Given two lists A of size m and B of length n, our goal is to construct a list of all elements in list A that are also in list B. Consider the following two algorithms to solve this problem. Initialize an empty list L. SORT* list B. for each item a A, if BinarySearch(a, B) notequalto 0 then Append a to list L. return L procedure Search2(List A of size m, List B of size n) Initialize an empty list L. for each item a A, if LinearSearch(a, B) notequalto 0 then Append a to list L. return L (a) Determine the runtime of Search1 in Theta notation, in terms of m and n. (b) Determine the runtime of Search2 in Theta notation, in terms of m and n. (c) When m Theta(1), which algorithm has an asymptotically faster runtime? (d) When m Theta(n), which algorithm has an asymptotically faster runtime? (e) Find a function f(n) so that when m Theta(f(n)), both algorithms have equal runtime asymptotically