Exercise $5.$ While studying hash tables, we implemented a version of Horner's rule for evaluating a polynomial in our lecture notes. Essentially, we have a polynomial of the form

$a_n{x}^n+a_{n-1}{x}^{n-1}+$dots$+a_2{x}^2+a_{1}x+a_0$

and we want to compute its value for a given $x.$ Implement a recursive version of the Horner's rule in C$++.$ You need to implement:

A function horner that

takes a vector where the coefficients $a_0,a_1,$dots,$a_n$ are stored, an int variable $n$ for the degree of the polynomial, and a double variable $x.$

computes the polynomial above for the given value of $x$ and returns it

A main function that reads the parameters $n,x,$ and the $n$ coefficients, makes a call to horner, and prints the output of evaluation.

Note: Full mark is only given to working codes.

$[10$ points$]$