#include <bits/stdc++.h>
using namespace std;
long long int table[64][2];
int main() {
  long long int s, x;
  cin >> s >> x;
  int l = 0;
  while ((1ll << l) <= s || (1ll << l) <= x) l++;
  table[l][0] = 1;
  for (int i = l - 1; i >= 0; i--)
    for (int c = 0; c < 2; c++)
      for (int j = 0; j < 2; j++)
        for (int k = 0; k < 2; k++)
          if ((c + j + k) % 2 == ((s >> i) & 1) && (j ^ k) == ((x >> i) & 1))
            table[i][c] += table[i + 1][(c + j + k) / 2];
  cout << table[0][0] - (s == x) * 2 << '\n';
}

### Prompt

Please formulate a CPP solution to the following problem:

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;
long long int table[64][2];
int main() {
  long long int s, x;
  cin >> s >> x;
  int l = 0;
  while ((1ll << l) <= s || (1ll << l) <= x) l++;
  table[l][0] = 1;
  for (int i = l - 1; i >= 0; i--)
    for (int c = 0; c < 2; c++)
      for (int j = 0; j < 2; j++)
        for (int k = 0; k < 2; k++)
          if ((c + j + k) % 2 == ((s >> i) & 1) && (j ^ k) == ((x >> i) & 1))
            table[i][c] += table[i + 1][(c + j + k) / 2];
  cout << table[0][0] - (s == x) * 2 << '\n';
}

```