module Exercise_6 where

import Data.Ratio
import Data.List

{-WETT-}
traceFractran :: [Rational] -> Integer -> [Integer]
traceFractran fractions x = x : if null muls then [] else traceFractran fractions $ truncate $ head muls
    where muls = filter whole $ map (* (x % 1)) fractions
          whole x = ceiling x == floor x
{-TTEW-}