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>
#define ll long long
#define mod 1000000007
#define pb push_back
#define pint pair<int,int>
using namespace std;

ll fact[200001],inv[100001];

ll gcd(ll a,ll b,ll*x,ll*y){
	if(a%b==0){
		*x=0;	*y=1;
		return b;
	}
	ll x1,y1,ans=gcd(b,a%b,&x1,&y1);
	*x=y1;	*y=x1-(a/b)*y1;
	return ans;
}

ll ncr(int n, int r){
	ll ans=fact[n];
	ans*=inv[r];	ans%=mod;
	ans*=inv[n-r];	ans%=mod;
	return ans;
}

int main(){
	ios::sync_with_stdio(false);
	cin.tie(0);
	int i,j,h,w,a,b;	cin>>h>>w>>a>>b;
	h--;	w--;
	fact[0]=1;
	for(i=1;i<=200000;i++){
		fact[i]=(i*fact[i-1])%mod;
	}

	ll x,y;
	gcd(fact[100000],mod,&x,&y);
	inv[100000]=((x%mod)+mod)%mod;

	for(i=100000;i>0;i--){
		inv[i-1]=(i*inv[i])%mod;
	}

	ll ans=0;
	for(j=b;j<=w;j++){
		ans+=(ncr(h-a+j,j)*ncr(a-1+w-j,w-j))%mod;	ans%=mod;
		//cout<<ans<<endl;
	}

	cout<<ans<<endl;

	return 0;
}