CF1566A 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] $