Candies Division

题意翻译

## 题目描述 求最大的$ans$，使得$ans\le n$且$ans\equiv r(mod\ k),r\le\lfloor\dfrac{k}{2}\rfloor$。 ## 输入格式 第1行输入1个整数$t(1\le t\le 5·10^4)$，为测试数据组数。 接下来$t$行，每行输入2个整数$n$和$k(1\le n,k\le 10^9)$。 ## 输出格式 $t$行，第$i$行输出第$i$个测试数据的$ans$。

题目描述

Santa has $ n $ candies and he wants to gift them to $ k $ kids. He wants to divide as many candies as possible between all $ k $ kids. Santa can't divide one candy into parts but he is allowed to not use some candies at all. Suppose the kid who recieves the minimum number of candies has $ a $ candies and the kid who recieves the maximum number of candies has $ b $ candies. Then Santa will be satisfied, if the both conditions are met at the same time: - $ b - a \le 1 $ (it means $ b = a $ or $ b = a + 1 $ ); - the number of kids who has $ a+1 $ candies (note that $ a+1 $ not necessarily equals $ b $ ) does not exceed $ \lfloor\frac{k}{2}\rfloor $ (less than or equal to $ \lfloor\frac{k}{2}\rfloor $ ). $ \lfloor\frac{k}{2}\rfloor $ is $ k $ divided by $ 2 $ and rounded down to the nearest integer. For example, if $ k=5 $ then $ \lfloor\frac{k}{2}\rfloor=\lfloor\frac{5}{2}\rfloor=2 $ . Your task is to find the maximum number of candies Santa can give to kids so that he will be satisfied. You have to answer $ t $ independent test cases.

输入输出格式

输入格式

The first line of the input contains one integer $ t $ ( $ 1 \le t \le 5 \cdot 10^4 $ ) — the number of test cases. The next $ t $ lines describe test cases. The $ i $ -th test case contains two integers $ n $ and $ k $ ( $ 1 \le n, k \le 10^9 $ ) — the number of candies and the number of kids.

输出格式

For each test case print the answer on it — the maximum number of candies Santa can give to kids so that he will be satisfied.

输入输出样例

输入样例 #1

5
5 2
19 4
12 7
6 2
100000 50010

输出样例 #1

5
18
10
6
75015

说明

In the first test case, Santa can give $ 3 $ and $ 2 $ candies to kids. There $ a=2, b=3,a+1=3 $ . In the second test case, Santa can give $ 5, 5, 4 $ and $ 4 $ candies. There $ a=4,b=5,a+1=5 $ . The answer cannot be greater because then the number of kids with $ 5 $ candies will be $ 3 $ . In the third test case, Santa can distribute candies in the following way: $ [1, 2, 2, 1, 1, 2, 1] $ . There $ a=1,b=2,a+1=2 $ . He cannot distribute two remaining candies in a way to be satisfied. In the fourth test case, Santa can distribute candies in the following way: $ [3, 3] $ . There $ a=3, b=3, a+1=4 $ . Santa distributed all $ 6 $ candies.