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 mod 1000000007
int H, W, A, B, i, fact[200009], inv[200009], factinv[200009], ret;
inline int ncr(int xx, int yy) {
	return 1LL * fact[xx] * factinv[yy] % mod * factinv[xx - yy] % mod;
}
int main() {
	fact[0] = 1;
	for (i = 1; i <= 200009; i++) fact[i] = 1LL * fact[i - 1] * i % mod;
	inv[1] = 1;
	for (i = 2; i <= 200009; i++) inv[i] = 1LL * inv[mod % i] * (mod - mod / i) % mod;
	factinv[0] = 1;
	for (i = 1; i <= 200009; i++) factinv[i] = 1LL * factinv[i - 1] * inv[i] % mod;
	scanf("%d%d%d%d", &H, &W, &A, &B);
	for (i = 0; i < W - B; i++) ret = (ret + 1LL * ncr(A + i - 1, i) * ncr(W - i + H - A - 2, H - A - 1)) % mod;
	printf("%d\n", ret);
	return 0;
}