OME 2018 Problem 5

Let $a, b$ be coprime positive integers. A positive integer $n$ is said to be weak if there do not exist any nonnegative integers $x, y$ such that $ax+by=n$ . Prove that if $n$ is a weak integer and $n < \frac{ab}{6}$ , then there exists an integer $k \geq 2$ such that $kn$ is weak.