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 5.4.1) (judge verdict: Accepted)

#include <stdio.h>

#define MAXN 200001
#define MOD 1000000007

long long f[MAXN], invf[MAXN];
int H, W, A, B;
long long ans;

long long modpow(long long x, long long y)
{
	long long ret = 1LL;

	while (y)
	{
		if (y & 1LL)
		{
			ret *= x;
			ret %= MOD;
		}
		x *= x;
		x %= MOD;
		y >>= 1LL;
	}

	return ret;
}

long long nCr(int n, int r)
{
	if (r == 0 || r == n) return 1;
	return ((f[n] * invf[n-r] % MOD) * invf[r] % MOD);
}

int main(void)
{
	int i;

	scanf("%d %d %d %d", &H, &W, &A, &B);

	f[0] = 1;
	for (i = 1; i <= H + W; ++i)
	{
		f[i] = f[i-1] * i % MOD;
		invf[i] = modpow(f[i], MOD-2);
	}

	for (i = B + 1; i <= W; ++i)
	{
		ans += nCr(H - A + i - 2, i - 1) * nCr(A + W - i - 1, W - i) % MOD;
	}
	printf("%lld\n", ans % MOD);

	return 0;
}