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: Time Limit Exceeded)

import Data.Array.IArray
main = do
    [h,w,a,b] <- return . map (read::String->Int) . words =<< getLine
    let	basicArray::Array (Int,Int) (Int,Int)
	basicArray = listArray ((1,1),(h,w))
			[(ro,co) | ro<-[1..h], co<-[1..w]]
	memz = 
	  let
	    zenka (r,c)	| r<=h-a    = ((fact $ c-1+r-1) `div` fact (c-1)) `div` fact (r-1)
			| c==b+1    = memz (r-1,c)
			| otherwise = memz (r,c-1) + memz (r-1,c)
	      where
		fact::Int->Integer
		fact 0 = 1
		fact n = toInteger n*fact (n-1)
	    zarray = amap zenka basicArray
	  in (zarray!)
    print $ memz (h,w) `mod` (10^9 + 7)