module Exercise_6 where

import Data.Ratio
import Data.List (find)
import Data.Ratio (Ratio, (%), denominator)

{-WETT-}
traceFractran :: [Rational] -> Integer -> [Integer]
traceFractran fracts n = n :
  case find (\f -> n `mod` denominator f == 0) fracts of
    Nothing -> []
    Just f -> traceFractran fracts $ truncate (fromIntegral n * f)
{-TTEW-}