Maximum sum subset of an array with an extra condition

Question

We are given numbers $n \leq 200$, $k \leq 10$ and an array of $3n$ positive integers not greater than $10^6$. Find the maximum possible sum of a subset of elements of this array, such that in every contiguous $n$ elements there are at most $k$ chosen.

As this is an old high-school level contest problem, I ask for some hints. Also, this means I know there exists a solution far quicker than the proposed by D.W. and most likely not very complicated, so the question is still open.

My ideas mostly involved dynamic programming. I was trying to calculate, for each prefix of the array, best score we can acquire. However, in order to do this, I think I would need to calculate it for every prefix, and every possible choosing of $k$ numbers in the last $n$ numbers of this prefix, resulting in complexity $O(n^{k+1})$, which is far from acceptable. Also, I thought of looking at pairs of positions in the array which are distant by $n$ and their relation to each other, but this approach fails, as in an optimal solution not in every contiguous $n$ element we would choose exactly $k$, sometimes it could be less.