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] 
/*Everything is Hard
 * Before Easy
 * Jai Mata Dii
 */

import java.io.*;
import java.util.*;

public class Main3 {
	static class FastReader{ BufferedReader br;StringTokenizer st;public FastReader(){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; }}
//	static FastReader sc = new FastReader();
	 static Scanner sc = new Scanner(System.in); 	
	static PrintWriter out = new PrintWriter(System.out);
	static int mod = (int) (1e9+7);
	public static void main (String[] args){
        int ttt = 1;
        ttt = sc.nextInt();
        z :for(int tc=1;tc<=ttt;tc++){
        	long n = sc.nextLong();
        	long s = sc.nextLong();
        	long addAt = (long) ((n+1L)/2L);
        	long ext = n - addAt + 1;
        	if(s<ext) {
        		out.write(0+"\n");
        		continue;
        	}
        	long ans = s/ext;
        	s -= (s/ext)*ext;
        	out.write(ans+"\n");
        }
		out.close();
	}
	static long gcd(long a,long b) { if(b==0) return a; return gcd(b,a%b); }
}