The following function divides one integer by another by the rather dubious process of making a series of random guesses until it happens to guess correctly.

int idiv$($int x$,$ int y$)\{$

$//$ Compute x $/$ y

if $($x $<=0)$

return x;

int k $=$ rand.nextInt$($x$+1)$;

while $(!($k$*$y $<=$ x && $($k$+1)*$y $>$ x$))$

k $=$ rand.nextInt$($x$+1)$;

return k;

$\}$

Assume that rand.nextInt$($n$),$ each time that it is called, returns a randomly selected integer in the range $0..$n$-1,$ inclusive, with every integer in that range being equally likely to occur on any given call, and that each nextInt$($n$)$ call runs in O$(1)$ time.

What is the average$-$case complexity of this function?

Group of answer choices

O$(1)$

O$($x$)$

O$($y$)$

O$($n$)$

O$($x $/$ y$)$

O$($log x$)$

O$($log y$)$

None of the given answers are correct.