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>

int main(){
    int h, w, a, b;
    scanf("%d %d %d %d", &h, &w, &a, &b);
    int ha = h-a, wb = w-b;
    int array1[h], array2[ha];
    int count = 0;

    for(int i=0; i<h; i++){
        array1[i] = 1;
    }
    for(int i=1; i<wb; i++){
        for(int j=h-2; j>=0; j--){
            array1[j] = array1[j+1] + array1[j];
        }
    }
    for(int i=0; i<ha; i++){
        array2[i] = 1;
    }
    for(int i=1; i<b; i++){
        for(int j=1; j<ha; j++){
            array2[j] = array2[j-1] + array2[j];
        }
    }

    for(int i=0; i<ha; i++){
        count += array1[i] * array2[i];
        printf("%d, %d, %d\n", array2[i], array1[i], array1[i]*array2[i]);
    }
    printf("%d", count % (1000000007));

    return 0;
}