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.*;

public class A {

	private static final FastScanner fs = new FastScanner();
	private static final int MOD = 1000000007;

	public static void main(String[] args) throws IOException {
		int cases = fs.nextInt();
		while (cases-- > 0)
			solve();
	}
	static void solve() throws IOException {
		int n = fs.nextInt();
		int s = fs.nextInt();

		if (n == 1) {
			System.out.println(s);
			return;
		}
		if (n == 2) {
			System.out.println(s/2);
			return;
		}
		int half = n/2;
		if (n%2 == 0) {
			int res = (s/half+1)/2;
			int res2= (s/(half+1) + 1 )/2;
			res = Math.max(res, res2);
			System.out.println(res);
		} else {
			System.out.println(s/(half+1));
		}
	}

	static class FastScanner {
		//I don't know how this works lmao
		public 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());
		}

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

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

		int[] nextInts(int n) {
			int[] a = new int[n];
			for (int i = 0; i < n; i++) a[i] = nextInt();
			return a;
		}
	}
}