You are given an integer array prices where prices[i] is the price of a stock in dollars on the ith day, and an integer k. You are allowed to make at most k transactions, where each transaction can be either of the following: Note that you must complete each transaction before starting another. Additionally, you can't buy or sell on the same day you are selling or buying back as part of a previous transaction. Return the maximum total profit you can earn by making at most k transactions.