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 Ruby (2.3.3) (judge verdict: Accepted)

h, w, a, b = gets.chomp.split(" ").map(&:to_i)

MOD = 10**9 + 7

def power(x, n)
  if n == 0
    return 1
  elsif n.even?
    return power(x * x, n / 2) % MOD
  else
    return x * power(x, n /2)**2 % MOD
  end
end

@fac = []
@fac[0] = @fac[1] = 1

2.upto(h + w - 2) do |i|
  @fac[i] = @fac[i - 1] * i % MOD
end

@faci = []
@faci[0] = @faci[1] = 1
@faci[h + w - 2] = power(@fac[h + w - 2], MOD - 2) % MOD
(h + w - 3).downto(2) do |i|
  @faci[i] = @faci[i + 1] * (i + 1) % MOD
end


def comb(n, k)
  return 0 if n < k
  return 0 if n < 0 || k < 0
  return @fac[n] * (@faci[k] * @faci[n - k] % MOD) % MOD
end

ans = 0

b.upto(w - 1) do |i|
  ans += comb(h - a - 1 + i, i) * comb(a + w - i - 2, w - i - 1)
  ans %= MOD
end
p ans % MOD