CF1918C.XOR-distance

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题目描述

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 $y$ .

输入格式

The first line contains a single integer $t$ ( $1 \le t \le 10^4$ ) — the number of test cases.

Each test case contains integers $a$ , $b$ , $r$ ( $0 \le a, b, r \le 10^{18}$ ).

输出格式

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

输入输出样例

输入#1

10
4 6 0
0 3 2
9 6 10
92 256 23
165 839 201
1 14 5
2 7 2
96549 34359 13851
853686404475946 283666553522252166 127929199446003072
735268590557942972 916721749674600979 895150420120690183

输出#1

2
1
1
164
542
5
3
37102
27934920819538516
104449824168870225

说明/提示

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 $x = 1$ .

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