Problem Statement

We have a rectangular room that is $H$ meters long and $W$ meters wide. We will cover this room with $A$ indistinguishable $2$ meters $\times$ $1$ meters rectangular tatami mats and $B$ indistinguishable $1$ meter $\times$ $1$ meter square tatami mats. The rectangular mats can be used in either direction: they can be $2$ meters long and $1$ meter wide, or $1$ meter long and $2$ meters wide. How many ways are there to do this? Here, it is guaranteed that $2A + B = HW$, and two ways are distinguished if they match only after rotation, reflection, or both.

Constraints

• All values in input are integers.
• $1 ≤ H, W$
• $HW ≤ 16$
• $0 ≤ A, B$
• $2A + B = HW$

Input

Input is given from Standard Input in the following format:

H W A B

Output

Print the answer.