Write an efficient algorithm for the following problem, 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: Triples
• Input: A set S of 3k positive integers and an integer B.
• Output: Print Yes - if S can be split into k triples such that each triple sum to B. Print No - if no such set exists.
• Example: Input: A = [4,7,2,3,4,4]. B = 12. Output: Yes (because of triples (7,2,3), (4,4,4) )
• Example: Input: A = [1,7,2,3,1,3]. B = 8. Output: No