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.*;
import java.text.*;
import java.math.*;
import java.util.regex.*;

public class JaiShreeRam{
	static Scanner in=new Scanner();
	static long mod = 1000000007;
	static ArrayList<ArrayList<Integer>> adj;
	public static void main(String[] args) throws Exception{
		int z=in.readInt();
		while(z-->0){
			solve();
		}
	}
		
	static void solve() {
		int n=in.readInt();
		int s=in.readInt();
		int m=(n+1)/2;
		int ans=s/(n-m+1);
		System.out.println(ans);
	}
	
	static int[] nextIntArray(int n){
		int[] arr= new int[n];
		int i=0;
		while(i<n){
			arr[i++]=in.readInt();
		}
		return arr;
	}
	static int[] nextIntArray1(int n){
		int[] arr= new int[n+1];
		int i=1;
		while(i<=n){
			arr[i++]=in.readInt();
		}
		return arr;
	}
	static long gcd(long a, long b) {
		if (b==0) return a;
		return gcd(b, a%b);
	}
	static class Scanner{
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st=new StringTokenizer("");
		String readString() {
			while (!st.hasMoreTokens())
				try {
					st=new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			return st.nextToken();
		}
		double readDouble() {
			return Double.parseDouble(readString());
		}
		int readInt() {
			return Integer.parseInt(readString());
		}
		long readLong() {
			return Long.parseLong(readString());
		}
	}	
}