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.*;
import java.io.*;

public class Main {
  public static int MEX(String str){
    boolean a = false;
    boolean b = false;
    boolean c = false;
    int count = 0;
    if(str.indexOf("1") == -1){
      a = true;
      count++;
    }
    if(str.indexOf("0") == -1){
      b = true;
      count++;
    }
    if(str.indexOf("2") == -1){
      c = true;
      count++;
    }
    if(count == 2){
      if(a && b){
        return 2;
      }else if(a && c){
        return 1;
      }else{
        return 0;
      }
    }else{
      if(a){
        return 1;
      }else if(b){
        return 0;
      }else{
        return 2;
      }
    }
  }
  public static void main(String[] args) throws IOException{
    Scanner scan = new Scanner(System.in);
    int N = Integer.parseInt(scan.nextLine());

    for(int i = 0; i < N; i++){
      String str = scan.nextLine();
      int a = MEX(str);
      //System.out.println(MEX(str));
      int sum = 0;
      for(int j = 0; j < str.length(); j++){
        sum += MEX(str.substring(j, j + 1));
        //System.out.print(MEX(str.substring(j, j + 1)) + " ");
      }
      if(sum < a){
        System.out.println(sum);
      }else{
        System.out.println(a);
      }
    }
  }
}