Problem 3. The Fibonacci k-step numbers are a generalization of the Fibonacci and Tetranacci sequences, where F_i = 0 for i 0, F₁ = 1, F₂ = 1, and for every j 3:

F_j = F_j1 + F_j2 + + F_jk,

i.e. F_j is the sum of the k previous numbers in the sequence. You will implement an OCaml function fib_k_step : int -> int -> int for computing these numbers efficiently.

(a) Implement an OCaml function sum_top k : int -> int list -> int, which accepts an integer k along with a list of integers, and sums up the first k elements of the list. If the list has length less than k, simply sum all the elements in the list (assume that an empty list evaluates to a sum of 0).

Starter Code:

let rec sum_top_k (k : int) (xs : int list) : int =