J - Tri-Knight

Have you ever imagined how a chess knight will move on a triangular grid? A triangular grid is a grid where each point has $6$ neighbors, formed in $60^{\circ}$ angles. The coordinates are written with respect to two axes, and in this problem, the two axes have an inner angle of $120^{\circ}$. $(X, Y)$ is the point that is reached by taking $X$ steps of unit length along the horizontal axis, and