#include <bits/stdc++.h>
using namespace std;
int main() {
  long long s, x, dp[60][2], ans;
  int i, j, k, ost;
  cin >> s >> x;
  ans = 0;
  if (s == x) ans = -2;
  memset(dp, 0, sizeof(dp));
  dp[0][0] = 1;
  for (i = 1; i < 50; i++) {
    for (j = 0; j < 2; j++) {
      for (k = 0; k < 2; k++) {
        for (ost = 0; ost < 2; ost++) {
          if ((j ^ k) != (x % 2)) continue;
          if (((j + k + ost) % 2) != (s % 2)) continue;
          dp[i][(j + k + ost) / 2] += dp[i - 1][ost];
        }
      }
    }
    s /= 2;
    x /= 2;
  }
  ans += dp[49][0];
  cout << ans << endl;
  return 0;
}

### 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;
int main() {
  long long s, x, dp[60][2], ans;
  int i, j, k, ost;
  cin >> s >> x;
  ans = 0;
  if (s == x) ans = -2;
  memset(dp, 0, sizeof(dp));
  dp[0][0] = 1;
  for (i = 1; i < 50; i++) {
    for (j = 0; j < 2; j++) {
      for (k = 0; k < 2; k++) {
        for (ost = 0; ost < 2; ost++) {
          if ((j ^ k) != (x % 2)) continue;
          if (((j + k + ost) % 2) != (s % 2)) continue;
          dp[i][(j + k + ost) / 2] += dp[i - 1][ost];
        }
      }
    }
    s /= 2;
    x /= 2;
  }
  ans += dp[49][0];
  cout << ans << endl;
  return 0;
}

```