Consider the following instance of the knapsack problem. Let the knapsack size be K = 14. There are n = 6 items. Each item is represented by a pair of integers, where the first integer indicates its size and the Second integer indicates its value. Here are the items: (6,5),(4,3),(2,1),(7,3),(4,10),(12,6). Build the dynamic programming table to solve the following two problems:

(a) Find a subset of items whose total size is K, and whose total value is maximized.

(b) Is there a subset of items whose total size is exactly K?