OMA 2020 Problem 2

Let $k\ge 1$ be an integer. Determine the smallest positive integer $n$ such that some cells on an $n \times n$ board can be painted black so that in each row and in each column there are exactly $k$ black cells, and furthermore, the black cells do not share a side or a vertex with another black square.

Clarification: You have to answer n based on $k$ .