import Data.List
import Data.Char
import Data.Ratio
import Data.Array hiding (index)

bernoulli :: Integer -> Rational
bernoulli n = b (fromIntegral n)
  where b 0 = 1%1
        b 1 = -1%2
        b m | mod 2 m == 1 = 0
            | otherwise = sum [(choosef m k) * (bernoullis!k) / (fromIntegral (k-m-1)) | k <- [0..m-1]]
        bernoullis = listArray (0, fromIntegral n) [b (fromIntegral k) | k <- [0..n]]
        choosef m k = (facts!m) % ((facts!k)*(facts!(m-k)))
        facts = listArray (0, n) [f (fromIntegral k) | k <- [0..n]]
        f 0 = 1
        f m = m * (facts!(m-1))