You are given a sorted array A$[1...$ n$]$ of n distinct integers. Describe a recursive algorithm that decides, in O$($log n$)$ time, if there is an index i such that A$[$i$]=$ i$.$ If such an index exists, the algorithm returns one such index. Otherwise, the algorithm returns No$.$You may describe your algorithm in plain English or in pseudocode. Justify the correct$-$ ness of your algorithm and explain why the running time is O$($log n$).$ You may use any result that was proven in cla