#include <bits/stdc++.h>
using namespace std;
template <typename T>
void print(T &xxx) {
  for (auto &it : xxx) cout << it << " ";
  cout << "\n";
}
long long computeXOR(long long n) {
  if (n % 4 == 0) return n;
  if (n % 4 == 1) return 1;
  if (n % 4 == 2) return n + 1;
  return 0;
}
void solve(long long tc) {
  long long a, b;
  cin >> a >> b;
  long long ans = a;
  long long xr = computeXOR(a - 1);
  if (xr == b) {
    cout << ans << "\n";
    return;
  }
  xr = xr ^ b;
  if (xr == a)
    ans += 2;
  else
    ans += 1;
  cout << ans << "\n";
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  long long t = 1;
  cin >> t;
  for (long long tc = 1; tc <= t; tc++) {
    solve(tc);
  }
  return 0;
}

### Prompt

Develop a solution in CPP to the problem described below:

Alice gave Bob two integers a and b (a > 0 and b ≥ 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](https://en.wikipedia.org/wiki/Bitwise_operation#XOR) of all the elements of the array.

Input

The input consists of multiple test cases. The first line contains an integer t (1 ≤ t ≤ 5 ⋅ 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 ≤ a ≤ 3 ⋅ 10^5; 0 ≤ b ≤ 3 ⋅ 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.

Example

Input


5
1 1
2 1
2 0
1 10000
2 10000


Output


3
2
3
2
3

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.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
template <typename T>
void print(T &xxx) {
  for (auto &it : xxx) cout << it << " ";
  cout << "\n";
}
long long computeXOR(long long n) {
  if (n % 4 == 0) return n;
  if (n % 4 == 1) return 1;
  if (n % 4 == 2) return n + 1;
  return 0;
}
void solve(long long tc) {
  long long a, b;
  cin >> a >> b;
  long long ans = a;
  long long xr = computeXOR(a - 1);
  if (xr == b) {
    cout << ans << "\n";
    return;
  }
  xr = xr ^ b;
  if (xr == a)
    ans += 2;
  else
    ans += 1;
  cout << ans << "\n";
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  long long t = 1;
  cin >> t;
  for (long long tc = 1; tc <= t; tc++) {
    solve(tc);
  }
  return 0;
}

```