a) Suppose L[0:n 1] is a sorted list of distinct integers (negative integers allowed). Design (describe at a high level, then give pseudocode) and analyze (best- and worst-case complexities) an algorithm similar to Binary Search that finds a fixed point, i.e., an index i such that L[i] = i or returns -1 if no such index exists. b) Prove (by mathematical induction) the correctness of the algorithm you have given in part a).