♥codeforces 627A-XOR Equation【数学】-蒲公英云

♥codeforces 627A-XOR Equation【数学】

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

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).

#include<stdio.h>
#include<string.h>
#include<algorithm>
#define LL long long
using namespace std;
int main()
{
    LL a,b;
    while(scanf("%I64d%I64d",&a,&b)!=EOF)
    {
        LL i,j;
        LL ans=0;
        if((a-b)>=0&&(a-b)%2==0)
        {
            LL wc=(a-b)/2;
            int cut=0;
            bool flag=true;
            if(a==b)
            ans-=2;
            while(b)
            {
                if(b&1)
                {
                    cut++;
                    if(wc&1)
                    {
                        flag=false;
                    }
                }
                if(!flag)
                {
                    break;
                }
                b/=2,wc/=2;
            }
             if(!flag) ans = 0;  
                else ans += (1LL<<cut);
        }
        printf("%I64d\n",ans);
    }
    return 0;
}