634_B. XOR Equation
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).
```python
s,x=map(int,input().split())
if x>s or (s-x)%2!=0:
    print(0)
else:
    mask=1
    res=1
    bit=0
    ND=(s-x)//2
    flag=False
    while bit<50:
        if (mask&x)>0:
            res*=2
        if mask&x>0 and ND&mask>0:
            flag=True
            break
        mask*=2
        bit+=1
    if(s==x):
        res-=2
    if flag:
        res=0
    print(res)
    
```