OBM 2022 Problem 3

Let $\{a_n\}_{n=0}^{\infty}$ be a sequence of integers numbers. Let $\Delta^1a_n=a_{n+1}-a_n$ for a non-negative integer $n$ . Define $\Delta^Ma_n= \Delta^{M-1}a_{n+1}- \Delta^{M-1}a_n$ . A sequence is patriota if there are positive integers $k,l$ such that $a_{n+k}=\Delta^Ma_{n+l}$ for all non-negative integers $n$ . Determine, with proof, whether exists a sequence that the last value of $M$ for which the sequence is patriota is $2022$ .