An m×n checkerboard has a white square in its upper-left corner. Starting in that corner a chess piece moves diagonally. Each time the chess piece comes to an edge of the board, it continues along the "reflected" diagonal path. This process ends when the chess piece hits a corner. The diagram below shows the path of the chess piece in the 4×5 case. For which values of m and n will the chess piece hit all of the white squares?
Source: KoMaL