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 $0$.

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 $(2, 1)$.