Best Time to Buy and Sell Stock IV

You are given an integer array `prices` where `prices[i]` is the price of a given stock on the `ith` day, and an integer `k`. Find the maximum profit you can achieve. You may complete at most `k` transactions. Note: You may not engage in multiple transactions simultaneously (i.e., you must sell the stock before you buy again). Example 1: Input: k = 2, prices = [2,4,1] Output: 2 Explanation: Buy on day 1 (price = 2) and sell on day 2 (price = 4), profit = 4-2 = 2. Example 2: Input: k = 2, prices = [3,2,6,5,0,3] Output: 7 Explanation: Buy on day 2 (price = 2) and sell on day 3 (price = 6), profit = 6-2 = 4. Then buy on day 5 (price = 0) and sell on day 6 (price = 3), profit = 3-0 = 3. Constraints: `0 <= k <= 100` `0 <= prices.length <= 1000` `0 <= prices[i] <= 1000`