B. Candies Division
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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.

Input

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.

Output

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.

Example
Input
5
5 2
19 4
12 7
6 2
100000 50010

Output
5
18
10
6
75015

Note

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.