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: Runtime Error)

import math 
H,W,A,B=map(int,input().split())
def C(n,m):
    if n*m==0:
        C =1
    else:
        bunbo=[0]*min(m,n)
        bunsi=[0]*min(m,n)
        for k in range(min(m,n)):
            bunbo[k]=min(m,n)-k
            bunsi[k]=n+m-k
        for k in range(min(m,n)):
            for j in range(min(n,m)):
                gcd=math.gcd(bunbo[k],bunsi[j])
                bunbo[k]=bunbo[k]//gcd
                bunsi[j]=bunsi[j]//gcd
        x=1
        y=1
        for k in range(min(n,m)):
            x=x*bunsi[k]
            y=y*bunbo[k]
        C=x//y
    return C
Total = C(H-1,W-1)
dame = 0
for k in range(B):
    dame += C(k,H-A-1)*C(W-1-k,A-1)
answer = (Total-dame)%(10**9+7)
print(int(answer))