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] 
#include <bits/stdc++.h>
using namespace std;
long long r[1234567], q[1234567], qr[1002][1002], rq[1002][1002];
long long rr[1002][1002], qq[1002][1002];
int main() {
  long long a, b = 0, c = 0, d = 1, e = 1, f = 123456789, g = 0, h = 1;
  long long i[1234567], j[1234567], k = 1, l = 0;
  long long t = 0, z, x = 1, y, w, v = 0, u = 1234, gcd, lcm, mod = 1e9 + 7;
  char gg, ff, kk;
  string m[1234567], n = "", o, s, ss, nn = "", oo, mm[1234567];
  map<long long, long long> aa;
  cin >> a;
  for (b = 1; b <= a; b++) {
    cin >> c >> d;
    g = c / 2;
    if (c % 2 == 0) {
      g--;
    }
    c -= g;
    d -= g % 2;
    cout << d / c << endl;
  }
}
