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: Accepted)

import Data.Bits
import qualified Data.Vector.Unboxed as VU

modulus :: Int
modulus = 10 ^ 9 + 7

modulus' :: Integer
modulus' = 10 ^ 9 + 7

addMod :: Int -> Int -> Int
addMod x y = (x + y) `mod` modulus

mulMod :: Int -> Int -> Int
mulMod x y = (x * y) `mod` modulus

powMod :: Int -> Int -> Int
powMod _ 0 = 1
powMod n m
    | m .&. 1 == 0 = mulMod x x
    | otherwise = mulMod n . powMod n $ m - 1 where
          x = powMod n $ m `div` 2

createFacts :: Int -> VU.Vector Int
createFacts n =
  VU.scanl (\x y -> if x == 0 then 1 else mulMod x y) 1 (VU.enumFromTo 1 $ n - 1)


invFacts :: Int -> VU.Vector Int -> Int
invFacts 0 facts = 1
invFacts x facts =
  if x == 0 then 1 else powMod ((facts VU.! x) `mod` modulus) (modulus - 2)

cmb :: Int -> Int -> VU.Vector Int -> Int
cmb x y facts = (facts VU.! (x + y)) `mulMod` ((invFacts x facts) `mulMod` (invFacts y facts))

routesVia :: Int -> Int -> Int -> Int -> VU.Vector Int -> Int
routesVia x y w h facts =
  (cmb x y facts) `mulMod` (cmb x' y' facts)
  where
    x' = w - x
    y' = h - y

allRoutes :: Int -> Int -> Int -> Int -> VU.Vector Int -> Int
allRoutes h w a b facts =
  sum $ map (\x -> routesVia (b + x) (h - a - 1 - x) (w - 1) (h - 1) facts)  [0..min (h - a -1) (w - b - 1)]

main = do
  [h, w, a, b] <- map (read :: String -> Int) . words <$> getLine
  let facts = createFacts(h + w - 1)
  let r = allRoutes h w a b facts
  putStrLn $ show $ r `mod` modulus