$5.(5)$ Let A$[1..$n$]$ be an array of n elements. Suppose it is known that A is unimodal, that is$,$ A$[$i$]$ is strictly increasing up to some index M$,$ and is strictly decreasing for indices i $>$ M$.$ Thus A$[$M$]$ is the maximum $($note that M may be $1$ or n$).$ Design a recursive O$($log n$)$ algorithm to find M in A: $($a$)$ describe your algorithm in English; $($b$)$ Show your algorithm takes O$($log n$)$ time