1. (6 pointsIn each of the following two parts, give a O-bound for k as a function of n: (a) n = k log2 k; (b) n = kk. Only your final answer will be graded in each case. Hints: As an example, if n = ka + 100k log2 k, then k = O(Vn). For parts (a) and (b), the answers are less obvious. One way to proceed is to make an educated guess and then iteratively refine it. For example, in part (a), since log2 k grows a lot more slowly than k, we might start out by guessing that k = O(n). But if k = O(n), then the RHS is (n log n), which grows faster than the LHS. This means that we should refine our initial guess by choosing a function that is o(n). Your successive guesses need not be chosen haphazardly. For example, a more systematic approach might take into account the ratio between the current RHS (i.e., the RHS associated with the current guess) and the LHS