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 ≤ 10^12, 0 ≤ x ≤ 10^12), 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).