A14545. 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.

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.

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 $[1, \underline{2}, 2]$