CN-SMO 2016 Problem 8

Let $\{ a_n\}$ be a series consisting of positive integers such that $n^2 \mid \sum_{i=1}^{n}{a_i}$ and $a_n\leq (n+2016)^2$ for all $n\geq 2016$ . Define $b_n=a_{n+1}-a_n$ . Prove that the series $\{ b_n\}$ is eventually constant.