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] 
// Piyush Nagpal
import java.util.*;
import java.io.*;
 public class C{
     
    static int MOD=1000000007;
    static PrintWriter pw;
    static FastReader sc;
    
    static 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());}
        
        public char nextChar() throws IOException {return next().charAt(0);}
 
        String nextLine(){
            String str = "";
            try {
                str = br.readLine();
            }
            catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
        public int[] intArr(int a,int b,int n) throws IOException {int[]in=new int[n];for(int i=a;i<b;i++)in[i]=nextInt();return in;}
        public long[] longArr(int a,int b,int n) throws IOException {long[]in=new long[n];for(int i=a;i<b;i++)in[i]=nextLong();return in;}
        
    }   
 
 
     public static long gcd(long a,long b){if( b>a ){return gcd(b,a);}if( b==0 ){return a;} return gcd(b,a%b);}
     public static long expo( long a,long b,long M ){long result=1;while(b>0){if( b%2==1 ){result=(result*a)%M;}a=(a*a)%M;b=b/2;}return result%M;}
    public static ArrayList<Long> Sieve(int n){boolean [] arr= new boolean[n+1];Arrays.fill(arr, true);ArrayList<Long> list= new ArrayList<>();for(int i=2;i<=n;i++){if( arr[i]==true ){list.add((long)i);}for(int j=2*i;j<=n;j+=i){arr[j]=false;}}return list;}
 
    public static void printarr(int [] arr){for(int i=0;i<arr.length;i++){pw.print(arr[i]+" ");}}
    public static void printarr(long [] arr){for(int i=0;i<arr.length;i++){pw.print(arr[i]+" ");}}
    
    // int [] arr=sc.intArr(a,b,n);  <b
    static void solve() throws Exception{
        int n=sc.nextInt(),s=sc.nextInt();

        if( n%2==0 ){
            int x=n/2;
            x++;
            pw.println(s/x);
        }else{
            int x=(n+1)/2;
            // x++;
            pw.println(s/x);
        }

   }
   
   public static void main(String[] args) throws Exception{
        try {
            System.setIn(new FileInputStream("input.txt"));
            System.setOut(new PrintStream(new FileOutputStream("output.txt")));
        } catch (Exception e) {
            System.err.println("Error");
        }
        sc= new FastReader();
        pw = new PrintWriter(System.out);

        int tc=1;
        tc=sc.nextInt();
        for(int ii=1;ii<=tc;ii++) {
//            pw.printf("Case #%d: "b, i);
            solve();
        }
       
        pw.flush();
 
    
 
    }
 
}