XOR Equation - VietMX's Blog

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

input

3 3

output

input

5 2

output

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).

Solution:

#include <bits/stdc++.h>
 
using namespace std;
 
int main() {
long long sum, x;
cin >> sum >> x;
long long a = (sum - x) / 2;
if (a < 0 || x + 2 * a != sum || (x & a) != 0) {
    cout << 0 << endl;
    return 0;
  }
  long long bits = 0;
  long long tmp = x;
  while (tmp > 0) {
bits += tmp & 1;
tmp >>= 1;
}
long long ans = 1LL << bits;
  if (a == 0) {
    ans -= 2;
  }
  cout << ans << endl;
  return 0;
}