Given a positive integer $n,$ i$.$e$.,n>0,$ and a radix $r,$ where $r2,$ the following pseudo$-$code computes the number of symbols required to represent $n$ with radix $r.$ Note that $r$ is an integer.

Run$-$time per instruction Frequency

num symbols larr$1$

$C_1$

while $nr$

nlarr$\frac{n}{r},C_3$

num$\_$symbols larr n$$m$\_$symbols $+11$ i $C_4$

$($a$)$ Fill in for each line of instruction, the number of times $($i$.$e$.,$ frequency$)$ the instruction is executed.

$($b$)$ Derive the expression for the run$-$time of the pseudo$-$code in terms of $n,r,$ and $C_1,C_2,C_3,$ and $C_4.$

See questions $1$ and $2$ on how the final expression should be written. The parameters "describing" the problem are $n$ and $r.$