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.*;

public class Main {
	static MyScanner sc = new MyScanner();
	static Output out=new Output();
	public static void main(String[] args) {
		int t=sc.nextInt();
		for(int i=0;i<t;i++) {
			solve();
		}
		out.flush();
	}
	
	public static void solve() {
		int n=sc.nextInt(),s=sc.nextInt();
		if(n==1)	out.println(s);
		else if(n==2)	out.println(s/2);
		else {
				out.println(s/(n/2+1));
		}
	}	
}























class MyScanner {

	BufferedReader br;
	StringTokenizer st;

	public MyScanner() {
		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;
	}

	public int[] nextIntArr(int n) {
		int a[] = new int[n];
		for (int i = 0; i < n; i++)
			a[i] = nextInt();
		return a;
	}

	public long[] nextLongArr(int n) {
		long a[] = new long[n];
		for (int i = 0; i < n; i++)
			a[i] = nextLong();
		return a;
	}

	public double[] nextDoubleArr(int n) {
		double a[] = new double[n];
		for (int i = 0; i < n; i++)
			a[i] = nextDouble();
		return a;
	}

	public String[] nextArr(int n) {
		String a[] = new String[n];
		for (int i = 0; i < n; i++)
			a[i] = next();
		return a;
	}

	public String[] nextLineArr(int n) {
		String a[] = new String[n];
		for (int i = 0; i < n; i++)
			a[i] = nextLine();
		return a;
	}
}
class Output{
	StringBuilder s=new StringBuilder();
	public void println() {
		s.append("\n");
	}
	public void println(Object x) {
		s.append(x+"\n");
	}
	
	public void print(Object x) {
		s.append(x+"");
	}
	
	public void flush() {
		System.out.println(s);
		s=new StringBuilder();
	}
}