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.

Input is given from Standard Input in the following format:

```
$H$ $W$ $A$ $B$
```

Print the answer.

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

4

There are four ways as follows:

18

There are six ways as follows, and their rotations.