Given three integers $l$, $r$, and $G$, find two integers $A$ and $B$ ($l \le A \le B \le r$) such that their greatest common divisor (GCD) equals $G$ and the distance $|A - B|$ is maximized.

If there are multiple such pairs, choose the one where $A$ is minimized. If no such pairs exist, output "-1 -1".

Input

The first line contains a single integer $t$ ($1 \le t \le 10^3$) — the number of test cases. Then, $t$ test cases follow.

Each test case consists of a single line containing three integers $l, r, G$ ($1 \le l \le r \le 10^{18}$; $1 \le G \le 10^{18}$) — the range boundaries and the required GCD.

Output

For each test case, output two integers $A$ and $B$ — the solution to the problem, or "-1 -1" if no such pair exists.

见题面 Input 部分

见题面 Output 部分