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: Runtime Error)

#include<stdio.h>
int main(){
  int M[100][100];
  int h,w,a,b,i,j;
  scanf("%d %d %d %d",&h,&w,&a,&b);
  for(i=0;i<h;i++)for(j=0;j<w;j++)M[i][j]=0;
  for(i=0;i<h-a;i++)M[i][0]=1;
  for(i=0;i<w;i++)M[0][i]=1;
  for(i=1;i<h;i++)for(j=1;j<w;j++)if(i<h-a|j>=b)M[i][j]=(M[i-1][j]+M[i][j-1])%1000000007;
  printf("%d",M[h-1][w-1]);
}