OMM 2017 Problem 1

A knight is placed on each square of the first column of a $2017 \times 2017$ board. A move consists in choosing two different knights and moving each of them to a square which is one knight-step away. Find all integers $k$ with $1 \leq k \leq 2017$ such that it is possible for each square in the $k$ -th column to contain one knight after a finite number of moves.

Note: Two squares are a knight-step away if they are opposite corners of a $2 \times 3$ or $3 \times 2$ board.