module Exercise05 where

-- 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
 | m == 0 = []
 | otherwise = cnt:(decompose (map (`div` 2) ds))
 where 
   m = product ds
   calc :: [Integer] -> Integer -> Integer
   calc [] _ = 0
   calc _ 0= 0
   calc (x:xs) k
    | mod x 2 == 0 = calc xs k
    | otherwise = (div k x) + (calc xs ((x-1) * (div k x)))
   cnt = calc ds m
{-TTEW-}