Given integers BasePay and Bonus, a binary string schedule of length n where '1' means work and '0' means rest, and an integer k, you may change up to k zeros to ones. Pay rules: each workday earns BasePay; if day i and day i-1 are both workdays, you earn an additional Bonus for day i. Return the maximum total pay achievable after up to k flips. Describe your algorithm and analyze its time and space complexity.