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 = alldims ds $ minimum ds

alldims :: [Integer] -> Integer -> [Integer]
alldims _ 0 = [] 
alldims xs min
        | any odd xs = pr : half 
        | otherwise = 0 : half    
        where   pr = product xs - product (map (\x -> if odd x then x-1 else x) xs)
                half = alldims (map (`div` 2) xs) (min `div` 2)              
{-TTEW-}