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: Wrong Answer)

#include <stdio.h>
unsigned long int conbination(int a,int b);

int main(void){
    int H=0,W=0,A=0,B=0;

    scanf("%d%d%d%d",&H,&W,&A,&B);
    unsigned long int total=0;
    if(W-B-1<=-0 && H-A-1<=0){
        printf("%d",1);
        return 0;
    }
    for(int i=0;i<W-B-1 || i<H-A-1;i++){
        total+=conbination((H-A-1-i)+(B+i),B+i)*conbination((A+i)+(W-B-1-i),A+i);
    }

    total%=1000000007;

    printf("%ld",total);
    return 0;
}

unsigned long int conbination(int a,int b){
    unsigned long int sigma=1;
    for(int i=1;i<=a;i++) sigma*=i;
    for(int i=1;i<=b;i++) sigma/=i;
    for(int i=1;i<=a-b;i++) sigma/=i;
    return sigma;
}