We are given a sequence of n positive numbers a1, . . . , an and a fixed number k > 0. We want to find a pair of numbers ai and aj such that j > i and aj ai = k. If there is no such pair we want to output false. This can be solved easily in (n^2) time by examining all pairs of numbers. Your task is to give a divide and conquer algorithm that runs in O(nlogn) time. Show the correctness of your algorithm and the analysis of its running time.