BALTIC-WAY 2013 Problem 2

Let $k$ and $n$ be positive integers and let $x_{1}, x_{2}, \ldots, x_{k}, y_{1}, y_{2}, \ldots, y_{n}$ be distinct integers. A polynomial $P$ with integer coefficients satisfies

$$P\left(x_{1}\right)=P\left(x_{2}\right)=\ldots=P\left(x_{k}\right)=54$$

and

$$P\left(y_{1}\right)=P\left(y_{2}\right)=\ldots=P\left(y_{n}\right)=2013 .$$

Determine the maximal value of $k n$.