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: Wrong Answer)

#include <stdio.h>
#include <math.h>

int factorial(int n) //n!
{
  int i,ans = 1;

  if(ans > 0)
    for(i = n;i > 0;i--)
      ans = ans * i;

  return ans;
}

int combination(int n,int r) //nCr
{
  int i,j = 1;

  for(i = n;i > n - r;i--)
    j = j * i;

  return j / factorial(r);
}

int main(void)
{
  int i,j,k,h,w,a,b,sum = 0,sub = 0;
  j = pow(10,9) + 7;

  scanf("%d %d %d %d",&h,&w,&a,&b);

  for(i = 0;i < h - a;i++)
    {
      if(i > 0)
	sub = combination(i + b - 1,i - 1);
      sum = sum + (combination(b + i,i) - sub) * combination(w - b + h - i - 2,w - b - 1);
      //  printf("i = %d: %d pattern\n",i,(combination(b + i,i) - sub) * combination(w - b + h - i - 2,w - b - 1));
      sub = 0;
    }
  printf("%d\n",sum % j);

  return 0;
}