#include <bits/stdc++.h>
using namespace std;
int m[3000005];
int main() {
  long long s, x;
  cin >> s >> x;
  long long ss = s >> 20;
  long long xx = x >> 20;
  for (int i = 0; i < (1 << 20); ++i) {
    int j = xx ^ i;
    m[i + j]++;
  }
  long long ans = 0;
  for (int i = 0; i < (1 << 20); ++i) {
    int j = (x ^ i) & ((1 << 20) - 1);
    if (((i + j) & ((1 << 20) - 1)) != (s & ((1 << 20) - 1))) continue;
    int k = (ss - ((i + j) >> 20));
    if (k >= 0) ans += m[k];
  }
  if (s == x) ans -= 2;
  cout << ans << '\n';
}

### 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;
int m[3000005];
int main() {
  long long s, x;
  cin >> s >> x;
  long long ss = s >> 20;
  long long xx = x >> 20;
  for (int i = 0; i < (1 << 20); ++i) {
    int j = xx ^ i;
    m[i + j]++;
  }
  long long ans = 0;
  for (int i = 0; i < (1 << 20); ++i) {
    int j = (x ^ i) & ((1 << 20) - 1);
    if (((i + j) & ((1 << 20) - 1)) != (s & ((1 << 20) - 1))) continue;
    int k = (ss - ((i + j) >> 20));
    if (k >= 0) ans += m[k];
  }
  if (s == x) ans -= 2;
  cout << ans << '\n';
}

```