#include <bits/stdc++.h>
using namespace std;
int main() {
  long long x, y;
  cin >> x >> y;
  long long z = x - y;
  cout << (z < 0 || z & 1 || (z / 2) & y
               ? 0
               : (1ll << __builtin_popcountll(y)) - 2 * (x == y));
}

### 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() {
  long long x, y;
  cin >> x >> y;
  long long z = x - y;
  cout << (z < 0 || z & 1 || (z / 2) & y
               ? 0
               : (1ll << __builtin_popcountll(y)) - 2 * (x == y));
}

```