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.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class Median {
	static StringBuilder solution = new StringBuilder();
	static PrintWriter pw = new PrintWriter(new OutputStreamWriter(System.out));

	public static void main(String[] args) {
		int t = nextInt();
		while(t-- != 0)
		{
			long n = nextLong();
			long s = nextLong();
			if(n == 1)
				pw.println(s);
			else if(n % 2 != 0)
			{
				pw.println(s/(n-(n/2)));
			}
			else {
				pw.println(s/(n-(n/2 - 1)));
			}
		}
		pw.close();
	}

	static StringTokenizer st;
	static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
 
	public static String nextLine() {
		String s = "";
		try {
			s = br.readLine();
		} catch (IOException e) {
			// TODO Auto-generated catch block
			e.printStackTrace();
		}
		return s;
	}
 
	public static String next() {
		while (st == null || !st.hasMoreElements()) {
			try {
				st = new StringTokenizer(br.readLine());
			} catch (IOException e) {
				e.printStackTrace();
			}
		}
		return st.nextToken();
	}
 
	public static int nextInt() {
		return Integer.parseInt(next());
	}
	public static long nextLong() {
		return Long.parseLong(next());
	}
}
