Let S, f , and g be as defined in Question 1 above. Design and analyze an algorithm that takes as input a positive integer k and computes f (k). Assume that the word size of the machine running your algorithm is O(g(k)) bits, and that the machine can add or multiply two word-sized integers in a single time step. Your algorithm should use O(g(k)) words of memory and run in O(k log k) time.