You are given two positive integers n and s. Find the maximum possible median of an array of n non-negative integers (not necessarily distinct), such that the sum of its elements is equal to s.

A median of an array of integers of length m is the number standing on the ⌈ {m/2} ⌉-th (rounding up) position in the non-decreasing ordering of its elements. Positions are numbered starting from 1. For example, a median of the array [20,40,20,50,50,30] is the ⌈ m/2 ⌉-th element of [20,20,30,40,50,50], so it is 30. There exist other definitions of the median, but in this problem we use the described definition.

Input

The input consists of multiple test cases. The first line contains a single integer t (1 ≤ t ≤ 10^4) — the number of test cases. Description of the test cases follows.

Each test case contains a single line with two integers n and s (1 ≤ n, s ≤ 10^9) — the length of the array and the required sum of the elements.

Output

For each test case print a single integer — the maximum possible median.

Example

Input


8
1 5
2 5
3 5
2 1
7 17
4 14
1 1000000000
1000000000 1


Output


5
2
2
0
4
4
1000000000
0

Note

Possible arrays for the first three test cases (in each array the median is underlined):

  * In the first test case [\underline{5}] 
  * In the second test case [\underline{2}, 3] 
  * In the third test case [1, \underline{2}, 2] 

import java.util.*;
import java.io.*;
import java.math.BigInteger;

public class P04 {
	static class FastReader{
		BufferedReader br ;
		StringTokenizer st;
		public FastReader() {
			br = new BufferedReader(new InputStreamReader(System.in));
			
		}
		String next() {
			while(st==null || !st.hasMoreElements()) {
				try {
					st = new StringTokenizer(br.readLine());
				}catch(IOException e) {
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}
		
		int nextInt() {
			return Integer.parseInt(next());
		}
		
		long nextLong() {
			return  Long.parseLong(next());
		}
		
		double nextDouble() {
			return Double.parseDouble(next());
		}
		
		float nextFloat() {
			return Float.parseFloat(next());
		}
		String nextLine() {
			String str = "";
			try {
				str = br.readLine();
			}catch(IOException e) {
				e.printStackTrace();
			}
			return str ;
		}
	}
	static void swap(int[] arr, int i, int j)
	{
	    int temp = arr[i];
	    arr[i] = arr[j];
	    arr[j] = temp;
	}

	static int partition(int[] arr, int low, int high)
	{	   
	    long pivot = arr[high];   
	    int i = (low - 1);
	    for(int j = low; j <= high - 1; j++)
	    {    
	        if (arr[j] < pivot)
	        {          
	            i++;
	            swap(arr, i, j);
	        }
	    }
	    swap(arr, i + 1, high);
	    return (i + 1);
	}
	static void quickSort(int[] arr, int low, int high)
	{
	    if (low < high)
	    {  
	        int pi = partition(arr, low, high);
	        quickSort(arr, low, pi - 1);
	        quickSort(arr, pi + 1, high);
	    }
	}
	public static long binarySearch(long arr[], long key){  
		  int  first =0,last =arr.length-1;
		   int mid = (first + last)/2;  
		   while( first <= last ){  
		      if ( arr[mid] < key ){  
		        first = mid + 1;     
		      }else if ( arr[mid] == key ){  
		    	 return mid;  
		      }else{  
		         last = mid - 1;  
		      }  
		      mid = (first + last)/2;  
		   }  
		   if ( first > last ){ 
			   return -1;
		       
		   } 
		   return -1;
		 }  
	static long fp(long a , long b , int n) {
		long res =1;
		while(b>0) {
			if((b&1)!=0) {             //when b is odd 
				res=(res*a%n)%n;
			}
			a=(a%n*a%n)%n;
			b=b>>1;
		}
		return res;
	}
	static long gcd (long a ,long b) {
		if(b==0) {
			return a;
		}
		return gcd(b,a%b);
	}
	public static void main(String[] args) {
		Scanner sc = new Scanner (System.in);
		FastReader fs = new FastReader();
		int t = fs.nextInt();
		while(t-->0) {
			int n = fs.nextInt();
			int s = fs.nextInt();
			if(n==1) {
				System.out.println(s);
			}
			else {
				
				if((n&1)==0) {
					System.out.println(s/(n-((n/2)-1)));
				}
				else {
					System.out.println(s/(n-(n/2)));
				}
			}
			
		}
		
    }
	

	private static int solve(int[] a,int b[], int n) {
		int flag =0;
		for(int j =0;j<n;j++) {
			if(a[j]!=b[j]) {
				flag=1;
			}
		}
		if(flag==0)return 0;
		int i=1;
		while(true) {
			if(i%2==0) {
				for(int j=1;j<n-1;j+=2) {
					if(a[j]>a[j+1]) {
						int temp =a[j];
						a[j]=a[j+1];
						a[j+1]=temp;
					}
				}
			}
			else {
				for(int j =0;j<n-2;j+=2) {
					if(a[j]>a[j+1]) {
						int temp =a[j];
						a[j]=a[j+1];
						a[j+1]=temp;
					}
				}
			}
			flag =0;
			for(int j =0;j<n;j++) {
				if(a[j]!=b[j])flag=1;
			}
			if(flag==0)return i;
			i++;
		}
       
		
		
	}

	private static long sumofn(long n) {
		int ans = 0;
		while(n>9) {
			ans+=n%10;
			n/=10;
		}
		ans+=n;
		return ans;
	}
	private static boolean palin(String s) {
		int i =0,j=s.length()-1;
		while(i<j) {
			if(s.charAt(i)!=s.charAt(j))return false;
			else {
				i++;
				j--;
			}
		}
		return true;
	}
}
			


