Egg carton packer

Pack egg orders into cartons for a farm stand and report what is left on the shelf.

The stand sells eggs in two carton sizes: a dozen carton holds 12 eggs and a half-dozen carton holds 6. Eggs are never sold loose and cartons are never left partly packed on purpose, but a carton may be only partly full if the order does not fill it.

For an order of n eggs, choose the cartons as follows:

1. Use the fewest cartons whose total capacity is at least n.
2. If several choices use that many cartons, take the one with the smallest total capacity (the least wasted space).

(For example, 7 eggs go into one dozen carton, 13 eggs into one dozen and one half-dozen.)

Orders are handled one after another. If the stand does not have all the cartons the chosen packing needs, the order is refused: nothing is taken from the shelf for it, and the stand does not substitute other cartons (two half-dozens never stand in for a dozen). Later orders are still handled.

Input: dozens and halves, the number of dozen and half-dozen cartons in stock at the start; orders, a list of egg counts in the order received.

Output: a list [dozens_left, halves_left, refused]: the cartons left after all orders and the number of refused orders.