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.*;
import java.lang.*;

public class Main {
    //input
    static out op = new out();
    static inp ip = new inp();
    static FastReader sc = new FastReader();
    static BufferedWriter output = new BufferedWriter( 
        new OutputStreamWriter(System.out));
    static long inf = (long)1e9+7;
   
   static long mod = (long)1e18+7;
   static long z = 0;

   static void sol() throws Exception{
      int n = ip.in();
        int s = ip.in();
        if(n == 1){
           op.sbln(s);
           return;
        }
        if(s%n == 0)op.sbln(s/(n/2));
        else op.sbln(s/(n/2 + 1));
   }
   
   
   static long gcd(long a,long b){
     if(b==0)
     return a;
     return gcd(b,a%b);
   }
   
   public static void main(String[] args) throws Exception { 
       
      int t = ip.in();
      while(t-- > 0){
         sol();
      }
      op.output.flush();
    }
   //  static class Node implements Comparable<Node>{
   //     int data;
   //     int ind;
   //    //  Node left,right;
   //    //  Node(){
   //    //       left = null;
   //    //       right = null;
   //    //  }
   //     Node(int ind,int data){
   //          this.data = data;
   //          this.ind = ind;
   //     }
    
   //       @Override
   //       public int compareTo(Node o) {
   //           if(this.data == o.data)
   //           return this.ind - o.ind;
   //           // TODO Auto-generated method stub
   //           return this.data - o.data;
   //       }
   //  }
}


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; 
    }

}
class inp{
    FastReader sc = new FastReader();
    int in(){
        int a = sc.nextInt();
        return a;
    }
    long lin(){
        long a = sc.nextLong();
        return a;
    }
    char cin(){
        char c = sc.next().charAt(0);
        return c;
    }
    char[] cain(){
        char[] a = sc.nextLine().toCharArray();
        return a;
    }
    int[] arrin(int n){
        int [] arr = new int[n];
        for(int i=0;i<n;i++)
            arr[i] = in();

        return arr;
    }
    int[] mm_arr(int[] arr){
        int max = Integer.MIN_VALUE;
        int min = Integer.MAX_VALUE;
        for(int i=0;i<arr.length;i++){
            max = Math.max(max,arr[i]);
            min = Math.min(min,arr[i]);
        }
        int ans[] = {max,min};
        return ans;
    }
    int[] srt(int[] arr){
        Arrays.sort(arr);
        return arr;
    }
    long pow(long a,long b){
        if(b == 0)return 1;
        long res = pow(a,b/2);
        //System.out.println(res + " " + b + " " + (b&1));
        if((b&1) == 0)return res*res;
        return a*res*res; 
    }

   //  boolean[] prime(){
   //     boolean prime[] = new boolean[100000001];
   //     Arrays.fill(prime,true);
   //     for (int p = 2; p * p <= 10000000; p++)
   //     {
   //          // If prime[p] is not changed,
   //          // then it is a prime
   //          if (prime[p] == true)
   //          {
   //              // Update all multiples
   //              // of p greater than or
   //              // equal to the square of it
   //              // numbers which are multiple
   //              // of p and are less than p^2
   //              // are already been marked.
   //              for (int i = p * p; i <= 10000000; i += p)
   //                 prime[i] = false;
   //          }
   //     }
   //     return prime;
   //  }
}
class out{
    BufferedWriter output = new BufferedWriter( 
        new OutputStreamWriter(System.out)); 

    void sb(String s) throws IOException {
        output.write(s);
    }
    void sbln(Object s) throws IOException {
        output.write(s+"\n");
    }
    void yes() throws IOException{
        output.write("YES\n");
    }
    void no() throws IOException{
        output.write("NO\n");
    }
}