The beloved Cookie Monster from Sesame Street has stumbled upon a table with sorted piles of cookies, each pile a positive integer. However, the monomaniacal obsessiveness of the Count who set up this crumbly fiesta has recently escalated to a whole new level of severity. The Count insists that these cookies must be eaten in the smallest possible number of moves. Each move chooses one of the remaining pile sizes p, and removes p cookies from every pile that contains at least p cookies (thus eradicating all piles with exactly p cookies), and leaves all smaller piles as they were.

Since the Count also has an unhealthy obsession with order and hierarchies, he expects these moves to be done in decreasing order of values of p. This function should return the list of moves, that allows Cookie Monster to scarf down these cookies. If there are a few optimal sequences of moves, choose the lexicographically largest one. Look at the example for [1, 2, 3, 4, 5, 6] input.

Input: List of integers (int).

Output: List of integers (int).

Examples:

assert cookie_monster([1, 2, 3]) == [2, 1]
assert cookie_monster([1, 2, 3, 4, 5, 6]) == [4, 2, 1]
assert cookie_monster([2, 3, 5, 8, 13, 21, 34, 55, 89]) == [55, 21, 8, 3, 2]
assert cookie_monster([1, 10, 17, 34, 43, 46]) == [46, 34, 17, 9, 1]

The above version of the Cookie Monster problem has been streamlined a bit to keep this problem simple enough to solve here. The more general problem formulation allows Cookie Monster to choose any subset of remaining piles, and remove the same freely chosen number of cookies from each pile in the chosen subset. Interested students can check out the article “On the Cookie Monster Problem” about the subtle complexities of the general problem formulation.

The mission was taken from Python CCPS 109. It is taught for Ryerson Chang School of Continuing Education by Ilkka Kokkarinen