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# (Mono 4.6.2.0) (judge verdict: Runtime Error)

using System;
public class Hello{
    public static void Main(){
        // Your code here!
        string[] input = Console.ReadLine().Split(' ');
        int h = int.Parse(input[0]);
        int w = int.Parse(input[1]);
        int a = int.Parse(input[2]);
        int b = int.Parse(input[3]);
        int[,] hw = new int[h,w];
        hw[0,0]=1;
        for(int i=1;i<h-a;i++){
            hw[i,0]=1;
        }
        for(int j=1;j<w;j++){
            hw[0,j]=1;
        }
        for(int i=1;i<h-a;i++){
            for(int j=1;j<b+1;j++){
                hw[i,j] = hw[i-1,j] + hw[i,j-1];
                if(hw[i,j]>1000000007){
                    hw[i,j]=hw[i,j]%1000000007;
                }
//                Console.WriteLine("hw{0}{1} {2}",i,j,hw[i,j]);
            }
        }
        for(int i=h-a-1;i<h-1;i++){
            hw[i+1,b+1] = hw[i,b+1];
        }
        for(int i=1;i<h;i++){
            for(int j=b;j<w;j++){
                hw[i,j] = hw[i-1,j] + hw[i,j-1];
                if(hw[i,j]>1000000007){
                    hw[i,j]=hw[i,j]%1000000007;
                }
            }
        }
        for(int i=0;i<h;i++){
            for(int j=0;j<w;j++){
//                Console.WriteLine("hw{0}{1} {2}",i,j,hw[i,j]);
            }
        }
        Console.WriteLine(hw[h-1,w-1]);
    }
}