time_limit_ms: 1000
memory_limit_mb: 256
Description: The little boy Nikita was given some cubes as a present. He decided to build a tower out of them.

Initially, the tower doesn't have any cubes. In one move, Nikita either puts exactly $1$ cube on top of the tower or removes exactly $1$ cube from the top of the tower. Is it possible that after $n$ moves, the resulting tower has exactly $m$ cubes?

Input: Each test contains multiple test cases. The first line of input contains a single integer $t$ ($1 \le t \le 100$) — the number of test cases. The description of the test cases follows.

The only line of each test case contains two integers $n$ and $m$ ($1 \le n, m \le 100$).

Output: For each test case, output "Yes" (without quotes) if Nikita can obtain a tower with $m$ cubes, and "No" (without quotes) otherwise.

You can output each letter in any case (lowercase or uppercase). For example, the strings "yEs", "yes", "Yes", and "YES" will be accepted as a positive answer.

Examples:
input:
3
3 3
2 4
5 3
output:
Yes
No
Yes

Note: In the first test case, Nikita can put $1$ cube on top of the tower $3$ times in a row, so the answer is "Yes".

In the second test case, Nikita can only end up with either a tower with no blocks or a tower with $2$ blocks, so the answer is "No".

Buggy Code:
y = int (input())

for i in range (0, y):
    n, m = map(int, input().split())
    if n < m:
        print('No')
    else:
        s = n - m
        o = True
        for j in range (0,s):
            o != o
        if o:
            print('YES')
        else:
            print('No')

**Instructions:**
- Focus on edge cases or scenarios that maximize the failure probability in faulty solutions.
- Due to the output length limit, you should generate a **small-scale** test input that is **complete and valid**.
- Output the test input directly, not code to generate it.

**Output format:**
```plaintext
{test input}
```

Think step by step.

Response:
```plaintext
3
1 1
2 1
3 2
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Little Nikita
time_limit_ms: 1000
memory_limit_mb: 256
Description: The little boy Nikita was given some cubes as a present. He decided to build a tower out of them.

Initially, the tower doesn't have any cubes. In one move, Nikita either puts exactly $1$ cube on top of the tower or removes exactly $1$ cube from the top of the tower. Is it possible that after $n$ moves, the resulting tower has exactly $m$ cubes?

Input: Each test contains multiple test cases. The first line of input contains a single integer $t$ ($1 \le t \le 100$) — the number of test cases. The description of the test cases follows.

The only line of each test case contains two integers $n$ and $m$ ($1 \le n, m \le 100$).

Output: For each test case, output "Yes" (without quotes) if Nikita can obtain a tower with $m$ cubes, and "No" (without quotes) otherwise.

You can output each letter in any case (lowercase or uppercase). For example, the strings "yEs", "yes", "Yes", and "YES" will be accepted as a positive answer.

Examples:
input:
3
3 3
2 4
5 3
output:
Yes
No
Yes

Note: In the first test case, Nikita can put $1$ cube on top of the tower $3$ times in a row, so the answer is "Yes".

In the second test case, Nikita can only end up with either a tower with no blocks or a tower with $2$ blocks, so the answer is "No".

Buggy Code:
import java.util.*;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int t = sc.nextInt();
        while (t-- > 0) {
            int n=sc.nextInt();
           int m=sc.nextInt();
           if(n>=m)
               System.out.println("YES");
           else
               System.out.println("NO");
        }
    }
}

**Instructions:**
- Focus on edge cases or scenarios that maximize the failure probability in faulty solutions.
- Due to the output length limit, you should generate a **small-scale** test input that is **complete and valid**.
- Output the test input directly, not code to generate it.

**Output format:**
```plaintext
{test input}
```

Think step by step.

Response:
```plaintext
3
1 2
2 3
4 2
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Little Nikita
time_limit_ms: 1000
memory_limit_mb: 256
Description: The little boy Nikita was given some cubes as a present. He decided to build a tower out of them.

Initially, the tower doesn't have any cubes. In one move, Nikita either puts exactly $1$ cube on top of the tower or removes exactly $1$ cube from the top of the tower. Is it possible that after $n$ moves, the resulting tower has exactly $m$ cubes?

