#include <bits/stdc++.h>
using namespace std;
const long long inf = 0x3f3f3f3f3f3f3f3fLL;
const long long N = 3e5 + 10;
const long long MOD = 1e9 + 7;
int32_t main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  long long s, x;
  cin >> s >> x;
  long long d = (s - x) / 2;
  if (d < 0 || x + 2 * d != s || (x & d) != 0) {
    cout << 0 << '\n';
    return 0;
  }
  long long f = 0;
  if (d == 0) f = 1;
  s -= d * 2;
  long long c = __builtin_popcountll(s);
  long long ans = (1LL << c);
  if (f) ans -= 2;
  cout << ans << '\n';
  return 0;
}

### 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;
const long long inf = 0x3f3f3f3f3f3f3f3fLL;
const long long N = 3e5 + 10;
const long long MOD = 1e9 + 7;
int32_t main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  long long s, x;
  cin >> s >> x;
  long long d = (s - x) / 2;
  if (d < 0 || x + 2 * d != s || (x & d) != 0) {
    cout << 0 << '\n';
    return 0;
  }
  long long f = 0;
  if (d == 0) f = 1;
  s -= d * 2;
  long long c = __builtin_popcountll(s);
  long long ans = (1LL << c);
  if (f) ans -= 2;
  cout << ans << '\n';
  return 0;
}

```