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>
#include <string>
#include <vector>
#include <algorithm>
using namespace std;

long long table[1000000] = { 0 };

long long fact(long long n);

int main() {
	long long h, w, a, b;
	scanf("%lld %lld %lld %lld", &h, &w, &a, &b);

	long long fh_a = fact(h - a), fa = fact(a);
	long long sum = 0;

	for (long long i = b ; i <= w; i++) {
		sum = (sum + (((fact(h - a + i) / (fh_a * fact(i))) % 1000000007LL) * 
			((fact(a + w + 1 - i) / (fa + fact(w + 1 - i))) % 1000000007LL)) % 1000000007LL) % 1000000007LL;
		
	}

	printf("%lld\n", sum);

	return 0;
}

long long fact(long long n) {
	if (table[n - 1] != 0)return table[n - 1];
	else if (n == 1) {
		table[0] = 1;
		return 1;
	}
	else {
		table[n - 1] = fact(n - 1);
		return table[n - 1];
	}
}