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 C (GCC 5.4.1) (judge verdict: Accepted)

#define q(x,y)(f[x]*h[y]%m*h[(x)-(y)]%m)
const z=2e5,m=1e9+7;long long H,W,A,B,i=2,f[1<<18],g[1<<18],h[1<<18],r;
main(){
for(f[0]=f[1]=g[1]=1;i<z;i++)f[i]=f[i-1]*i%m,g[i]=g[m%i]*(m-m/i)%m;
for(h[0]=i=1;i<z;i++)h[i]=h[i-1]*g[i]%m;
for(scanf("%d%d%d%d",&H,&W,&A,&B),i=0;i<W-B;i++)r=(r+q(A+i-1,i)*q(W-i+H-A-2,H-A-1))%m;
i=!printf("%d\n",r);
}