Codeforces Round 611 (Div. 3) |
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Finished |
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:
$$$\lfloor\frac{k}{2}\rfloor$$$ 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.
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.
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.
5 5 2 19 4 12 7 6 2 100000 50010
5 18 10 6 75015
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.
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