CF2020C Bitwise Balancing

You are given three non-negative integers $ b $ , $ c $ , and $ d $ . Please find a non-negative integer $ a \in [0, 2^{61}] $ such that $ (a\, |\, b)-(a\, \&\, c)=d $ , where $ | $ and $ \& $ denote the [bitwise OR operation](https://en.wikipedia.org/wiki/Bitwise_operation#OR) and the [bitwise AND operation](https://en.wikipedia.org/wiki/Bitwise_operation#AND), respectively. If such an $ a $ exists, print its value. If there is no solution, print a single integer $ -1 $ . If there are multiple solutions, print any of them.

Each test contains multiple test cases. The first line contains the number of test cases $ t $ ( $ 1 \le t \le 10^5 $ ). The description of the test cases follows. The only line of each test case contains three positive integers $ b $ , $ c $ , and $ d $ ( $ 0 \le b, c, d \le 10^{18} $ ).

For each test case, output the value of $ a $ , or $ -1 $ if there is no solution. Please note that $ a $ must be non-negative and cannot exceed $ 2^{61} $ .

In the first test case, $ (0\,|\,2)-(0\,\&\,2)=2-0=2 $ . So, $ a = 0 $ is a correct answer. In the second test case, no value of $ a $ satisfies the equation. In the third test case, $ (12\,|\,10)-(12\,\&\,2)=14-0=14 $ . So, $ a = 12 $ is a correct answer.