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: Wrong Answer)

object Main {
  def bfs(r: Int, u: Int, w: Int, h: Int, a: Int, b: Int): BigInt = {
    if(r == w && u == h)
      1
    else if(r > w || u > h)
      0
    else if(r <= b && u >= h - a + 1)
      0
    else
      bfs(r, u+1, w, h, a, b) + bfs(r+1, u, w, h, a, b)
  }

  def main(args: Array[String]):Unit = {
    val n = io.StdIn.readLine.split(" ").map(_.toInt)
    val ba = (Math.pow(10, 9) + 7).toInt
    println(bfs(1, 1, n(0), n(1), n(2), n(3)))
  }
}