When we search in Google for "A B C D" this is equivalent to searching for "A AND B AND C AND D", i. e. searching for all documents that contain all four keywords A, B, C and D. We ask you to design an algorithm that does so efficiently. The first thing a search engine does is to generate a hit-list for each keyword. A hit-list is a sorted sequence of document-identifiers (doc-id’s) that contain the keyword in question. Let the hit-lists be in the form of sorted arrays A[1..a], B[1..b], C[1..c], D[1..d] of doc-id’s for the four keywords respectively. Let the lengths of the arrays A, B, C and D be respectively a, b, c, d, where a = n 3 , b = n lg n, c = n 2 and d = n for some parameter n. Give an efficient algorithm that generates the hit-list of doc-ids in which all four keywords A, B, C, D appear; this output hit-list should also be sorted by doc-id. How big is the output hit-list ? Express your answer in asymptotic notation in terms of n with a bound that is as asymptotically tight as possible. Express the running time of your proposed efficient algorithm in terms of n using asymptotic notation (as tight as possible).