BALKAN-SL 2021 C2

Let $K$ and $N>K$ be fixed positive integers. Let $n$ be a positive integer and let $a_{1}, a_{2}, \ldots, a_{n}$ be distinct integers. Suppose that whenever $m_{1}, m_{2}, \ldots, m_{n}$ are integers, not all equal to 0 , such that $\left|m_{i}\right| \leqslant K$ for each $i$, then the sum

$$\sum_{i=1}^{n} m_{i} a_{i}$$

is not divisible by $N$. What is the largest possible value of $n$ ?