#include <bits/stdc++.h>
using namespace std;
long long h(long long s, long long x) {
  if (s == 1) {
    if (x == 1) return 2;
  }
  if (s == 0) {
    if (x == 0) return 1;
    return 0;
  }
  if (s % 2 == 1) {
    if (x % 2 == 0)
      return 0;
    else {
      return 2 * h(s / 2, x / 2);
    }
  } else {
    if (x % 2 == 1)
      return 0;
    else {
      return h(s / 2, x / 2) + h((s - 2) / 2, x / 2);
    }
  }
}
int main() {
  long long x, s;
  cin >> s >> x;
  long long ok = 0;
  if (s == x) {
    ok = 2;
  }
  cout << h(s, x) - ok;
}

### Prompt

Your task is to create 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 h(long long s, long long x) {
  if (s == 1) {
    if (x == 1) return 2;
  }
  if (s == 0) {
    if (x == 0) return 1;
    return 0;
  }
  if (s % 2 == 1) {
    if (x % 2 == 0)
      return 0;
    else {
      return 2 * h(s / 2, x / 2);
    }
  } else {
    if (x % 2 == 1)
      return 0;
    else {
      return h(s / 2, x / 2) + h((s - 2) / 2, x / 2);
    }
  }
}
int main() {
  long long x, s;
  cin >> s >> x;
  long long ok = 0;
  if (s == x) {
    ok = 2;
  }
  cout << h(s, x) - ok;
}

```