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 expo(int x, int y){
    int z=1;
    for(int i=0;i<y;i++){
        z *= x;
    }
    return z;
}

int kaizyo(int x){
    int y=1;
    while(x>0){
        y*=x;
        x--;
    }
    return y;
}

int comp(int a, int b){
    int c;
    c = kaizyo(a)/(kaizyo(b)*kaizyo(a-b));
    return c;
}

int main(void){
    int H, W, A, B;
    scanf("%d%d%d%d", &H, &W, &A, &B);
    int C[W];
    for(int i=B;i<W;i++){
        C[i]=comp((i+H-A-1),i);
        int d;
        d = comp((W+A-i-2), (A-1));
        C[i]*=d;
    }
    int res=0;
    for(int i=B;i<W;i++){
        res += C[i];
    }
    res = res%(expo(10, 9)+7);
    printf("%d\n", res);
    return 0;
}