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: Accepted)

#include<bits/stdc++.h>

using namespace std;

typedef long long ll;

const ll mod=1e9+7;

ll fact[200010];//階乗の値を保存
ll rfact[200010];//逆元の値を保存

ll mod_pow(ll x, ll p){
        ll res=1;
        while(p){
                if(p&1){
                        res=res*x%mod;
                }
                x=x*x%mod;
                p/=2;
        }
        return res;
}

ll nCr(ll n, ll r){
        return fact[n]*rfact[r]%mod*rfact[n-r]%mod;
}

int main(){
        fact[0]=1;
        rfact[0]=1;
        for(int i=1;i<200010;i++){
                fact[i]=i*fact[i-1]%mod;
                rfact[i]=mod_pow(fact[i], mod-2);
        }
        ll H, W, A, B;
        cin>>H>>W>>A>>B;
        ll ans=0;
        //行けるところを到達した時のx座標で場合分けしている。
        for(int i=B+1;i<=W;i++){
                //1, 1→　H-A, i
                int h=H-A-1, w=i-1;
                ll tmp=nCr(h+w, h);
                //cout<<h+w<<"C"<<h<<"="<<tmp<<endl;
                //H-A+1, i→　H, W
                h=A-1, w=W-i;
                tmp*=nCr(h+w, w);
                //cout<<"tmp*"<<h+w<<"C"<<w<<"="<<tmp<<endl;
                ans+=tmp%mod;
        }
        cout<<ans%mod<<endl;

}