Provide a dynamic programming solution to the problem by following the described steps:

We are given n types of coin denominations with integer values V1, V2, ..., Un. Given an integer t, we would like to compute the minimum number of coins to make change for t (i.e., we would like to compute the minimum number of coins that add up to t, where repetitions are allowed). We know that one of the coins has value 1, so we can always make change for any amount of money t. For example, if we have coin denominations of 1, 2, and 5, then the optimal solution for t = 9 is 5, 2, 2. Steps: (i) Identify the last question you need to answer in developing a solution. *(ii)* Define and prove optimal substructure. (iii) Define subproblems, express the solution to the overall problem in terms of the subproblems. (iv) Formulate a recursive solution to the subproblems. Do not forget to specify the base case(s). (v) Characterize the runtime of the resulting procedure assuming that you would implement your solution using a bottom-up procedure. *(vi)* Provide the pseudo code of the bottom-up procedure you use to compute the value of the optimal solution, as well as the procedure for reconstructing the optimal solution