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: Memory Limit Exceeded)

#include <iostream>
#include <cstdio>

#define N 1000000007

using namespace std;

int main() {
	int h, w, a, b;
	cin >> h >> w >> a >> b;

	int **dp;

	dp = new int*[h];
	dp[0] = new int[h*w];
	for(int i=1; i<h; i++) dp[i] = dp[0] + i*w;

	for(int i=0; i<h-a; i++) dp[i][0]=1;
	for(int j=0; j<w; j++) dp[0][j]=1;

	for(int i=1; i<h-a; i++)
		for(int j=1; j<w; j++)
			dp[i][j] = (dp[i-1][j] + dp[i][j-1])%N;

	for(int i=h-a; i<h; i++) dp[i][b]=dp[h-a-1][b];
	for(int i=h-a; i<h; i++)
		for(int j=b+1; j<w; j++)
			dp[i][j] = (dp[i-1][j] + dp[i][j-1])%N;

	cout << dp[h-1][w-1] << endl;

/*
	for(int i=0; i<h; i++) {
		for(int j=0; j<w; j++) printf("%4d", dp[i][j]);
		cout << endl;
	}
*/

	return 0;
}