import Data.List
import Data.Ratio

chooose :: Integer -> Integer -> Integer
chooose' n 0 = 1
chooose' 0 k = 0
chooose' n k = if k * 2 > n then chooose n (n-k) else chooose n k
chooose n 0 = 1
chooose 0 k = 0
chooose n k = chooose (pred n) (pred k) * n `div` k


bernoulli :: Integer -> Rational
bernoulli n = sum [sum [s v * chooose' k v * v^n | v <- [0..k]] % (succ k)| k <- [0..n]]
    where s n = if odd n then -1 else 1