D. ConstructOR
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

You are given three integers $a$, $b$, and $d$. Your task is to find any integer $x$ which satisfies all of the following conditions, or determine that no such integers exist:

• $0 \le x \lt 2^{60}$;
• $a|x$ is divisible by $d$;
• $b|x$ is divisible by $d$.

Here, $|$ denotes the bitwise OR operation.

Input

Each test contains multiple test cases. The first line of input contains one integer $t$ ($1 \le t \le 10^4$) — the number of test cases.

Each test case consists of one line, containing three integers $a$, $b$, and $d$ ($1 \le a,b,d \lt 2^{30}$).

Output

For each test case print one integer. If there exists an integer $x$ which satisfies all of the conditions from the statement, print $x$. Otherwise, print $-1$.

If there are multiple solutions, you may print any of them.

Example
Input
812 39 56 8 14100 200 2003 4 62 2 218 27 3420 666 69987654321 123456789 999999999
Output
18
14
-1
-1
0
11
25599
184470016815529983
Note

In the first test case, $x=18$ is one of the possible solutions, since $39|18=55$ and $12|18=30$, both of which are multiples of $d=5$.

In the second test case, $x=14$ is one of the possible solutions, since $8|14=6|14=14$, which is a multiple of $d=14$.

In the third and fourth test cases, we can show that there are no solutions.