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

ll dp[200010];
ll gt[200010];
ll ksm(ll a,ll b)
{
    ll ans=1;
    for(;b;b>>=1,a=a*a%mod) if(b&1) ans=ans*a%mod;
    return ans;
}
ll C(ll m,ll n)
{
    return (gt[m]*ksm(gt[n],mod-2)%mod)*ksm(gt[m-n],mod-2)%mod;
}
int main()
{

    gt[0]=1;
    for(int i=1;i<=200005;i++)
    {
        gt[i]=gt[i-1]*i%mod;
    }
    //freopen("input.txt","r",stdin);
    ios::sync_with_stdio(false);
    int H,W,A,B;cin>>H>>W>>A>>B;
    ll sum=0;
    for(int i=1;i<=W-B;i++)
    {
        dp[i]=C(H-A-1+B+i-1,B+i-1);
        sum=(sum+1ull*(dp[i]-dp[i-1]+mod)*C(A+W-B-i,A)%mod)%mod;
    }
    cout<<sum<<endl;
}