We are given a non-negative integer n and an array P[1..n] of prices. We wish to cut the rod into a number of pieces whose lengths sum to n in order to sell the pieces. We are paid P[i] for selling a piece of length i. Our goal is to find the maximum total selling price for our pieces of rod. Consider a variant of the problem where we can cut the rod into at most k pieces where k ≤ n is given as part of the input. Describe an efficient algorithm for this version of the problem.