For this problem consider the problem of finding the maximum element in a list of integers. Maximum Integer in a List (MAX) Input: A list of integers A[a...b]. Output: A[i] for some a lessthanorequalto i lessthanorequalto b such that A[i] greaterthanorequalto A[j] for all a lessthanorequalto j lessthanorequalto b. Let M(A[a...b]) represent the output of the MAX problem on input A[a...b]. Let Max(a, b) be a simple function that returns the maximum of two elements. Let m = [a + b/2] be the midpoint between a and b. Below is a self-reduction for the MAX problem. State a recursive algorithm using pseudocode for finding the maximum element based on this self-reduction. M(A[a...b]) = {A[a] if a = b Max(A[a], M(A[a + 1...b])) if a b A[a] if a = b Max(A[m], Max(M(A[a...m - 1]), M(A[m + 1...b])) if a