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++14 (GCC 5.4.1) (judge verdict: Time Limit Exceeded)

#include<iostream>

using namespace std;
#define int long long
const int mod=1e9+7;

int powpow(int x, int n){
    if(n==0) return 1;
    else if(n%2==0) return powpow(x*x%mod, n/2)%mod;
    else if(n%2==1) return x*powpow(x, n-1)%mod;
}

int makeinv(int x, int p){
    return powpow(x, p-2);
}
int fact(int n){
    int ret=1;
    for(int i=1; i<=n; i++){
        ret*=i;
        ret%=mod;
    }
    return ret;
}
int comb(int n, int r){
    return (fact(n)%mod*makeinv(fact(n-r), mod)%mod*makeinv(fact(r), mod)%mod)%mod;
}

signed main(){

    int H, W, A, B;
    cin>> H>> W>> A>> B;

    int ans=0;
    for(int j=B; j<W; j++){
        int s, t;
        s=comb((H-A-1)+j, j);
        t=comb((H-1-(H-A))+(W-j-1), A-1);
        ans+=s*t;
        ans%=mod;
    }

    cout<< ans<< endl;

    return 0;
}