Notation: N denotes the set of natural numbers {0, 1, 2, R:r> 1 ), R+-(z e R : r > 0), and R21-( 1. In the binary-search problem we take as input a sorted array A with n elements, and a key k and we return the largest element in A which isn't strictly greater than k. That is we return max(z E A:k).orNIL if all z E A satisfy>k. Write a pseudocode for binary search that uses recursion and where the number of key comparisons is proportional to log (