A14535. MEXor Mixup

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 $\operatorname{MEX}$ (<a>Minimum EXcluded</a>) 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](https://en.wikipedia.org/wiki/Bitwise_operation#XOR) of all the elements of the array.

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.

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.

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.