You have n files with data on your hard drive, files have sizes m1 GB,…,mn GB. You want to save them on clouds for backup. You have accounts on K file hosting services. On each of these services first p GB are free, and you have to pay if you exceed the limit. You want to save your files on that clouds in such a way that you do not have to pay for additional space. Is it possible to do so? If the answer is yes, how to do it?

Represent this problem as an algorithmic problem. What is this algorithmic problem? Is it possible to solve it in a polynomial time? What algorithm would you use to find a solution? Explain you answers.