CF 627A. XOR Equation 位运算

A. XOR Equation

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

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).

#include
#include
#include
#include
#include
#include
#define ysk(x)  ((ll)1<<(x))
using namespace std;
typedef long long ll;
const int INF =0x3f3f3f3f;
ll s,x;
//思路核心： s=a+b= (a^b)+ 2*(a&b);

int main()
{
    while(~scanf("%I64d%I64d",&s,&x))
    {
        if(s