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)

MOD = 1000000007
FACT = []
INV = []

def conv(s,t)
  (FACT[s] * INV[s-t] % MOD) * INV[t] % MOD
end

def calc_fact(n)
  FACT[0] = 1
  INV[0] = pow(FACT[0], MOD-2)
  for i in 1..n
    FACT[i] = FACT[i-1] * i % MOD
    INV[i] = pow(FACT[i], MOD-2)
  end
end

def pow(x,n)
  if n == 0
    1
  elsif n % 2 == 0
    pow(x*x%MOD, n/2) % MOD
  else
    x * pow(x, n-1) % MOD
  end
end

h, w, a, b = gets.chomp.split(' ').map{|x| x.to_i}
calc_fact(h+w-2)

ans = 0
for i in 1..(h-a)
  ans = (ans + (conv(i+b-2, i-1) * conv(h+w-b-i-1, w-b-1))) % MOD
end

print (ans)