#include <bits/stdc++.h>
using namespace std;
long long a, b, sol;
int main() {
  sol = 1;
  scanf("%lld%lld", &a, &b);
  sol *= ((1LL) << __builtin_popcountll(b));
  if (((a - b) & 1) || (((a - b) >> 1) & b)) {
    puts("0");
    return 0;
  }
  if (a == b) sol -= 2;
  if (!(a & 1) && !b) {
    puts("1");
    return 0;
  }
  cout << sol;
  return 0;
}

### Prompt

In cpp, your task is to solve 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 a, b, sol;
int main() {
  sol = 1;
  scanf("%lld%lld", &a, &b);
  sol *= ((1LL) << __builtin_popcountll(b));
  if (((a - b) & 1) || (((a - b) >> 1) & b)) {
    puts("0");
    return 0;
  }
  if (a == b) sol -= 2;
  if (!(a & 1) && !b) {
    puts("1");
    return 0;
  }
  cout << sol;
  return 0;
}

```