A13079 | Candies Division

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.

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.