#include <bits/stdc++.h>
using namespace std;
template <typename S, typename T>
ostream& operator<<(ostream& out, pair<S, T> const& p) {
  out << '(' << p.first << ", " << p.second << ')';
  return out;
}
template <typename T>
ostream& operator<<(ostream& out, vector<T> const& v) {
  int l = v.size();
  for (int i = 0; i < l - 1; i++) out << v[i] << ' ';
  if (l > 0) out << v[l - 1];
  return out;
}
void tr() { cout << endl; }
template <typename S, typename... Strings>
void tr(S x, const Strings&... rest) {
  cout << x << ' ';
  tr(rest...);
}
long long up = 31;
long long s, x;
long long cnt;
int main() {
  cin >> s >> x;
  int up = 0;
  for (int i = 0; i < 60; i++) {
    if ((x & (1ll << i)) > 0) up = i;
  }
  for (int i = 0; i <= up; i++) {
    if ((x & (1ll << i)) > 0) {
      cnt++;
      s -= (1ll << i);
    }
  }
  bool ok = true;
  if (s % 2) ok = false;
  for (int i = 0; i <= up; i++) {
    if ((x & (1ll << i)) > 0 and (s & (1ll << (i + 1))) > 0) ok = false;
  }
  if (ok) {
    if (s > 0)
      cout << (1ll << cnt) << endl;
    else
      cout << (1ll << cnt) - 2 << endl;
  } else {
    cout << 0 << endl;
  }
  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>
using namespace std;
template <typename S, typename T>
ostream& operator<<(ostream& out, pair<S, T> const& p) {
  out << '(' << p.first << ", " << p.second << ')';
  return out;
}
template <typename T>
ostream& operator<<(ostream& out, vector<T> const& v) {
  int l = v.size();
  for (int i = 0; i < l - 1; i++) out << v[i] << ' ';
  if (l > 0) out << v[l - 1];
  return out;
}
void tr() { cout << endl; }
template <typename S, typename... Strings>
void tr(S x, const Strings&... rest) {
  cout << x << ' ';
  tr(rest...);
}
long long up = 31;
long long s, x;
long long cnt;
int main() {
  cin >> s >> x;
  int up = 0;
  for (int i = 0; i < 60; i++) {
    if ((x & (1ll << i)) > 0) up = i;
  }
  for (int i = 0; i <= up; i++) {
    if ((x & (1ll << i)) > 0) {
      cnt++;
      s -= (1ll << i);
    }
  }
  bool ok = true;
  if (s % 2) ok = false;
  for (int i = 0; i <= up; i++) {
    if ((x & (1ll << i)) > 0 and (s & (1ll << (i + 1))) > 0) ok = false;
  }
  if (ok) {
    if (s > 0)
      cout << (1ll << cnt) << endl;
    else
      cout << (1ll << cnt) - 2 << endl;
  } else {
    cout << 0 << endl;
  }
  return 0;
}

```