In class, we discussed a stack with three operations: Push, Pop, and MultiPop(k). The MultiPop(k) operation is implemented as a series of k pops. Push and Pop each take 1 unit of time, and MultiPop(k) takes k units of time. Using amortized analysis, we determined that the average cost of an operation, over n operations, was 2 units of time. Suppose we modify this stack and now, 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 (they can no longer be popped after they are backed up). Writing k elements to the hard drive takes k units of time, and deleting all k elements also takes k units of time. 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. State your answer in terms of the average cost per operation, in dollars (that is, do not use big-O notation).