B. MEXor Mixuptime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputAlice 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.InputThe 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.OutputFor 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.ExampleInput
5
1 1
2 1
2 0
1 10000
2 10000
Output
3
2
3
2
3
NoteIn 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.
5
1 1
2 1
2 0
1 10000
2 10000

3 2 3 2 3 
['bitmasks', 'greedy', '*1000']