a$.$ What is the time efficiency of the brute$-$force algorithm for computing

$a^n$ as a function of $n?$ As a function of the number of bits in the binary

representation of $n?$

b$.$ If you are to compute $a^n$modm where $a>1$ and $n$ is a large positive integer,

how would you circumvent the problem of a very large magnitude of $a^n?$