Let $n$ and $m$ be positive integers. On one turn, an $n$-$m$-knight can move either horizontally by $n$ squares and vertically by $m$ squares or vertically by $n$ squares and horizontally by $m$ squares. (For instance, the usual chess knight, all possible target squares of one move of which are depicted by bullets in the figure, is a $1$-$2$-knight.) Can an $n$-$m$-knight on an infinite in every direction chessboard return to the initial square in exactly $2019$ turns?