#include <bits/stdc++.h>
using namespace std;
int main(int argc, char *argv[]) {
  long long s, x;
  long long ans = 1;
  cin >> s >> x;
  int rem = 0;
  for (int d = (50); d >= (0); d--) {
    bool S = (s & (1LL << d));
    bool X = (x & (1LL << d));
    if (!S && !X)
      rem = 0;
    else if (S && X) {
      if (rem) ans = 0;
      ans *= 2;
      rem = 0;
    } else if (S && !X)
      rem = 1;
    else {
      if (!rem) ans = 0;
      ans *= 2;
      rem = 1;
    }
  }
  if (s == x) ans -= 2;
  if (rem) ans = 0;
  cout << ans << endl;
  return 0;
}

### Prompt

Please provide a Cpp coded solution 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;
int main(int argc, char *argv[]) {
  long long s, x;
  long long ans = 1;
  cin >> s >> x;
  int rem = 0;
  for (int d = (50); d >= (0); d--) {
    bool S = (s & (1LL << d));
    bool X = (x & (1LL << d));
    if (!S && !X)
      rem = 0;
    else if (S && X) {
      if (rem) ans = 0;
      ans *= 2;
      rem = 0;
    } else if (S && !X)
      rem = 1;
    else {
      if (!rem) ans = 0;
      ans *= 2;
      rem = 1;
    }
  }
  if (s == x) ans -= 2;
  if (rem) ans = 0;
  cout << ans << endl;
  return 0;
}

```