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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;
import java.util.Arrays;
import java.util.ArrayList;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.TreeSet;
import java.util.TreeMap;
import java.util.PriorityQueue;

import java.util.Iterator;

public class First {

    public static void main(String[] args) {
        FastScanner fs = new FastScanner();
        int T = fs.nextInt();
        for (int tt = 0; tt < T; tt++) {

            solve(fs);
        }
    }
    static void solve(FastScanner fs)
    {
        int n=fs.nextInt(), s=fs.nextInt();

        int left=-1;
        if(n%2==0)
        {
            left=n/2-1;
        }
        else
            left=n/2;

        pn((s)/(n-left));
                  
    }
    static int MOD=(int)(1e9+7);
    
    static long gcd(long a, long b) 
    {
        if (a == 0)
            return b;    
        return gcd(b%a, a);
    }
    static void pn(Object o) { System.out.println(o); } 
    static void p(Object o) { System.out.print(o); }
    static void flush() { System.out.flush(); }

    static void debugInt(int[] arr)
    {
        for(int i=0;i<arr.length;++i)
            System.out.print(arr[i]+" ");
        System.out.println();
    }
    static void debugIntInt(int[][] arr)
    {
        for(int i=0;i<arr.length;++i)
        {
            for(int j=0;j<arr[0].length;++j)
                System.out.print(arr[i][j]+" ");
            System.out.println();
        }
        System.out.println();
    }
    static void debugLong(long[] arr)
    {
        for(int i=0;i<arr.length;++i)
            System.out.print(arr[i]+" ");
        System.out.println();
    }
    static void debugLongLong(long[][] arr)
    {
        for(int i=0;i<arr.length;++i)
        {
            for(int j=0;j<arr[0].length;++j)
                System.out.print(arr[i][j]+" ");
            System.out.println();
        }
        System.out.println();
    }
    static long[] takeLong(int n, FastScanner fs)
    {
        long[] arr=new long[n];
        for(int i=0;i<n;++i)
            arr[i]=fs.nextLong();
        return arr;
    } 
    static long[][] takeLongLong(int m, int n, FastScanner fs)
    {
        long[][] arr=new long[m][n];
        for(int i=0;i<m;++i)
            for(int j=0;j<n;++j)
                arr[i][j]=fs.nextLong();
        return arr;
    } 
    static int[] takeInt(int n, FastScanner fs)
    {
        int[] arr=new int[n];
        for(int i=0;i<n;++i)
            arr[i]=fs.nextInt();
        return arr;
    } 
    static int[][] takeIntInt(int m, int n, FastScanner fs)
    {
        int[][] arr=new int[m][n];
        for(int i=0;i<m;++i)
            for(int j=0;j<n;++j)
                arr[i][j]=fs.nextInt();
        return arr;
    } 
    static class FastScanner {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer("");
        String next() {
            while (!st.hasMoreTokens())
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }
        int[] readArray(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++) a[i] = nextInt();
            return a;
        }
        long nextLong() {
            return Long.parseLong(next());
        }
    }


}
class Pair
{
    
}