module Exercise05 where
import Data.Bits ( Bits(shiftL, shiftR) )
-- 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 [] = []
decompose ds = decomposeRec ds (product ds) (length ds)

decomposeRec :: [Integer] -> Integer -> Int -> [Integer]
decomposeRec _ 0 _              =  []
decomposeRec ds size dim        = (size - shiftL newsize dim) : decomposeRec inner newsize dim 
    where       newsize  = product inner
                inner    = map ( `shiftR` 1) ds
{-TTEW-}