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: Memory Limit Exceeded)

#include <stdio.h>
#include <stdlib.h>
#define MOD 1000000007

int main(void) {
	int h,w,a,b,i,j;
	int** map;
	
	scanf("%d %d %d %d",&h,&w,&a,&b);

	map = (int**)calloc(h, sizeof(int));
	for (i = 0;i < h;i++) {
		map[i] = (int *)calloc(w, sizeof(int));
	}

	for (i = 0;i < w;i++) {
		map[0][i] = 1;
	}
	for (i = 0;i < h-a;i++) {
		map[i][0] = 1;
	}
	
	for (i = 1;i < h;i++) {
		for(j = ((i >= h-a) ? b : 1);j < w;j++) {
			map[i][j] = (map[i-1][j]+map[i][j-1])%MOD;
		}
	}
	
	printf("%d\n",map[h-1][w-1]);
	
	return 0;
}