Red Green Grids

There is an empty grid (all cells are colored white) of $N$ rows and $M$ columns. Chef can fill each cell with either `RED` or `GREEN` color. Chef defines a *valid* path as a path of cells starting from $(1,1)$ and ending at $(N,M)$, where, Chef moves either `right` or `down` by $1$ cell each time. For a particular grid, Chef defines the *score* of the grid as the number of *valid* paths contain