Consider the following Python function where $L$ is a list of numbers, $x$ and $y$ are the indices of $L.$ It can be assumed that in the initial call to $S,x=0$ and $y=$len$(L)-1$ :

def $S(L,x,y)$ :

if $x>y$ :

return $0$

elif $x=y$ :

return $L[x]$

else:

$m=\frac{x+y}{\frac{?}{?}}2$

return $S(L,x,m)+S(L,m+1,y)$

HINT: If you are having problems with this question, it is suggested that you use a global variable to track the print statements. Solving this problem will require you to employ approaches that is different from the lectures.

A$.$ Write a recurrence relation for the above function that indicates the number of times the function $S$ is called. Please irclude the base case as $d_1$ and the recursive case as $d_k.$

B$.$ If the input to the function is that the length of $L$ is $2024.$ How many times does the function S get called? HINT: It is better to complete $4C$ before answering this question.

C$.$ Solve for the above recurrence relation by finding the analytical formula $d_n$ where $n$ is the length of $L.$