#include <bits/stdc++.h>
using namespace std;
using ll = long long;
int main() {
  ll s, x;
  cin >> s >> x;
  if (s - x < 0) {
    cout << 0 << endl;
    return 0;
  }
  ll m = s - x;
  if (m & 1) {
    cout << 0 << endl;
    return 0;
  }
  m >>= 1;
  if ((x & m) != 0) {
    cout << 0 << endl;
    return 0;
  }
  const int cnt = __builtin_popcountll(x);
  if (m == 0) {
    cout << (1LL << cnt) - 2 << endl;
  } else {
    cout << (1LL << cnt) << endl;
  }
}

### Prompt

Develop a solution in cpp to the problem described below:

Two positive integers a and b have a sum of s and a bitwise XOR of x. How many possible values are there for the ordered pair (a, b)?

Input

The first line of the input contains two integers s and x (2 ≤ s ≤ 1012, 0 ≤ x ≤ 1012), the sum and bitwise xor of the pair of positive integers, respectively.

Output

Print a single integer, the number of solutions to the given conditions. If no solutions exist, print 0.

Examples

Input

9 5


Output

4


Input

3 3


Output

2


Input

5 2


Output

0

Note

In the first sample, we have the following solutions: (2, 7), (3, 6), (6, 3), (7, 2).

In the second sample, the only solutions are (1, 2) and (2, 1).

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
int main() {
  ll s, x;
  cin >> s >> x;
  if (s - x < 0) {
    cout << 0 << endl;
    return 0;
  }
  ll m = s - x;
  if (m & 1) {
    cout << 0 << endl;
    return 0;
  }
  m >>= 1;
  if ((x & m) != 0) {
    cout << 0 << endl;
    return 0;
  }
  const int cnt = __builtin_popcountll(x);
  if (m == 0) {
    cout << (1LL << cnt) - 2 << endl;
  } else {
    cout << (1LL << cnt) << endl;
  }
}

```