module Exercise05 where
import Data.List
-- 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 
        |0 `elem`ds =[]
        | otherwise = decompose2 ds (biggest ds) 0

decompose2 ::[Integer]->Integer->Integer->[Integer]
decompose2 ds y x
        |y==1 =[biggest2 ds y-x]
        |otherwise = decompose2 ds (y`div`2) (b*2^length ds)++[b-x]
        where b =biggest2 ds y

biggest ::[Integer]->Integer
biggest ds= 2^minimum [log2 y| y<-ds]

biggest2 ::[Integer]->Integer->Integer
biggest2 ds x =product [y `div` x| y<-ds]

{-TTEW-}