Statement

A herd of horseys is heading to the International Olympiad for Horses in Teams (IOHT). They are currently positioned at cell (0, 0) on a rectangular board of size N × M. They can move only by making L-shaped jumps: W tiles in one direction (either horizontal or vertical) and then H tiles in a perpendicular direction. Their goal is to reach the cell where the IOHT is held. However, they do not know its location in advance. They ask for your help to determine whether it is possible for them to visit every cell on the board using only these L-shaped jumps.