#include <bits/stdc++.h>
using namespace std;
const double PI = acos(-1.0);
const double eps = 1e-10;
const int oo = 1e9;
int check(long long s, long long x) {
  long long i, j, kl = 0;
  for (i = 1; i < s; ++i) {
    j = s - i;
    if ((i ^ j) == x) ++kl;
  }
  return kl;
}
long long solve(long long s, long long x) {
  long long p, kl, ans;
  p = s - x;
  if ((p < 0) || (p & 1) || ((p >> 1) & x)) return 0;
  kl = 0;
  while (x) {
    if (x & 1) ++kl;
    x >>= 1;
  }
  ans = (1LL << kl);
  if (p == 0) ans -= 2;
  return ans;
}
int main() {
  if (0) {
    freopen("input.txt", "w", stdout);
    srand(time(NULL));
    return 0;
  }
  long long s, x;
  cin >> s >> x;
  cout << solve(s, x) << endl;
  return 0;
}

### Prompt

Generate 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;
const double PI = acos(-1.0);
const double eps = 1e-10;
const int oo = 1e9;
int check(long long s, long long x) {
  long long i, j, kl = 0;
  for (i = 1; i < s; ++i) {
    j = s - i;
    if ((i ^ j) == x) ++kl;
  }
  return kl;
}
long long solve(long long s, long long x) {
  long long p, kl, ans;
  p = s - x;
  if ((p < 0) || (p & 1) || ((p >> 1) & x)) return 0;
  kl = 0;
  while (x) {
    if (x & 1) ++kl;
    x >>= 1;
  }
  ans = (1LL << kl);
  if (p == 0) ans -= 2;
  return ans;
}
int main() {
  if (0) {
    freopen("input.txt", "w", stdout);
    srand(time(NULL));
    return 0;
  }
  long long s, x;
  cin >> s >> x;
  cout << solve(s, x) << endl;
  return 0;
}

```