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 9.2.1) (judge verdict: Accepted)

#include<stdio.h>
int mbk(long long a,int n,int m){return n?(mbk((a*a)%m,n/2,m)*(n%2?a:1))%m:1;}
int inv(int a,int m){return mbk((long long)a,m-2,m);}
long long p[200010],q[200010],M=1e9+7;
long long aCb(int a,int b){
  //printf("%d %d\n",a,b);
  if(a<=b)return 1;
  if(b==0)return 1;
  return (p[a]*q[b])%M*q[a-b]%M;
}
int main(){
  int h,w,a,b,i;
  long long ans=0;
  scanf("%d %d %d %d",&h,&w,&a,&b);
  p[0]=1;
  for(i=1;i<200005;i++)p[i]=(p[i-1]*i)%M;
  for(i=0;i<200005;i++)q[i]=inv(p[i],M);
  for(i=0;i<h-a;i++){
    ans=(ans+(aCb(b-1+i,i)*aCb(h-i-1+w-b-1,h-i-1)%M))%M;
  }
  printf("%lld\n",ans);
  return 0;
}