Codeforces Round 833 (Div. 2) |
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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:
Here, $$$|$$$ denotes the bitwise OR operation.
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 $$$d$$$ ($$$1 \le a,b,d \lt 2^{30}$$$).
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.
812 39 56 8 14100 200 2003 4 62 2 218 27 3420 666 69987654321 123456789 999999999
18 14 -1 -1 0 11 25599 184470016815529983
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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