Median Maximization
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 $$$\lceil {\frac{m}{2}} \rceil$$$-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 $$$\lceil \frac{m}{2} \rceil$$$-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.
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 $$$[1, \underline{2}, 2]$$$ 
The input consists of multiple test cases. The first line contains a single integer $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of test cases. Description of the test cases follows.Each test case contains a single line with two integers $$$n$$$ and $$$s$$$ ($$$1 \le n, s \le 10^9$$$) — the length of the array and the required sum of the elements.
For each test case print a single integer — the maximum possible median.
for s in [*open(0)][1:]:
    (n, s) = map(int, s.split())
    print(s // (n // 2 + 1))
def x():
    (n, s) = map(int, input().split())
    x = n + 1 - (n + 1) // 2
    return str(s // x)
t = int(input())
a = []
for _ in range(t):
    a.append(x())
print('\n'.join(a))
def i():
    (n, m) = map(int, input().split())
    c = n - (n + 1) // 2 + 1
    return str(m // c)
t = int(input())
a = []
for _ in range(t):
    a.append(i())
print('\n'.join(a))