-- divide rounding up
(/^) :: Int -> Int -> Int
x /^ y = (x + y - 1) `div` y

-- all values must be at positive, must be sorted by descending value!
test = reverse [(1,7), (2,4), (3,2), (4,2)] :: [(Int, Int)]
target = 7 :: Int

-- Given the remaining input, current partial solution and remaining target
-- returns a possible skinny pack represented by its multiplicities in the list
-- monad.
skinnies :: [(Int, Int)] -> [(Int, Int)] -> Int -> [[(Int, Int)]]

-- leaf case, need to cover the bin without any extra
skinnies [(v,m)] cs t | t /^ v <= m = return ((v,max 0 (t/^v)) : cs)
                      | otherwise = []

skinnies ((v,m) : vms) cs t = do
  c <- [0 .. t /^ v]  -- don't pick more than necessary
  skinnies vms ((v,c) : cs) (t - c * v)