a. Find an algorithm for solving the following problem: Given a positive

integer n, find the list of positive integers whose product is the largest

among all the lists of positive integers whose sum is n. For example, if

n is 4, the desired list is 2, 2 because 2 2 is larger than 1 1 1 1,

2 1 1, and 3 1. If n is 5, the desired list is 2, 3.

b. What is the desired list if n 2001?