Median Maximization

题意翻译

已知有一个长度为 $n$ 的数列，其所有元素的和为 $s$。请求出这个数列的中位数的最大值。 此处，我们定义中位数为该数列中第 $\lceil\frac n2\rceil$ 大的数，其中 $\lceil x\rceil$ 表示对 $x$ 向上取整，例如 $\lceil 1.5\rceil=2$。 数据范围： - $t$ 组数据，$1\leqslant t\leqslant 10^4$。 - $1\leqslant n,s\leqslant 10^9$。 Translated by Eason_AC 2021.9.14

题目描述

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.

输入输出格式

输入格式

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.

输出格式

For each test case print a single integer — the maximum possible median.

输入输出样例

输入样例 #1

8
1 5
2 5
3 5
2 1
7 17
4 14
1 1000000000
1000000000 1

输出样例 #1

5
2
2
0
4
4
1000000000
0

说明

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] $