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.InputStreamReader;
import java.util.Arrays;
import java.util.StringTokenizer;

import static java.lang.System.out;

public class RoundGlobal16A
{
    public static void main(String[] args) throws Exception
    {
        BufferedReader infile = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer(infile.readLine());
        int T = Integer.parseInt(st.nextToken());
        StringBuilder sb = new StringBuilder();
        while(T-->0)
        {
            st = new StringTokenizer(infile.readLine());
            long n = Long.parseLong(st.nextToken());
            long s = Long.parseLong(st.nextToken());

            if(n == 1){
                sb.append(s);
            } else if(n == 2){
                sb.append(s/2);
            } else if(s == 1){
                sb.append(0);
            } else {
                sb.append(s);
            }
            sb.append("\n");
        }
        out.println(sb);
        //BufferedReader infile = new BufferedReader(new FileReader("input.txt"));
        //System.setOut(new PrintStream(new File("output.txt")));
    }
    public static int[] readArr(int N, BufferedReader infile, StringTokenizer st) throws Exception
    {
        int[] arr = new int[N];
        st = new StringTokenizer(infile.readLine());
        for(int i=0; i < N; i++)
            arr[i] = Integer.parseInt(st.nextToken());
        return arr;
    }
    public static void print(int[] arr)
    {
        //for debugging only
        for(int x: arr)
            out.print(x+" ");
        out.println();
    }

    public static long[] readArr2(int N, BufferedReader infile, StringTokenizer st) throws Exception
    {
        long[] arr = new long[N];
        st = new StringTokenizer(infile.readLine());
        for(int i=0; i < N; i++)
            arr[i] = Long.parseLong(st.nextToken());
        return arr;
    }
    public static boolean isPrime(long n)
    {
        if(n < 2) return false;
        if(n == 2 || n == 3) return true;
        if(n%2 == 0 || n%3 == 0) return false;
        long sqrtN = (long)Math.sqrt(n)+1;
        for(long i = 6L; i <= sqrtN; i += 6) {
            if(n%(i-1) == 0 || n%(i+1) == 0) return false;
        }
        return true;
    }
    public static long gcd(long a, long b)
    {
        if(a > b)
            a = (a+b)-(b=a);
        if(a == 0L)
            return b;
        return gcd(b%a, a);
    }

    public static int lcm(int a, int b) {
        return (a * b) / lcm(a, b);
    }

    public static String sort(String s){
        char[] c = s.toCharArray();
        Arrays.sort(c);
        return new String(c);
    }

    static String deleteIth(String str, int i)
    {
        str = str.substring(0, i) +
                str.substring(i + 1);
        return str;
    }
}