Description:
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, and $$$|y|$$$ is absolute value of $$$y$$$.
Input Format:
The first line contains a single integer $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of test cases.
Each test case contains integers $$$a$$$, $$$b$$$, $$$r$$$ ($$$0 \le a, b, r \le 10^{18}$$$).
Output Format:
For each test case, output a single number — the smallest possible value.
Note:
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 $$$x = 1$$$.