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.*;

public class A {

    public static void main(String[] args) {
        int t = f.nextInt();while(t-- > 0)
            solve();
        out.close();
    }

    static void solve() {
        int n = f.nextInt(), s = f.nextInt();

        int left = n/2;
        int right = n - left;

        s -= left;
        System.out.println(Math.max(0, s/right));
    }

    private static void mySort(int[] arr) {
        for(int i=0;i<arr.length;i++) {
            int rand = (int) (Math.random() * arr.length);
            int loc = arr[rand];
            arr[rand] = arr[i];
            arr[i] = loc;
        }
        Arrays.sort(arr);
    }



    static FastReader f = new FastReader();
    static PrintWriter out = new PrintWriter(System.out);

    static class FastReader {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st;

        String next() {
            while(st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch(IOException ioe) {
                    ioe.printStackTrace();
                }
            }
            return st.nextToken();
        }

        String nextLine() {
            String s = "";
            try {
                s = br.readLine();
            } catch(IOException ioe) {
                ioe.printStackTrace();
            }

            return s;
        }

        int  nextInt() {
            return Integer.parseInt(next());
        }

        double  nextDouble() {
            return Double.parseDouble(next());
        }

        long  nextLong() {
            return Long.parseLong(next());
        }
    }
}
