CF1918C XOR-distance

You are given integers $ a $ , $ b $ , $ r $ . Find the smallest value of $ |({a \oplus x}) - ({b \oplus x})| $ among all $ 0 \leq x \leq r $ . $ \oplus $ is the operation of [bitwise XOR](https://en.wikipedia.org/wiki/Bitwise_operation#XOR), and $ |y| $ is [absolute value](https://en.wikipedia.org/wiki/Absolute_value) of $ y $ .

The first line contains a single integer $ t $ ( $ 1 \le t \le 10^4 $ ) — the number of test cases. Each test case contains integers $ a $ , $ b $ , $ r $ ( $ 0 \le a, b, r \le 10^{18} $ ).

For each test case, output a single number — the smallest possible value.

In the first test, when $ r = 0 $ , then $ x $ is definitely equal to $ 0 $ , so the answer is $ |{4 \oplus 0} - {6 \oplus 0}| = |4 - 6| = 2 $ . In the second test: - When $ x = 0 $ , $ |{0 \oplus 0} - {3 \oplus 0}| = |0 - 3| = 3 $ . - When $ x = 1 $ , $ |{0 \oplus 1} - {3 \oplus 1}| = |1 - 2| = 1 $ . - When $ x = 2 $ , $ |{0 \oplus 2} - {3 \oplus 2}| = |2 - 1| = 1 $ . Therefore, the answer is $ 1 $ . In the third test, the minimum is achieved when $ x = 1 $ .