Suppose you have two separate sorted arrays of numbers, A[1... m] and B[1... n], where all the numbers in A and B are distinct. Given an integer k where 1sksm+ n, design an algorithm that finds the kth smallest element in the merge of arrays A and B in O(lg k) time. (Note: Explicitly merging the sorted arrays A and B will take 0(m + n) time, which is too much. Your algorithm, from the point it receives the unmerged arrays A and B, to the point at which it outputs the kth smallest element, must run in Olg k) time.) In your solution, be sure to: a. present your algorithm using prose and pictures and b. analyze the running time of your algorithm