Assume you are shopping and plan to spend exactly A dollars. You are interested in t items, each of them has unlimited supply and they are worth C1, C2, ..., Ct dollars accordingly. Design a dynamic programming algorithm to compute the number of ways to spend exactly A dollars. And explain its running time in details.

For example, when A = 4 and C = {1, 2}, you have three ways: {1, 1, 1, 1}, {1, 1, 2}, {2, 2}.