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 Scala (2.11.7) (judge verdict: Time Limit Exceeded)

import scala.collection.mutable.ArrayBuffer
import scala.util.control.Breaks
import java.lang.Math
object Main{
  def main(args:Array[String]) = {

    val sc = new java.util.Scanner(System.in)
    val H = sc.nextInt
    val W = sc.nextInt
    val A = sc.nextInt
    val B = sc.nextInt

    var dp = Array.ofDim[Long](W)
    var tmp = Array.ofDim[Long](W)


    for(i <- 0 until H){
      for(j <- 0 until W){
        if(i>=H-A && j<=B-1) {
          dp(j) = 0
        }else if(i==0 || j==0){
          dp(j)=1L
        }else{
          dp(j)=(tmp(j)+dp(j-1))%1000000007L
        }
      }
      for(j <- 0 until W){
        tmp(j)=dp(j)
      }
    }

    println(dp(W-1)%1000000007L)

  }
}