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: Accepted)

#include <stdio.h>
#include <stdlib.h>
#define MAX_H 100000
#define MAX_W 100000
#define MAX_C 1000000007

long long H, W, A, B;
long long fact[MAX_H+MAX_W];
long long i_fact[MAX_H+MAX_W];

long long bin_pow(long long x){
    long long n=MAX_C-2, p=x, y=1;
    while (n>0) {
        if (n%2==0){
            p = ((long long)p*p) % MAX_C;
            n = n/2;
        } else {
            y = ((long long)y*p) % MAX_C;
            n--;
        }
    }
    return y;
}

void set(){
    long long i;
    fact[0] = 1; i_fact[0] = 1;
    for (i=1; i<=H+W-2; i++){
        fact[i] = ((long long)fact[i-1] * i) % MAX_C;
        i_fact[i] = bin_pow(fact[i]);
    }
}

long long combi(long long n, long long r){
    long long y;
    y = (fact[n] * i_fact[r]) % MAX_C;
    y = (y * i_fact[n-r]) % MAX_C;
    return y;
}

int main(){
    long long x, y, ans=0, i;
    scanf("%lld%lld%lld%lld", &H, &W, &A, &B);
    set();
    x = B; y = H-A-1;
    for (i=B; i<W; i++) {
        ans += combi(H-A+i-1, i) * combi(W+A-i-2, A-1);
        ans = ans % MAX_C;
    }
    printf("%lld\n", ans);
    
    return 0;
}