In the introductory lecture on Divide and Conquer, an example algorithm for using divide and conquer for multiplication of integers was given, along with an optimization under the assumption that the second parameter, b$,$ was even.

$(5$ pts$)$ Considering the optimized version, for what input values will the algorithm work? Will it work for any even b$,$ or is the restriction more significant than that. Why is this the case?

$(5$ pts$)$ Adjust the optimized algorithm so that it will work for arbitrary integer values of b$.$ Prove, or at least argue, the correctness of your approach. The algorithm should retain

worst case performance.