import Data.Maybe (isJust, listToMaybe)
-- Find linear combinations of positive integers
solve :: Integer -> [Integer] -> Maybe [Integer]
-- If we've made it to the end with zero left, good!
solve 0 []     = Just []
-- Otherwise, this way isn't the way to go.
solve _ []     = Nothing
-- If one of the elements of the input list is zero, just multiply that element by one.
solve n (0:xs) = case solve n xs of
                      Nothing -> Nothing
                      Just ys -> Just (1:ys)
solve n (x:xs) =   listToMaybe                    -- take first solution if it exists
                 . map (\ (m, Just ys) -> m:ys)   -- put multiplier at front of list
                 . filter (isJust . snd)          -- remove nonsolutions
                 . zip [1 ..]                     -- tuple in the multiplier
                 . map (\ m -> solve (n - m) xs)  -- use each multiple
                 $ [x, x + x .. n]                -- the multiples of x up to n
 
main = mapM_ print [solve 11 [1, 2], solve 1 [1, 2]]

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