module Exercise_6 where

import Data.Ratio
import Data.List

{-WETT-}
traceFractran :: [Rational] -> Integer -> [Integer]
traceFractran f n =
  case (find (\x -> numerator x * n `mod` denominator x == 0) f) of 
    Just fract -> n:(traceFractran f (numerator fract * n `div` denominator fract))
    Nothing    -> [n]
{-TTEW-}