ConstructOR

Description:

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.

Sample Input:

8
12 39 5
6 8 14
100 200 200
3 4 6
2 2 2
18 27 3
420 666 69
987654321 123456789 999999999

Sample 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.