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] 
  /* package codechef; // don't place package name! */
import java.util.*;
import java.lang.*;
import java.io.*;
import java.math.BigInteger;

/* Name of the class has to be "Main" only if the class is public. */
public class hello
{
     static class Pair implements Comparable<Pair>{
        int power=0;
        int bonus=0;
        public Pair(int power,int bonus){
            this.power=power;
            this.bonus=bonus;
        }
        public int compareTo(Pair o){
            return this.power-o.power;
        }
    }
     static class FastReader 
    { 
        BufferedReader br; 
        StringTokenizer st; 
  
        public FastReader() 
        { 
            try {
               br=new BufferedReader(new FileReader("input.txt"));
               PrintStream out= new PrintStream(new FileOutputStream("output.txt"));
               System.setOut(out);
            }
  
            // Catch block to handle the exceptions
            catch (Exception e) {
                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()); 
        } 
  
        String nextLine() 
        { 
            String str = ""; 
            try
            { 
                str = br.readLine(); 
            } 
            catch (IOException e) 
            { 
                e.printStackTrace(); 
            } 
            return str; 
        } 
    } 
    public static void main (String[] args) throws java.lang.Exception
    {

       try{
        FastReader sc=new FastReader();
        BufferedWriter out = new BufferedWriter(
            new OutputStreamWriter(System.out));
        int t=sc.nextInt();
        while(t-->0){

            long n = sc.nextLong();
            long s = sc.nextLong();

         //ArrayList<Long> list = new ArrayList<>();

            if(s<n)
                System.out.println(0);
            else
            {
                long k = s/n;

                long p = s%n;

                long mid = n/2;

                if(mid == n)
                {
                    System.out.println(k+p);
                }
                else
                {
                    System.out.println(k);
                }
            }

        }
    }catch(Exception e){
            return;
        }
    }
}