Project Euler Problem 053

import Data.List

nck :: Integral a => a -> a -> a
nck n k = product [n-k+1..n] `quot` product [1..k]
ans1 :: Int
ans1 = length $ filter (>1000000) [nck n k | n<-[1..100],k<-[1..100::Integer]]
count :: Integral b => b -> b -> b
count maxn limit= imp maxn 0 where
  imp n r = case over n r of
    Nothing -> 0
    Just r' -> (n - 2*r'+1) + imp (n-1) r'
  over n r = find ((>limit).(nck n)) [r..(maxn`quot`2)]
ans2 :: Integer
ans2 = count 100 1000000
--4075
main :: IO ()
main = print ans1