We have an infinite sequence of integers $\{x_n\}$, such that $x_1 = 1$, and, for all $n \ge 1$, it holds that $x_n < x_{n+1} \le 2n$. Prove that there are two terms of the sequence,$x_r$ and $x_s$, such that $x_r - x_s = 2018$.