Suppose you are given an algorithm BinRep$($b$)$ that generates the binary representation of a given decimal integer b with time complexityGiven n in NOand$($loga$,$bb$).$ in N we want to compute

$f_{a,b}(n)=a^{3^n},$modb;

that is a to the power of $3$n modulo b$.$

i$.$ Write pseudocode for an algorithm to compute fa$,$b$($n$).$

ii$.$ Determine the efficiency class of the time complexity of your algorithm in item $($i$)$ for fa$,$b$($n$),$ when a$,$b are fixed natural numbers.

iii. Compute

$f_{2,21}(8)=2^{3^8},$mod$21$

using either your own algorithm in the previous part or the binary$-$exponentiation algorithm. Trace your steps while computing f$2,21(8)$ for this question.