Suppose you are given a new hardware device that can merge k > 2 different sorted lists of total size n into a single sorted list in O(n) time, independent of the value of k. Such a device could, for example, be based on a hardware streaming system or could be based on a network protocol. Show that you can use this device to sort n elements in O(n log n / log k) time. That is, if k is Θ(√n), then you can use this device to sort in linear time.