#include <bits/stdc++.h>
#pragma GCC optimize("-O2")
using namespace std;
template <typename Arg1>
void __f(const char* name, Arg1&& arg1) {
  std::cerr << name << " = " << arg1 << std::endl;
}
template <typename Arg1, typename... Args>
void __f(const char* names, Arg1&& arg1, Args&&... args) {
  const char* comma = strchr(names + 1, ',');
  std::cerr.write(names, comma - names) << " = " << arg1 << " |";
  __f(comma + 1, args...);
}
const long double PI = acos(-1.0);
const int INF = 0x3f3f3f3f;
long long sum, x, diff, ans;
void solve() {
  cin >> sum >> x;
  diff = sum - x;
  if (diff < 0 || diff % 2) {
    cout << 0;
    return;
  }
  diff /= 2;
  if ((diff & x) != 0) {
    cout << 0;
    return;
  }
  long long cntbits = __builtin_popcountll(x);
  ans = 1LL << cntbits;
  if (diff == 0) ans -= 2;
  cout << ans;
}
int main() {
  ios_base::sync_with_stdio(false), cin.tie(0), cout.tie(0);
  int t;
  t = 1;
  while (t--) {
    solve();
  }
  return 0;
}

### Prompt

Your task is to create 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>
#pragma GCC optimize("-O2")
using namespace std;
template <typename Arg1>
void __f(const char* name, Arg1&& arg1) {
  std::cerr << name << " = " << arg1 << std::endl;
}
template <typename Arg1, typename... Args>
void __f(const char* names, Arg1&& arg1, Args&&... args) {
  const char* comma = strchr(names + 1, ',');
  std::cerr.write(names, comma - names) << " = " << arg1 << " |";
  __f(comma + 1, args...);
}
const long double PI = acos(-1.0);
const int INF = 0x3f3f3f3f;
long long sum, x, diff, ans;
void solve() {
  cin >> sum >> x;
  diff = sum - x;
  if (diff < 0 || diff % 2) {
    cout << 0;
    return;
  }
  diff /= 2;
  if ((diff & x) != 0) {
    cout << 0;
    return;
  }
  long long cntbits = __builtin_popcountll(x);
  ans = 1LL << cntbits;
  if (diff == 0) ans -= 2;
  cout << ans;
}
int main() {
  ios_base::sync_with_stdio(false), cin.tie(0), cout.tie(0);
  int t;
  t = 1;
  while (t--) {
    solve();
  }
  return 0;
}

```