Within a Python file named recursion fun.py$,$ write the following functions:

$($a$)(4$ points$)$ power$($b$,$ n$)$

Returns the value of bn for any numeric b and any integer n $($including negative integers$).$

Do not use any loops, and do not use any built$-$in ways of computing powers. This function

must be recursive. Hint: this is extremely similar to the power $2$ function that we wrote

in class.

$($b$)(4$ points$)$ count negatives$($stuff$)$

Returns how many negative integers $($i$.$e$.,<0)$ are contained in stuff. You may assume

that stuff is a list of integers. Do not use any loops, and do not use any built$-$in ways of

searching a list. This function must be recursive.

$($c$)(4$ points$)$ all short$($stuff$)$

Returns whether or not stuff contains only $$short$$ strings. We$$ll define a $$short$$ string

as being $8$ characters or less in length. If stuff is empty, this should return True. You

may assume that stuff is a list of strings. Do not use any loops, and do not use any

built$-$in ways of searching a list. This function must be recursive.

$($d$)(6$ points$)$ binary search$($stuff$,$ target$)$

Returns the index of target within the list stuff if it exists, or False if it doesn$$t exist.

You may assume that stuff is a sorted list of integers, and target is an integer. Do not

use any loops, and do not use any built$-$in ways of searching a list. This must be done

recursively; you can write a recursive helper function if needed.

$($e$)(6$ points$)$ After your function definitions in recursion fun.py$,$ write some tests for your

functions. Each test should call the function with specific argument$($s$)$ and print the return

value. Be sure to test at least the following scenarios:

$1$