Algorithm $3.$ Double Loop

Input:array A of n items, some constant k

$1$: function DOUBLE$-$LOOP$($A$)$

$2$: for i $=1$ to n do

$3$: for j $=1$ to k do

$4$: some costly calculation involving only Ai

$5$: some calculation involving Ai and Aj

$6$: return something

$($a$)[5$ points$]$ Using the tightest asymptotic representation, from $\backslash$Theta $,$ O$,$ or $\backslash$Omega $,$ derive the asymptotic time

complexity of the loop above.