#include <bits/stdc++.h>
using namespace std;
map<pair<long long, long long>, long long> vis, ans;
long long fun(long long s, long long x, long long c) {
  long long a, b, s_b, x_b;
  if (s == 0) {
    if (x == 0 && c == 0)
      return 1;
    else
      return 0;
  }
  if (vis[make_pair(s, c)] == 1) {
    return ans[make_pair(s, c)];
  }
  s_b = s % 2;
  x_b = x % 2;
  if (x_b == 0) {
    if (s_b == 0 && c == 1) return 0;
    if (s_b == 1 && c == 0) return 0;
    a = fun(s >> 1, x >> 1, 0);
    b = fun(s >> 1, x >> 1, 1);
    vis[make_pair(s, c)] = 1;
    ans[make_pair(s, c)] = a + b;
    return a + b;
  } else {
    if (s_b == 0 && c == 0) return 0;
    if (s_b == 1 && c == 1) return 0;
    if (s_b == 0 && c == 1) {
      a = fun(s >> 1, x >> 1, 1);
      b = fun(s >> 1, x >> 1, 1);
    } else if (s_b == 1 && c == 0) {
      a = fun(s >> 1, x >> 1, 0);
      b = fun(s >> 1, x >> 1, 0);
    }
    vis[make_pair(s, c)] = 1;
    ans[make_pair(s, c)] = a + b;
    return a + b;
  }
}
int main() {
  long long s, x;
  scanf("%lld", &s);
  scanf("%lld", &x);
  long long ans = fun(s, x, 0);
  if ((0 ^ s) == x) ans -= 2;
  cout << ans << endl;
  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;
map<pair<long long, long long>, long long> vis, ans;
long long fun(long long s, long long x, long long c) {
  long long a, b, s_b, x_b;
  if (s == 0) {
    if (x == 0 && c == 0)
      return 1;
    else
      return 0;
  }
  if (vis[make_pair(s, c)] == 1) {
    return ans[make_pair(s, c)];
  }
  s_b = s % 2;
  x_b = x % 2;
  if (x_b == 0) {
    if (s_b == 0 && c == 1) return 0;
    if (s_b == 1 && c == 0) return 0;
    a = fun(s >> 1, x >> 1, 0);
    b = fun(s >> 1, x >> 1, 1);
    vis[make_pair(s, c)] = 1;
    ans[make_pair(s, c)] = a + b;
    return a + b;
  } else {
    if (s_b == 0 && c == 0) return 0;
    if (s_b == 1 && c == 1) return 0;
    if (s_b == 0 && c == 1) {
      a = fun(s >> 1, x >> 1, 1);
      b = fun(s >> 1, x >> 1, 1);
    } else if (s_b == 1 && c == 0) {
      a = fun(s >> 1, x >> 1, 0);
      b = fun(s >> 1, x >> 1, 0);
    }
    vis[make_pair(s, c)] = 1;
    ans[make_pair(s, c)] = a + b;
    return a + b;
  }
}
int main() {
  long long s, x;
  scanf("%lld", &s);
  scanf("%lld", &x);
  long long ans = fun(s, x, 0);
  if ((0 ^ s) == x) ans -= 2;
  cout << ans << endl;
  return 0;
}

```