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.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.HashMap;
import java.util.Scanner;
import java.util.StringTokenizer;

public class Main {
	
	static FastScanner fs = new FastScanner();

	public static void main(String[] args) {
		
		
		int t = fs.nextInt();
		while(t-->0) {
			int n = fs.nextInt(), s = fs.nextInt();
//			int[] a = fs.readArray(n);
			int med = (n+1)/2;
			n -= med-1;
			s -= med-1;
			System.out.println(s/n);
		}	
	}
	
	
	
	
	
	
	
	
	
	
	
	
	
	
	
	
	
	
	
	
	
	public static int[] readArray(int n){
		int[] a = new int[n];
		for(int i=0 ; i<n ; i++) {
			a[i] = fs.nextInt();
		}
        return a;
    }
	
	public static void printArray(int[] n){
        for(int e:n) {
        	System.out.print(e + " ");
        }
        System.out.println();
    }
	
	static int[] sort(int[] a) {
		ArrayList<Integer> l=new ArrayList<>();
		for (int i:a) l.add(i);
		Collections.sort(l);
		for (int i=0; i<a.length; i++) a[i]=l.get(i);
		return a;
	}
	
	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;
		}
		String[] readStringArray(int n) {
			String[] a=new String[n];
			for (int i=0; i<n; i++) a[i]=next();
			return a;
		}
		long nextLong() {
			return Long.parseLong(next());
		}
	}
	
//	BufferedWriter output = new BufferedWriter(
//            new OutputStreamWriter(System.out));
// 
//        for (int i = 0; i < gfg.length; i++) {
//            output.write(gfg[i] + "\n");
//        }
// 
//        output.flush();
	

}
