CMO 2019 Problem 4

Let $n$ be an integer greater than 1 , and let $a_{0}, a_{1}, \ldots, a_{n}$ be real numbers with $a_{1}=a_{n-1}=0$. Prove that for any real number $k$,

$$\left|a_{0}\right|-\left|a_{n}\right| \leq \sum_{i=0}^{n-2}\left|a_{i}-k a_{i+1}-a_{i+2}\right|$$