module Exercise_6 where

import Data.List
import Data.Ratio

{-WETT-}
traceFractran :: [Rational] -> Integer -> [Integer]
traceFractran rs n
  | Just ff <- tmp = n : traceFractran rs (numerator ff)
  | otherwise = [n]
  where
    tmp = find ((== 1) . denominator) $ map (* (n % 1)) rs

{-TTEW-}
isPowerOfTwo 1 = True
isPowerOfTwo x
  | x `mod` 2 == 0 = isPowerOfTwo (x `div` 2)
  | otherwise = False