#include <bits/stdc++.h>
using namespace std;
using pii = pair<int, int>;
using ll = long long;
const int INF = (int)1e9 + 7, mod = (int)1e9 + 9, pw = 31, N = (int)1e5 + 123,
          M = (int)1e6 + 123;
const double eps = 1e-11;
const long long inf = 1e18;
ll n, m, ans = 0;
bitset<60> a, b, d;
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(NULL);
  cin >> n >> m;
  ll res = 0;
  a = n;
  b = m;
  if ((n - m) % 2 != 0 || n % 2 != m % 2) {
    cout << "0";
    return 0;
  }
  d = (n - m) / 2;
  if ((d & b).count()) {
    cout << "0";
    return 0;
  }
  cout << (1ll << (b.count())) - (n == m ? 2 : 0);
  return 0;
}

### Prompt

Construct a cpp code solution to the problem outlined:

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;
using pii = pair<int, int>;
using ll = long long;
const int INF = (int)1e9 + 7, mod = (int)1e9 + 9, pw = 31, N = (int)1e5 + 123,
          M = (int)1e6 + 123;
const double eps = 1e-11;
const long long inf = 1e18;
ll n, m, ans = 0;
bitset<60> a, b, d;
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(NULL);
  cin >> n >> m;
  ll res = 0;
  a = n;
  b = m;
  if ((n - m) % 2 != 0 || n % 2 != m % 2) {
    cout << "0";
    return 0;
  }
  d = (n - m) / 2;
  if ((d & b).count()) {
    cout << "0";
    return 0;
  }
  cout << (1ll << (b.count())) - (n == m ? 2 : 0);
  return 0;
}

```