Write an efficient algorithm for the problem below, briefly describe why it is a correct algorithm, and analyze the time complexity. If you cannot find any polynomial-time algorithm, then give a backtracking algorithm.

• Problem: Split Into Two
• Input: A set S of positive integers.
• Output: Print Yes - if there is a subset A of S such that the sum of the numbers in A is equal to the sum of the numbers in (S \ A). Print No - if no such set exists.
• Example: Input: A = [4,7,5,4,4]. Output: Yes (because A = {7,5} and (S\A) = {4,4,4})
• Example: Input: A = [1,7,5,7,3]. Output: No