import Data.Ratio
import Data.List
import Data.Char

bernoulli :: Integer -> Rational
bernoulli n
 |n==0 = fromIntegral 1
 |otherwise = last (bern n [1] 1)
 where bern y xs nn |length xs -1== fromIntegral y = xs
                 |otherwise =  bern y (xs ++ [sum[(choose nn (k-1))%(k-nn-2)*(last (take (fromIntegral k) xs))|k<-[1..nn]]]  ) (nn+1)

choose :: Integer ->  Integer ->  Integer
n `choose` k = product [n-k+1..n] `div` product (enumFromTo 1 k)