Let$$s say that you are playing a game where you are hopping along a path with n spaces. For each space i$,$ you get a reward of vi points for landing on space i$.$ Each turn you can hop up to $5$ spaces and you are trying to maximize the total amount of points you earn. However, you must reach the end of the path within k hops or you lose the game. What is the maximum total number of points you can earn and which hops should you make to achieve this maximum?

Give a polynomial time algorithm for this problem, explain why your algorithm is correct, and analyze its runtime.

NOTE: the k constraint of max jumps is very important and makes this problem signficantly harder