module Exercise05 where
 
import Data.List (product)
import Data.List (minimum)

-- May or may not be useful: computes the logarithm base 2 (rounded down) of the given number.
-- You don't have to move this into the WETT tags if you want to use it.
log2 :: (Integral a, Num b) => a -> b
log2 = let go acc n = if n <= 1 then acc else go (acc + 1) (n `div` 2) in go 0


{-WETT-}
decompose :: [Integer] -> [Integer]
decompose ds 
        | product ds == 0 = []
        | otherwise =  helpDecompose ds 0 (log2 (minimum ds)) (length ds)

helpDecompose :: [Integer] -> Integer -> Integer -> Int -> [Integer]
helpDecompose ds sum exponent dimension
        | exponent == 0 = [(product ds - sum) `div` 1]
        | otherwise = helpDecompose ds (sum + x*((2^exponent)^dimension)) (exponent-1) dimension ++ [((getProdukt ds (2^exponent)) - sum) `div` ((2^exponent)^dimension)] 
        where x = ((getProdukt ds (2^exponent)) - sum) `div` ((2^exponent)^dimension)

getProdukt :: [Integer] -> Integer -> Integer
getProdukt ds number = product [(x `div` number)*number | x <- ds]
{-TTEW-}