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 9.2.1) (judge verdict: Accepted)

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
const int mod=7+1e9;
ll gcd(ll x,ll y){return y?gcd(y,x%y):x;}
ll lcm(ll x,ll y){return x/gcd(x,y)*y;}
ll qpow(ll a,ll b,ll p){a%=p; ll ret=1;for(;b;b>>=1,a=a*a%p) if(b&1) ret=ret*a%p; return ret;}
ll getInv(ll x,ll p){return qpow(x,p-2,p);}
const int N=5+2e5;
ll n[N];
ll C(ll a,ll b){ return n[a]*getInv(n[b]*n[a-b]%mod,mod)%mod;}
int main(){
    ll h,w,a,b; cin>>h>>w>>a>>b;
    n[0]=1;
    for(int i=1;i<N;i++) n[i]=n[i-1]*i%mod;
    ll ans=0;
    for(int i=b+1;i<=w;i++)
        ans=(ans+C(h-a-1+i-1,h-a-1)*C(a-1+w-i,w-i)%mod)%mod;
    ans=(ans+mod)%mod;
    cout<<ans<<'\n';
}