MEXor Mixup

2000ms

262144K

Description:

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.

Input:

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.

Output:

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.

Sample Input:

Sample Output:

Note:

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.

Informação

Provedor Codeforces

Código CF1567B