CF1567B.MEXor Mixup

普及/提高-

通过率：0%

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题目描述

Alice gave Bob two integers $a$ and $b$ ( $a > 0$ and $b \ge 0$ ). Being a curious boy, Bob wrote down an array of non-negative integers with $\operatorname{MEX}$ value of all elements equal to $a$ and $\operatorname{XOR}$ value of all elements equal to $b$ .

What is the shortest possible length of the array Bob wrote?

Recall that the $\operatorname{MEX}$ (Minimum EXcluded) of an array is the minimum non-negative integer that does not belong to the array and the $\operatorname{XOR}$ of an array is the bitwise XOR of all the elements of the array.

输入格式

The input consists of multiple test cases. The first line contains an integer $t$ ( $1 \leq t \leq 5 \cdot 10^4$ ) — the number of test cases. The description of the test cases follows.

The only line of each test case contains two integers $a$ and $b$ ( $1 \leq a \leq 3 \cdot 10^5$ ; $0 \leq b \leq 3 \cdot 10^5$ ) — the $\operatorname{MEX}$ and $\operatorname{XOR}$ of the array, respectively.

输出格式

For each test case, output one (positive) integer — the length of the shortest array with $\operatorname{MEX}$ $a$ and $\operatorname{XOR}$ $b$ . We can show that such an array always exists.

输入输出样例

输入#1
```
5
1 1
2 1
2 0
1 10000
2 10000
```
输出#1
```
3
2
3
2
3
```

说明/提示

In the first test case, one of the shortest arrays with $\operatorname{MEX}$ $1$ and $\operatorname{XOR}$ $1$ is $[0, 2020, 2021]$ .

In the second test case, one of the shortest arrays with $\operatorname{MEX}$ $2$ and $\operatorname{XOR}$ $1$ is $[0, 1]$ .

It can be shown that these arrays are the shortest arrays possible.

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