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: Wrong Answer)

#include <iostream>
#include <cstdio>
#define MOD int(1e9+7)
using namespace std;
long long H,W,A,B,ans = 0,face = 0;
long long combi(long long a,long long b){
	long long s = 1;
	if(b == 0 || a == b){
		return 1;
	}
	b = min(b,a-b);
	for (long long i = 0; i < b; ++i)
	{
		s *= (a-i);
	}
	for (long long i = b; i > 1; --i)
	{
		s /= i;
	}
	// cout << a << " " << b << ":" << s << "\n";
	face = s;
	return s;
}
int main(){
	cin >> H >> W >> A >> B;
	long long C = W-B;
	long long D = H-A;
	for (long long i = 0; i < C; ++i)
	{
		if(face != 0){
			face = face*(B+D-1+i)*(C-i);
			face = face/((B+i)*(A+C-1-i));
		}else{
			face = combi(B+D-1+i,D-1)*combi(A+C-2-i,A-1);
		}
		ans += face;
		ans %= MOD;
	}
	cout << ans << "\n";
	return 0;
}