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 Haskell (GHC 7.10.3) (judge verdict: Wrong Answer)

import Data.Array

po :: (Integral a) => a
po = 10^9 + 7

main :: IO ()
main = do
  [h, w, a, b] <- map read . words <$> getLine
  let
    fact = array (0,h+w) ((0,1) : [(i, i*fact!(i-1) `mod` po) | i <- [1..h+w]])
    combi n m = if m == 0 then 1 else (fact ! n) `div` (fact ! m) `div` (fact ! (n-m))
  print $ sum [combi (h-a-1+i) i * combi (w-1-i+a-1) (a-1) | i <- [b..(w-1)]] `mod` po