You are given three arrays A[1 : n], B[1 : n], and C[1 : n] of positive integers. The goal is to decide whether or not there are indices i, j, k [1 : n] such that A[i] B[j] = C[k]; in other words, is it the case that there are numbers in A and B whose multiplication belongs to C. Examples: When n = 3, and A = [1, 3, 4], B = [2, 3, 5], and C = [1, 3, 5], the answer is Yes, because for instance we have A[1] B[3] = C[3] or A[1] B[2] = C[2]. When n = 3 and A = [1, 3, 4], B = [2, 4, 6], and C = [7, 9, 11], the answer is No. (a) Suppose all the numbers in C belong to the set 1, 2, . . . , n2 . Design and analyze an algorithm with worst-case runtime of O(n 2 ) for the problem in this case. (b) Now suppose C can be any arbitrary array of n integers. Design and analyze a randomized algorithm with expected worst-case runtime of O(n 2 ) for the problem in this case. Note: Actually, this problem also has a deterministic algorithm that runs in worst-case O(n 2 ) time. But you do not need to design such an algorithm for this problem (although if you do, you will receive the full credit for both parts (a) and (b)).