Let A be an array of n arbitrary and distinct numbers. A has the following property: If we imagine B as being the sorted version of A, then any element that is at position i in array A would, in B, be at a position j such that |i j| k. In other words, each element in A is not farther than k positions away from where it belongs in the sorted version of A. Suppose you are given such an array A, and you are told that A has this property for a particular value of k (that value of k is also given to you). Design an O(n log k) time algorithm for sorting A. Briefly explain why your algorithm is correct.