Problem:
Score : 400 points

Problem Statement

We have a large square grid with H rows and W columns.
Iroha is now standing in the top-left cell.
She will repeat going right or down to the adjacent cell, until she reaches the bottom-right cell.

However, she cannot enter the cells in the intersection of the bottom A rows and the leftmost B columns. (That is, there are A×B forbidden cells.) There is no restriction on entering the other cells.

Find the number of ways she can travel to the bottom-right cell.

Since this number can be extremely large, print the number modulo 10^9+7.

Constraints

1 ≦ H, W ≦ 100,000

1 ≦ A < H

1 ≦ B < W

Input

The input is given from Standard Input in the following format:

H W A B

Output

Print the number of ways she can travel to the bottom-right cell, modulo 10^9+7.

Sample Input 1

2 3 1 1

Sample Output 1

2

We have a 2×3 grid, but entering the bottom-left cell is forbidden. The number of ways to travel is two: "Right, Right, Down" and "Right, Down, Right".

Sample Input 2

10 7 3 4

Sample Output 2

3570

There are 12 forbidden cells.

Sample Input 3

100000 100000 99999 99999

Sample Output 3

1

Sample Input 4

100000 100000 44444 55555

Sample Output 4

738162020

Solution in Python (3.4.3) (judge verdict: Wrong Answer)

H,W,A,B = [int(n) for n in input().split(" ")]
answers = []
for total in range(B,W):
    disp = 1
    for n in range(1,total+(H-A)):
        disp *= n
    for m in range(1,H-A ):
        disp //= m
    for t in range(1,total + 1):
        disp //= t
    answers.append(disp)
for cnt,total in enumerate(range(B,W)):
    disp = 1
    for n in range(1,(W - total - 1) + (H - (H - A))):
        disp  *= n
    for m in range(1,H- (H - A)):
        disp //= m
    for t in range(1,W-total):
        disp //= t
    answers[cnt] *= disp
print(sum(answers))