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.

Input

Input is given from Standard Input in the following format:
H W A B

Output

Print the answer.

Constraints

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

Sample Input 1

2 2 1 2

Sample Output 1

4

There are four ways as follows:

Sample Input 2

3 3 4 1

Sample Output 2

18

There are six ways as follows, and their rotations.

Sample Input 3

4 4 8 0

Sample Output 3

36

见题面 Input 部分

见题面 Output 部分