Direct Recursion occurs when a method calls itself $($i$.$e$.$ method f calls f$).$ Indirect Recursion however occurs when a method calls another one, which in return calls the first one $($directly or indirectly; i$.$e$.$ f calls g$,$ which calls f$,$ or f calls g$,$ which calls h$,$ which calls f$).$ Consider the use of an indirect recursive method called fun$($int n$),$ which accepts a positive integer n $>=2$ and is defined as follows:

int fun $($int n$)\{$ if $($n $<=2)$ return $1000$; else return fun$2($n$-5)$ ;$\}$ where fun$2$ is defined as follows:

int fun$2($int n$)\{$ if $($n $<=2)$ return $200$; else return $5*$ fun$3($n$-2)$;$\}$ where fun$30$ is defined as follows:

int fun$3($int n$)\{$ if $($n $<=2)$ return $10$; else return $3*$ fun $($n$+3)$;$\}$

Assume recursive frames are stored on a stack. Given a value k $>=100$ as a parameter to fun$10,$ which of the following is the most accurate?

$$The method will result in stack growth of size $0($log k$).$

$$The method will result in stack growth of size $0($k$).$

$$The method will result in stack growth of size $0($k$\}).$

$$Regardless of the value of k$,$ recursion calls will never end, resulting