Could you please solve it using dp and provide the presucode (written by yourself ) and running time.

thank you

Here is yet another variation on the change-making problem (Exercise 6.17). Given an unlimited supply of coins of denominations zi,T2, ...-n , we wish to make change for a value v using at most k coins; that is, we wish to find a set of 3 k coins whose total value is v. This might not be possible: for instance, if the denominations are 5 and 10 and k = 6, then we can make change for 55 but not for 65. Give an efficient dynamic-programming algorithm for the following problem. 1,72,.. ,^n, Input:....Tn; k; . Question: Is it possible to make change for v using at most k coins, of denominations ,z