627_A. 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
R = lambda: map(int, input().split())
s, x = R()
if s < x or (s - x) & 1:
    print(0)
    exit(0)
u, d = (s - x) // 2, x
res = 1
while u or d:
    uu, dd = u & 1, d & 1
    if uu and dd:
        res *= 0
    elif uu == 0 and dd == 1:
        res *= 2
    u, d = u >> 1, d >> 1
if s == x:
    res = max(0, res - 2)
print(res)
```