Problem 1: Suppose we have a standard stack with Push and Pop operations, each costing 1 unit of time. In addition, for backup purposes, every time the stack reaches k elements, we write a copy to the hard drive (here k is some fixed value specified by the user) and delete all elements from the stack. Writing to the hard drive takes k units of time (1 unit of time per element), and deleting all elements takes an additional k units of time (1 unit of time per element). Consider a sequence of n operations, and perform an amortized running time analysis to find an upper bound on the average length of time that each operation can take. Report your answer in units of time, not big-O notation.