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.*;
//solve harder problems
//upsolve
//use gitgud
//learn from everything
//USACO
public class Contest1566A
{
	static class InputReader {
		BufferedReader reader;
		StringTokenizer tokenizer;
		public InputReader(InputStream stream) {
			reader = new BufferedReader(new InputStreamReader(stream), 32768);
			tokenizer = null;
		}
		String next() { // reads in the next string
			while (tokenizer == null || !tokenizer.hasMoreTokens()) {
				try {
					tokenizer = new StringTokenizer(reader.readLine());
				} catch (IOException e) {
					throw new RuntimeException(e);
				}
			}
			return tokenizer.nextToken();
		}
		public int nextInt() { // reads in the next int
			return Integer.parseInt(next());
		}
		public long nextLong() { // reads in the next long
			return Long.parseLong(next());
		}
		public double nextDouble() { // reads in the next double
			return Double.parseDouble(next());
			}
		}
	static InputReader r = new InputReader(System.in);
	static PrintWriter pw = new PrintWriter(System.out);
	public static void main(String[] args)
	{
		//LOOK FOR INT OVERFLOW
		//LOOK FOR SCOPE ERROR
		//Add negatives
		//SORT BOTH ARRAYS
		//CHECK THE LAST ONE THAT IS OUT LOOP
		//SORT BY BOTH VALUES
		//DON'T ADD STRINGS,USE STRING BUILDER
		int t = r.nextInt();
		while (t > 0)
		{
			t--;
			int n = r.nextInt(); int s = r.nextInt();
			pw.println(s/(n/2+1));
		}
		
		pw.close();
	}
}