KöMaL 2018 B4925

Show that if the mean of the non-negative real numbers $a_1,a_2,\dots,a_{2017}$ is 1, then the following inequality holds: $\frac{a_1}{a_1^{2018} + a_2 + a_3 + \ldots +a_{2017}} + \frac{a_2}{a_2^{2018} + a_3 + a_4 + \ldots +a_{2017} + a_1} + \ldots +$ $+ \frac{a_{2017}}{a_{2017}^{2018} + a_1 + a_2 + \ldots +a_{2016}} \le 1.$