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.BufferedReader;

import java.io.IOException;
import java.io.InputStreamReader;
import java.util.*;


public class Solve {
	static FastReader in=new FastReader();
    static final Random random=new Random();
    static long mod=1000000007L;
    static HashMap<Integer,Integer>map=new HashMap<>();
    static void ruffleSort(long[] a) {
        int n=a.length;
        for (int i=0; i<n; i++) {
            int oi=random.nextInt();
			long temp=a[oi];
            a[oi]=a[i]; a[i]=temp;
        }
        Arrays.sort(a);
    }
    public static int upper_bound(ArrayList<Integer> arr, int ele) {
    	int si = 0;
    	int ei = arr.size()-1;
    	int ans = -1;
    	while(si<=ei) {
    		int mid = (si + ei)/2;
    		if(arr.get(mid)<ele) {
    			si = mid +1;
    		}else {
    			ans = mid;
    			ei = mid -1;
    			
    		}
    	}
    	return ans;
    	
    }
    public static int lower_bound(ArrayList<Integer> arr, int ele) {
    	int si = 0;
    	int ei = arr.size()-1;
    	int ans = -1;
    	while(si<=ei) {
    		int mid = (si + ei)/2;
    		if(arr.get(mid)<=ele) {
    			ans = mid;
    			si = mid +1;
    		}
    		
    		else {
    			ei = mid -1;
    			
    			
    		}
    	}
    	return ans;
    	
    }
    
    
    
    
	
	public static void main(String[]args) {
FastReader res = new FastReader();
		
		int t = res.nextInt();
		
		
		while(t>0) {
			int n = res.nextInt();
			int s = res.nextInt();
			int si = 0;
			int ei = s;
			int ans = 0;
			while(si<=ei) {
				int mid = (si +ei)/2;
				int x = s - mid;
				int pos = 0;
				if(n%2==0) {
					pos = n - n/2;
				}else {
					pos = n - (n/2 +1);
				}
				if(pos*mid<=x) {
					ans = mid;
					si = mid +1;
				}else {
					ei = mid -1;
				}
				
			}
			System.out.println(ans);
			
			
			
        		
        	
        	
        	
        	
        	
        	
        	

			
			t--;
			
			
			
			
			
			
	        
			
			
			
		}
	}
	static int max(int a, int b)
    {
        if(a<b)
        	return b;
        return a;
    }
 
 
    static void ruffleSort(int[] a) {
        int n=a.length;
        for (int i=0; i<n; i++) {
            int oi=random.nextInt(n), temp=a[oi];
            a[oi]=a[i]; a[i]=temp;
        }
        Arrays.sort(a);
    }
 
    static < E > void print(E res)
    {
        System.out.println(res);
    }
 
 
    static  int gcd(int a,int b)
    {
        if(b==0)
        {
            return a;
        }
        return gcd(b,a%b);
    }
 
    static int lcm(int a, int b)
    {
        return (a / gcd(a, b)) * b;
    }
 
 
    static int abs(int a)
    {
        if(a<0)
            return -1*a;
        return a;
    }
	 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());
	        }
	        String nextLine()
	        {
	            String str = "";
	            try
	            {
	                str = br.readLine();
	            }
	            catch (IOException e)
	            {
	                e.printStackTrace();
	            }
	            return str;
	        }
	 
	        int [] readintarray(int n) {
	            int res [] = new int [n];
	            for(int i = 0; i<n; i++)res[i] = nextInt();
	            return res;
	        }
	        long [] readlongarray(int n) {
	            long res [] = new long [n];
	            for(int i = 0; i<n; i++)res[i] = nextLong();
	            return res;
	        }
	    }
	 
	}
class pair{
	int x;
	int y;
}
