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: Time Limit Exceeded)

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#define MAXHW 100000
#define N 1000000007

long int pattern(int H, int W, const int cW, int A, int B);
int isAble(int H, int W, const int cW, int A, int B);
int main (int argc, char *argv[]) {
	int H, W, A, B;
	scanf("%d %d %d %d[^\n]", &H, &W, &A, &B);
	if (H < 1 || H >= MAXHW || W < 1 || W >= MAXHW) return -1;
	if (A < 1 || A >= H || B < 1 || B >= W) return -1;
	printf("%d\n", (int)pattern(H, W, W, A, B) % N);
	return 0;
}

long int pattern(int H, int W, const int cW, int A, int B) {
	int ret = 0;
	if (H == 1 && W == 1) return 1;
	if (isAble(H, W - 1, cW, A, B)) ret += pattern(H, W - 1, cW, A, B);
	if (isAble(H - 1, W, cW, A, B)) ret += pattern(H - 1, W, cW, A, B);
	return ret;
}

int isAble(int H, int W, const int cW, int A, int B) {
	if (H < 1 || W < 1) return 0;
	if (H <= A && W > cW - B) return 0;
	return 1;
}