Problem $2$:

$8**2=16pts$

A music streaming service manages playlists and user interactions. They need to perform specific operations on their data structures to enhance user experience.

Define a recursive function playlist$-$duration that takes two lists: songLengths and repeatCounts. The function should return a new list where each element is the total duration of the corresponding song after considering how many times it is repeated. If one list is shorter, assume the missing elements in repeatCounts are $1,$ and missing elements in songLengths are $0.$

$\backslash$table$[[$Sample Input: songLengths,Sample Input: repeatCounts,Sample Output$],[\text{'}(200180240),\text{'}(231),\text{'}(400540240)],[\text{'}(150220),,(3),\text{'}(450220)]]$

Define a recursive function cumulative$-$playlist$-$duration, which takes a list of song durations and returns a new list where each element represents the cumulative duration up to that point. If the cumulative sum at any point exceeds $1000,$ it should stop adding further songs to the playlist and ensure the last element in the list is $1000.$ You may use a helper function to handle the recursion.

$\backslash$table$[[$Sample Input: songDurations,Sample Output$],[\text{'}(200300400200),\text{'}(2005009001000)],[\text{'}(500600700),,(5001000)],[,(250250500300),(2505001000)],[\text{'}(800200100),\text{'}(8001000)],[,(1001100),,(1000)]]$