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 (2.13.1) (judge verdict: Accepted)

object Main extends App {
  val sc = new java.util.Scanner(System.in)
  val h, w, a, b = sc.nextInt()
  val mod = 1000000007

  def plus(a: Long, b: Long): Long = (a + b) % mod
  def times(a: Long, b: Long): Long = (a * b) % mod

  def pow(a: Long, n: Int, res: Long = 1): Long = {
    if (n == 0) {
      res
    } else if ((n&1) == 0) {
      pow(times(a,a), n >> 1, res)
    } else {
      pow(times(a,a), n >> 1, times(res,a))
    }
  }

  def inv(a: Long): Long = pow(a, mod-2)

  def initFactTable(n: Int): Array[Long] = {
    (1 to n).scanLeft(1L)(times(_,_)).toArray
  }

  val fact = initFactTable(h + w)

  def initInvFactTable(n: Int): Array[Long] = {
    (1 to n).scanRight(inv(fact(n)))(times(_,_)).toArray
  }

  val invFact = initInvFactTable(h + w)

  def comb(n: Int, k: Int): Long = {
    times(times(fact(n), invFact(k)), invFact(n-k))
  }

  val ans = (0 until (h - a).min(w - b)).map( i =>
    times(comb(b + h - a - 1, b + i), comb(a + w - b - 1, a + i))
  ).reduceLeft(plus)

  println(ans)
}