Let n be a nonnegative integer. We are given a list A = a_1, ..., a_n of n positive integers and a positive integer x. We will compute the number of list elements that are factors of x. Here is a recursive algorithm to solve this problem, where % is the modulus operator. HowManyFactors (A list of n positive integers, x: positive integer) if n = 0 then return 0 B:= a_1, a_2, ... a_n-1 if x % a_n = 0 then return 1 + HowManyFactors (B, x) return HowManyFactors (B, x) Prove that this algorithm correctly returns the number of elements in the list A that are factors of x. Let T(n) be the running time of this algorithm. Write a recurrence relation that T(n) satisfies. Assume that the list A is stored in a data structure such that removing an element from the list takes time linear in the number of list elements. Use your answer to part (b) find the runtime of this algorithm in theta notation