A14394. Mikasa

You are given two integers $n$ and $m$ . Find the $\operatorname{MEX}$ of the sequence $n \oplus 0, n \oplus 1, \ldots, n \oplus m$ . Here, $\oplus$ is the [bitwise XOR operator](https://en.wikipedia.org/wiki/Bitwise_operation#XOR).

$\operatorname{MEX}$ of the sequence of non-negative integers is the smallest non-negative integer that doesn't appear in this sequence. For example, $\operatorname{MEX}(0, 1, 2, 4) = 3$ , and $\operatorname{MEX}(1, 2021) = 0$ .

The first line contains a single integer $t$ ( $1 \le t \le 30\,000$ ) — the number of test cases.

The first and only line of each test case contains two integers $n$ and $m$ ( $0 \le n, m \le 10^9$ ).

For each test case, print a single integer — the answer to the problem.

In the first test case, the sequence is $3 \oplus 0, 3 \oplus 1, 3 \oplus 2, 3 \oplus 3, 3 \oplus 4, 3 \oplus 5$ , or $3, 2, 1, 0, 7, 6$ . The smallest non-negative integer which isn't present in the sequence i. e. the $\operatorname{MEX}$ of the sequence is $4$ .

In the second test case, the sequence is $4 \oplus 0, 4 \oplus 1, 4 \oplus 2, 4 \oplus 3, 4 \oplus 4, 4 \oplus 5, 4 \oplus 6$ , or $4, 5, 6, 7, 0, 1, 2$ . The smallest non-negative integer which isn't present in the sequence i. e. the $\operatorname{MEX}$ of the sequence is $3$ .

In the third test case, the sequence is $3 \oplus 0, 3 \oplus 1, 3 \oplus 2$ , or $3, 2, 1$ . The smallest non-negative integer which isn't present in the sequence i. e. the $\operatorname{MEX}$ of the sequence is $0$ .