#include <bits/stdc++.h>
using namespace std;
#pragma GCC diagnostic ignored "-Wunused-result"
#pragma GCC diagnostic ignored "-Wmissing-declarations"
long long get_ans(long long s, long long x) {
  if (s == 0 && x == 0) return 1;
  int bx = x % 2;
  int bs = s % 2;
  long long ans = 0;
  if (bx) {
    if (bs) ans += 2 * get_ans(s / 2, x / 2);
  } else {
    if (!bs) {
      if (s >= 2) ans += get_ans(s / 2 - 1, x / 2);
      ans += get_ans(s / 2, x / 2);
    }
  }
  return ans;
}
int main() {
  ios_base::sync_with_stdio(false);
  long long s, x;
  cin >> s >> x;
  long long t = s == x ? 2 : 0;
  cout << max(0LL, get_ans(s, x) - t) << endl;
}

### 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;
#pragma GCC diagnostic ignored "-Wunused-result"
#pragma GCC diagnostic ignored "-Wmissing-declarations"
long long get_ans(long long s, long long x) {
  if (s == 0 && x == 0) return 1;
  int bx = x % 2;
  int bs = s % 2;
  long long ans = 0;
  if (bx) {
    if (bs) ans += 2 * get_ans(s / 2, x / 2);
  } else {
    if (!bs) {
      if (s >= 2) ans += get_ans(s / 2 - 1, x / 2);
      ans += get_ans(s / 2, x / 2);
    }
  }
  return ans;
}
int main() {
  ios_base::sync_with_stdio(false);
  long long s, x;
  cin >> s >> x;
  long long t = s == x ? 2 : 0;
  cout << max(0LL, get_ans(s, x) - t) << endl;
}

```