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

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

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 $x = 1$.