CF1748D.ConstructOR

普及/提高-

通过率：0%

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题目描述

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.

输入格式

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 $d$ ( $1 \le a,b,d \lt 2^{30}$ ).

输出格式

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.

输入输出样例

输入#1

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

输出#1

18
14
-1
-1
0
11
25599
184470016815529983

说明/提示

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.

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