module Exercise_6 where

import Data.Ratio

-- Could have been implemented using find and Data.Maybe, but I kinda like the fact
-- that this requires no additional imports.
traceFractran :: [Rational] -> Integer -> [Integer]
{-WETT-}
traceFractran xs n = n:if null y then mempty else traceFractran xs . numerator $ head y
        where y = fmap (==1) denominator `filter` map (* toRational n) xs
{-TTEW-}