How to prove that the next language in the alphabet is not an automaton?

Question

Discrete Math

How to solve this problem? As I understand it, you need to use the lemma about the growth of automata languages, but even with its application I can’t solve it.

Problem:
Prove that the following language K in the alphabet {a, b} is not automaton:
K = {w : the length of the word w is divisible by three and its middle third consists of only letters a}