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.*;
import java.util.*;

public class Main {

	public static void main(String[] args) {
		
			FastReader sc=new FastReader();
			int t=sc.nextInt();
			while(t>0) {
				int n=sc.nextInt();
				int k=sc.nextInt();
				if(n>k) {
					System.out.println(0);
				}else if(n==0) {
					System.out.println(0);
				}else if(n==1) {
					System.out.println(k);
				}else if(n==2) {
					System.out.println(k/2);
				}else {
				// 	int m=(n%2==0?n/2:(n/2)+1); 
				// 	int left=n-m+1;
				// 	int x=k/left; int y=k%left;
				    int m=(n/2)+1;
				    int x=k/m;
					    System.out.println(x);
				}
				
				
				t--;
			}
		
	}
	static class FastReader {
		BufferedReader br;
		StringTokenizer st;

		public FastReader()
		{
			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;
		}
	}

}