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] 
from collections import defaultdict
import math
 
# from functools import reduce
# from math import comb, gcd # n! / (k! * (n - k)!)
# from collections import defaultdict
# from sys import stdout
 
 
NO = 'NO'
YES = 'YES'
MOD = 1000000007
ALPH = 'abcdefghijklmnopqrstuvwxyz'
 
def input_int():
    return int(input())
 
def input_list():
    return input().split(' ')
 
def input_list_int():
    return list(map(int, input_list()))
 
def list_int_to_str(a, sep = ' '):
    return sep.join(str(x) for x in a) 
 
global_ans = []
def pr(a):
    global_ans.append(a)
 
def z_func(s):
    n = len(s)
    z = [0] * n
    l = r = 0
    for i in range(1, n):
        if r >= i:
            z[i] = min(z[i - l], r - i + 1)
        while z[i] + i < n and s[z[i]] == s[z[i] + i]:
            z[i] += 1
        if i + z[i] - 1 > r:
            l = i
            r = i + z[i] - 1
    return z
 
def is_prime(n):
    d = 2
    while n % d != 0:
        d += 1
    return d == n


def solve():
    n, s = input_list_int()
    t = math.ceil(n / 2) - 1
    # pr(v)
    ans = s  // (n - t)
    pr(max(0, ans))

query_count = 1
query_count = input_int()
 
 
while query_count:
    query_count -= 1
    solve()
 
for global_ans_line in global_ans:
    print(global_ans_line)
 
 