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 Aqueous {
		
		static MyScanner sc = new MyScanner();
		
		static class pair{

			
			long num;
			int ind;
			
				public pair(long num, int ind) {
					this.num = num;
					this.ind = ind;
				}
		}
		
		
		public static void main(String[] args) {
	
			
			int t = sc.nextInt();
			
				while(t-->0) {
					
					long n = sc.nextLong();
					long s = sc.nextLong();
					
					if(s<n) {
						
						if(s>((n+1)/2)) {
							System.out.println(1);
						}
						else {
							System.out.println(0);
						}
					}
					else if(s==n) {
						System.out.println(1);
					}
					else {
						
						if(n%2==0) {
							
							long temp = n/2;
							temp++;
							
							System.out.println(s/temp);
						}
						else {
							
							long temp = n/2;
							temp++;
							System.out.println(s/temp);
						}
					}
				}
		}
		 		
		static void ruffleSort(int a[]) {

	          int n = a.length;

	          Random r = new Random();

	          for (int i = 0; i < n; i++) {

	              int oi = r.nextInt(n);
	              int temp = a[oi];
	              a[oi] = a[i];
	              a[i] = temp;
	          }

	          Arrays.sort(a);
	      }
		
		
		static void ruffleSort(long a[]) {

	          int n = a.length;

	          Random r = new Random();

	          for (int i = 0; i < n; i++) {
	              int oi = r.nextInt(n);

	              long temp = a[oi];
	              a[oi] = a[i];
	              a[i] = temp;
	          }

	          Arrays.sort(a);
	      }

		
		
	    public static 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;
	        }

	    }
	}
