Let there be a $2718281 \times 2718281$ grid of squares with some squares coloured black and others coloured white.It is not possible to have unicoloured grids, i.e there must be at least one square of each colour in this grid.

A grid is called $beautiful$ if it looks the same even when the entire square is rotated by $90^{\circ}$ anticlockwise around its center any number of times. A $beautiful$ grid also looks the same when it is reflected across a line joining mid points of opposite sides or a line joining opposite corners . Fin the number of possible $beautiful$ grids. Since the answer can be large, compute the answer modulo $(10^9+7)$