#include <bits/stdc++.h>
using namespace std;
struct H {
  long long x, y;
};
long long m, n, v, t, x;
H w[30];
int C(H a, H b) { return a.x < b.x; }
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  for (cin >> t; t--;) {
    cin >> n >> m;
    v = x = 0;
    for (int p = 1 << 29; p; p >>= 1) {
      if (x + (p - 1) <= m) {
        w[v++] = {(n ^ x) & ~(p - 1), (n ^ x) | (p - 1)};
        x |= p;
      }
    }
    sort(w, w + v, C);
    w[v].x = 1 << 30;
    x = -1;
    for (int i = 0; i <= v; i++) {
      if (x + 1 != w[i].x) break;
      x = w[i].y;
    }
    cout << x + 1 << '\n';
  }
}

### Prompt

Generate a cpp solution to the following problem:

You are given two integers n and m. Find the \operatorname{MEX} of the sequence n ⊕ 0, n ⊕ 1, …, n ⊕ m. Here, ⊕ 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. 

Input

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

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

Output

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

Example

Input


5
3 5
4 6
3 2
69 696
123456 654321


Output


4
3
0
640
530866

Note

In the first test case, the sequence is 3 ⊕ 0, 3 ⊕ 1, 3 ⊕ 2, 3 ⊕ 3, 3 ⊕ 4, 3 ⊕ 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 ⊕ 0, 4 ⊕ 1, 4 ⊕ 2, 4 ⊕ 3, 4 ⊕ 4, 4 ⊕ 5, 4 ⊕ 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 ⊕ 0, 3 ⊕ 1, 3 ⊕ 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.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
struct H {
  long long x, y;
};
long long m, n, v, t, x;
H w[30];
int C(H a, H b) { return a.x < b.x; }
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  for (cin >> t; t--;) {
    cin >> n >> m;
    v = x = 0;
    for (int p = 1 << 29; p; p >>= 1) {
      if (x + (p - 1) <= m) {
        w[v++] = {(n ^ x) & ~(p - 1), (n ^ x) | (p - 1)};
        x |= p;
      }
    }
    sort(w, w + v, C);
    w[v].x = 1 << 30;
    x = -1;
    for (int i = 0; i <= v; i++) {
      if (x + 1 != w[i].x) break;
      x = w[i].y;
    }
    cout << x + 1 << '\n';
  }
}

```