Input: Each test contains multiple test cases. The first line of input contains a single integer $t$ ($1 \le t \le 100$) — the number of test cases. The description of the test cases follows.

The only line of each test case contains two integers $n$ and $m$ ($1 \le n, m \le 100$).

Output: For each test case, output "Yes" (without quotes) if Nikita can obtain a tower with $m$ cubes, and "No" (without quotes) otherwise.

You can output each letter in any case (lowercase or uppercase). For example, the strings "yEs", "yes", "Yes", and "YES" will be accepted as a positive answer.

Examples:
input:
3
3 3
2 4
5 3
output:
Yes
No
Yes

Note: In the first test case, Nikita can put $1$ cube on top of the tower $3$ times in a row, so the answer is "Yes".

In the second test case, Nikita can only end up with either a tower with no blocks or a tower with $2$ blocks, so the answer is "No".

Buggy Code:
import java.util.*;
public class LittleNikitha{
    public static void main(String []args){
        Scanner sc=new Scanner(System.in);
        int t=sc.nextInt();
        while(t -->0){
        int n=sc.nextInt();
        int m=sc.nextInt();
        if(n>=m){
            System.out.println("Yes");
        }else{
            System.out.println("No");
        }
    }
    }
}

**Instructions:**
- Focus on edge cases or scenarios that maximize the failure probability in faulty solutions.
- Due to the output length limit, you should generate a **small-scale** test input that is **complete and valid**.
- Output the test input directly, not code to generate it.

**Output format:**
```plaintext
{test input}
```

Think step by step.

Response:
```plaintext
1
100 1
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Verify Password
time_limit_ms: 2000
memory_limit_mb: 256
Description: Monocarp is working on his new site, and the current challenge is to make the users pick strong passwords.

Monocarp decided that strong passwords should satisfy the following conditions:

  * password should consist only of lowercase Latin letters and digits;    * there should be no digit that comes after a letter (so, after each letter, there is either another letter or the string ends);    * all digits should be sorted in the non-decreasing order;    * all letters should be sorted in the non-decreasing order.

Note that it's allowed for the password to have only letters or only digits.

Monocarp managed to implement the first condition, but he struggles with the remaining ones. Can you help him to verify the passwords?

Input: The first line contains a single integer $t$ ($1 \le t \le 1000$) — the number of testcases.

The first line of each testcase contains a single integer $n$ ($1 \le n \le 20$) — the length of the password.

The second line contains a string, consisting of exactly $n$ characters. Each character is either a lowercase Latin letter or a digit.

Output: For each testcase, print "YES" if the given password is strong and "NO" otherwise.

Examples:
input:
5
4
12ac
5
123wa
9
allllmost
5
ac123
6
011679
output:
YES
NO
YES
NO
YES

Note: In the second testcase, the letters are not sorted in the non-decreasing order.

In the fourth testcase, there is a digit that comes after a letter — digit '1' after a letter 'c'.

Buggy Code:
/**
 *   author:    karvalian
 *   created:   30.05.2024 19:48:23
**/
#include <bits/stdc++.h>

using namespace std;

#ifdef LOCAL
#include "algo/debug.h"
#else
#define debug(...) 42
#endif
int main() {
	ios::sync_with_stdio(false);
	cin.tie(0);
	int tt;
	cin >> tt;
	while (tt--) {
		int n;
		cin >> n;
		string s;
		cin >> s;
		vector<int> letters;
		vector<char> alphas;
		bool ans = 1;
		for (int i = 1; i < n; i++) {
			if (isdigit(s[i]) && !isdigit(s[i - 1])) {
				ans = 0;
			}
			if (isdigit(s[i])) {
				letters.push_back(s[i]);
			} else {
				string test = "abcdefghijklmnopqrstuvwxyz";
				if (find(test.begin(), test.end(), s[i]) == test.end()) {
					ans = 0;
				}
				alphas.push_back(s[i]);
			}
		}
		if (!is_sorted(letters.begin(), letters.end())) {
			ans = 0;
		} else if (!is_sorted(alphas.begin(), alphas.end())) {
			ans = 0;
		}
		cout << (ans ? "YES": "NO") << "\n";
	}
	return 0;
}

**Instructions:**
- Focus on edge cases or scenarios that maximize the failure probability in faulty solutions.
- Due to the output length limit, you should generate a **small-scale** test input that is **complete and valid**.
- Output the test input directly, not code to generate it.

**Output format:**
```plaintext
{test input}
```

Think step by step.

Response:
```plaintext
3
5
a1b2c
6
abc123
4
12ab
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Verify Password
time_limit_ms: 2000
memory_limit_mb: 256
Description: Monocarp is working on his new site, and the current challenge is to make the users pick strong passwords.

