Consider the following program that runs on input $n$ :

Set $S=1,$ and $k=1$

while $kn$

$($a$)$ Replace $S$ with $2S$

$($b$)$ Replace $k$ with $k+1$

endwhile

Print $S$

$($a$)$ How many steps does the program take $($as a function of $n)?$ Explain your reasoning.