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: Time Limit Exceeded)

using System;
using System.Collections;
using System.Collections.Generic;

namespace A
{
    class Program
    {
        public class TupleList<T1, T2, T3> : List<Tuple<int, int, string>>
        {
            public void Add(int item1, int item2, string s)
            {
                Add(new Tuple<int, int, string>(item1, item2, s));
            }
        }
        static void Main(string[] args)
        {
            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 height = 0;
            int[,] cache = new int[h, 2];

            cache[0, 0] = 1;
            for (int i = 0; i < h-a; i++) cache[i, 0] = 1;
            for(int i = 1; i< w; i++)
            {
                height = 0;
                cache[0, 1] = 1;
                if (i < b) height = h - a;
                else height = h;
                for(int j = 1; j< height; j++)
                {
                    cache[j, 1] = (cache[j - 1, 1] + cache[j, 0]) % 1000000007;
                }

                for(int j = 0; j< height; j++)
                {
                    cache[j, 0] = cache[j, 1];
                }
            }

            Console.WriteLine(cache[h-1, 1]);
        }
    }
}