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.PrintWriter;
import java.util.ArrayList;
import java.util.Collections;
import java.util.StringTokenizer;

public class A implements Runnable {

	public static void main(String[] args) throws Exception {

		new Thread(null, new A(), "SwapnilGanguly", 1 << 20).start();
	}

	public void run() {

		SwapScanner sc = new SwapScanner();
		PrintWriter pr = new PrintWriter(System.out);

		int T = sc.nextInt();

		while (T-- > 0) {

			int n = sc.nextInt(), s = sc.nextInt();

			int nonZero = n - (n % 2 == 0 ? n / 2 - 1 : n / 2);

			pr.println(s / nonZero);
		}

		pr.close();
	}

	public static void 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);
	}

	public static class SwapScanner {

		BufferedReader br;
		StringTokenizer st;

		public SwapScanner() {

			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;
		}

		int[] readArray(int n) {

			int[] ar = new int[n];

			for (int i = 0; i < n; i++)
				ar[i] = nextInt();

			return ar;
		}
	}
}