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 (2.7.6) (judge verdict: Accepted)

h,w,a,b=map(int,raw_input().split(' '))
mod=1000000007
inv=[0]*(h+w)
fact=[0]*(h+w)

def ex(x,y):
    if y==0: return 1
    elif y==1: return x%mod
    elif y%2==0: return ex(x,y/2)**2%mod
    else: return ex(x,y/2)**2*x%mod

#factorial
fact[0]=1
for j in range(1,h+w):
    fact[j]=fact[j-1]*j%mod

inv[h+w-1]=ex(fact[h+w-1],mod-2)
for j in reversed(range(h+w-1)):
    inv[j]=inv[j+1]*(j+1)%mod

    

def nck(x,y):
    return fact[x]*inv[y]*inv[x-y]%mod

su=0
for j in range(h-a):
    su=(su+nck(b-1+j,b-1)*nck(h-1-j+w-1-b,w-1-b))%mod

print su