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.*;


/** 
__                  __
( _)                ( _)
/ / \\              / /\_\_
/ /   \\            / / | \ \
/ /     \\          / /  |\ \ \
/  /   ,  \ ,       / /   /|  \ \
/  /    |\_ /|      / /   / \   \_\
/  /  |\/ _ '_| \   / /   /   \    \\
|  /   |/  0 \0\    / |    |    \    \\
|    |\|      \_\_ /  /    |     \    \\
|  | |/    \.\ o\o)  /      \     |    \\
\    |     /\\`v-v  /        |    |     \\
| \/    /_| \\_|  /         |    | \    \\
| |    /__/_ `-` /   _____  |    |  \    \\
\|    [__]  \_/  |_________  \   |   \    ()
/    [___] (    \         \  |\ |   |   //
|    [___]                  |\| \|   /  |/
/|    [____]                  \  |/\ / / ||
(  \   [____ /     ) _\      \  \    \| | ||
\  \  [_____|    / /     __/    \   / / //
|   \ [_____/   / /        \    |   \/ //
|   /  '----|   /=\____   _/    |   / //
__ /  /        |  /   ___/  _/\    \  | ||
(/-(/-\)       /   \  (/\/\)/  |    /  | /
(/\/\)           /   /   //
_________/   /    /
\____________/    (



*/

public class Main {
	public static void main(String[] args) {
		Scanner sc=new Scanner(System.in);
		int t=sc.nextInt();
		
		while(t-- >0) {
			int n=sc.nextInt();
			int s=sc.nextInt();
			
				int c=(int)Math.ceil(n*1.0/2*1.0);
				n=n-(c-1);
				System.out.println(s/n);
			
		}
		
	}
}
