XOR-distance

题面翻译

给定三个正整数 $a,b,r$，请你选择一个非负整数 $x\in[0,r]$，使 $| (a\oplus x)-(b\oplus x)|$ 最小。其中 $\oplus$ 为按位异或运算符，$|m|$ 表示 m 的绝对值。

多测，$a,b,r\le10^{18}$ 。

提示：c++ 中，请使用 (1ll<<k) 来计算一个大于 int 范围的位运算值。

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.

样例 #1

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

样例输出 #1

2
1
1
164
542
5
3
37102
27934920819538516
104449824168870225

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 $x = 1$ .