Monocarp decided that strong passwords should satisfy the following conditions:

  * password should consist only of lowercase Latin letters and digits;    * there should be no digit that comes after a letter (so, after each letter, there is either another letter or the string ends);    * all digits should be sorted in the non-decreasing order;    * all letters should be sorted in the non-decreasing order.

Note that it's allowed for the password to have only letters or only digits.

Monocarp managed to implement the first condition, but he struggles with the remaining ones. Can you help him to verify the passwords?

Input: The first line contains a single integer $t$ ($1 \le t \le 1000$) — the number of testcases.

The first line of each testcase contains a single integer $n$ ($1 \le n \le 20$) — the length of the password.

The second line contains a string, consisting of exactly $n$ characters. Each character is either a lowercase Latin letter or a digit.

Output: For each testcase, print "YES" if the given password is strong and "NO" otherwise.

Examples:
input:
5
4
12ac
5
123wa
9
allllmost
5
ac123
6
011679
output:
YES
NO
YES
NO
YES

Note: In the second testcase, the letters are not sorted in the non-decreasing order.

In the fourth testcase, there is a digit that comes after a letter — digit '1' after a letter 'c'.

Buggy Code:
#include <bits/stdc++.h>

using namespace std;

int test, n;
char a[30], b[30], c[30], d[30];

void px(char s[], int l) {
	for (int i = 1; i <= l; i++)
		for (int j = i + 1; j <= l; j++)
			if (s[j] > s[i])
				swap(s[j], s[i]);
}

int main() {
	scanf("%d", &test);
	for (int i = 1; i <= test; i++) {
		scanf("%d", &n);
		char str[30];
		scanf("%s", str);
		bool ok = true;
		int len = strlen(str);
		for (int j = 0; j < len; j++)
			if (!((str[j] >= '0' && str[j] <= '9') || (str[j] >= 'a' && str[j] <= 'z'))) {
				ok = false;
				break;
			}
		for (int j = 0; j < len - 1; j++)
			if (str[j] >= 'a' && str[j] <= 'z' && str[j + 1] >= '0' && str[j + 1] <= '9') {
				ok = false;
				break;
			}
		int len1 = 0, len2 = 0;
		for (int j = 0; j < len; j++)
			if (str[j] >= 'a' && str[j] <= 'z')
				c[len1] = a[++len1] = str[j];
		for (int j = 0; j < len; j++)
			if (str[j] >= '0' && str[j] <= '9')
				d[len2] = b[++len2] = str[j];
		px(a, len1);
		px(b, len2);
		int cnt = 0;
		for (int j = 1; j <= len1; j++)
			if (a[j] == c[j])
				++cnt;
		int k = 0;
		for (int j = 1; j < len1; j++)
			if (a[j] == a[j + 1])
				++k;
		if (cnt == len1 && len1 && k != len1 - 1)
			ok = false;
		cnt = 0;
		for (int j = 1; j <= len2; j++)
			if (b[j] == d[j])
				++cnt;
		k = 0;
		for (int j = 1; j < len2; j++)
			if (b[j] == b[j + 1])
				++k;
		if (cnt == len2 && len2 && k != len2 - 1)
			ok = false;
		if (ok)
			printf("YES\n");
		else
			printf("NO\n");
	}
	return 0;
}

**Instructions:**
- Focus on edge cases or scenarios that maximize the failure probability in faulty solutions.
- Due to the output length limit, you should generate a **small-scale** test input that is **complete and valid**.
- Output the test input directly, not code to generate it.

**Output format:**
```plaintext
{test input}
```

Think step by step.

Response:
```plaintext
5
4
12ac
5
123wa
5
ac123
6
011679
5
a1b2c
```