AT_arc208_c [ARC208C] Mod of XOR

You are given positive integers $ C $ and $ X $ that are less than $ 2^{30} $ . Determine whether there exists a positive integer $ n $ that satisfies all of the following conditions, and if it exists, find one such $ n $ . - $ 1\le n < 2^{60} $ - $ (n \oplus C) \bmod n=X $ Here, $ n \oplus C $ denotes the bitwise $ \mathrm{XOR} $ of $ n $ and $ C $ . You are given $ T $ test cases, solve each of them. What is bitwise $ \mathrm{XOR} $ ? The bitwise $ \mathrm{XOR} $ of non-negative integers $ X $ and $ Y $ , $ X \oplus Y $ , is defined as follows: - When $ X \oplus Y $ is written in binary, the digit in the $ 2^k $ place ( $ k \geq 0 $ ) is $ 1 $ if exactly one of the digits in the $ 2^k $ place of $ X $ and $ Y $ written in binary is $ 1 $ , and $ 0 $ otherwise. For example, $ 3 \oplus 5 = 6 $ (in binary: $ 011 \oplus 101 = 110 $ ).

The input is given from Standard Input in the following format: > $ T $ $ \text{case}_1 $ $ \text{case}_2 $ $ \vdots $ $ \text{case}_T $ Each test case is given in the following format: > $ C $ $ X $

Output the answers for each test case in order, separated by newlines. For each test case, if there does not exist an $ n $ that satisfies all conditions, print `-1`. Otherwise, print $ n $ that satisfies all conditions. If there are multiple $ n $ that satisfy all conditions, any of them will be accepted.

### Sample Explanation 1 Consider the first test case. $ n=7 $ satisfies all conditions because $ (n\oplus C) \bmod n = (7 \oplus 10) \bmod 7 = 13\bmod 7 = 6=X $ . Therefore, printing $ 7 $ on the first line will be accepted. Other than this, printing $ n=12,18,19 $ etc. will also be accepted. ### Constraints - $ 1\le T\le 2\times 10^5 $ - $ 1\le C,X < 2^{30} $ - All input values are integers.