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 <cstdio>
typedef long long LL;
const int maxn=1e5+10;
const int mod=1e9+7;
LL H,W,a,b;
LL s[2*maxn+10],inv[2*maxn+10];

inline LL qpow(LL a,LL b) {
    LL res=1;
    while (b) {
        if (b&1) res=res*a%mod;
        a=a*a%mod;
        b>>=1;
    }
    return res%mod;
}

void _init() {
    s[0]=s[1]=1;
    for (int i=2;i<=2*maxn;i++)
        s[i]=s[i-1]*i%mod;

    inv[0]=1; inv[2*maxn]=qpow(s[2*maxn],mod-2);
    for (int i=2*maxn-1;i>=1;i--) inv[i]=inv[i+1]*(i+1)%mod;
}

LL C(LL m,LL n) {
    return s[m]*inv[n]%mod*inv[m-n]%mod;
}

int main() {
    _init();
    scanf("%lld%lld%lld%lld",&H,&W,&a,&b);
    LL ans=0;
    for (int i=b+1;i<=W;i++)
        ans=(ans+C(H-a+i-2,H-a-1)*C(W+a-i-1,a-1)%mod)%mod;
    printf("%lld\n", ans);
    return 0;
}