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.math.*;
import java.security.*;
import java.text.*;
import java.time.LocalTime;
import java.util.*;
import java.util.concurrent.*;
import java.util.regex.*;


public class A {
	

	public static void main(String[] args) {
    	FastScanner scan = new FastScanner();
    	PrintWriter out = new PrintWriter(System.out);
    	
    	int T = 1;
    	T = scan.nextInt();
    		for(int tt=0; tt<T; tt++) {
    			int n = scan.nextInt(), s = scan.nextInt();
    			int num = n - ((n-1) / 2);
    			System.out.println(s / num);
    		}
	}
	
	
	
	/*
	static class IntComparator implements Comparator<Integer> {

		public int compare(Integer o1, Integer o2) {
		//	return Integer.compare(a[o1], a[o2]);
			return 0;
		}
	}
	*/
	
	
	public static void printIntArray(int [] a) {
		for(int i: a) System.out.print(i + " ");
		System.out.println();
	}
	
	public static void swapInt(int a, int b) {
		int temp = a;
		a = b;
		b = temp;
	}

	
	  public static void sort(int [] a) {
	    	ArrayList<Integer> b = new ArrayList<>();
	    	for(int i: a) b.add(i);
	    	Collections.sort(b);
	    	for(int i=0; i<a.length; i++) a[i]= b.get(i);
	    }
	  
	  public static void reverse(int [] a) {
	    	ArrayList<Integer> b = new ArrayList<>();
	    	for(int i: a) b.add(i);
	    	Collections.reverse(b);
	    	for(int i=0; i<a.length; i++) a[i]= b.get(i);
	    }


		
	
	
    static class FastScanner{
    	
    	BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    	StringTokenizer st = new StringTokenizer("");
    	String next() {
    		while(!st.hasMoreTokens())
    			try {
    				st = new StringTokenizer(br.readLine());
    			} catch (IOException e){
    				e.printStackTrace();
    			}
    		return st.nextToken();
    	}
    	
    	int nextInt() {
    		return Integer.parseInt(next());
    	}
    	
    	int [] readArray(int n) {
    		int [] a = new int[n];
    		for(int i=0; i<n ; i++) a[i] = nextInt();
    		return a;
    	}
    	
    	long nextLong() {
    		return Long.parseLong(next());
    	}
    	
    	
    }
    
    
   
}

