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).
#include <bits/stdc++.h>
using namespace std;
struct _ {
  _() {
    ios::sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);
  }
} _;
int main() {
  long long s, x;
  cin >> s >> x;
  auto diff = (s - x);
  if (diff % 2 || diff < 0 || (x << 1) & diff) {
    cout << 0;
  } else {
    long long count = 1;
    for (int i = 63; i >= 0; --i)
      if ((x >> i) & 1) count <<= 1;
    cout << count - 2 * (diff == 0);
  }
}
