#P1554C. Mikasa
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ID: 6022
Type: RemoteJudge
1000ms
256MiB
Tried: 0
Accepted: 0
Difficulty: (None)
Uploaded By:
Hydro
Tags> Mikasa
No submission language available for this problem.
Description
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.
$\operatorname{MEX}$ 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.
Input
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 $m$ ($0 \le n, m \le 10^9$).
Output
For each test case, print a single integer — the answer to the problem.
Samples
5
3 5
4 6
3 2
69 696
123456 654321
4
3
0
640
530866
Note
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 $0$.