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: Accepted)

H,W,A,B=map(int,input().split())
mod=10**9+7
kaijo=[0]*(H+W+1)
kaijo[0]=1
for i in range(1,H+W+1):
    kaijo[i]=(kaijo[i-1]*i)%mod
gyaku=[0]*(H+W+1)
gyaku[H+W]=pow(kaijo[H+W],mod-2,mod)
for i in range(H+W,0,-1):
    gyaku[i-1]=(gyaku[i]*i)%mod
def conb(x,k):
    return (kaijo[x]*gyaku[k]*gyaku[x-k])%mod
ans=0
for i in range(W-B):
    ans=(ans+conb(H-A-1+B+i,H-A-1)*conb(A-1+W-1-B-i,A-1))%mod
print(ans)