RIOPLATENSE 2022 Problem 2

Let $m,n\geq 2$ . One needs to cover the table $m \times n$ using only the following tiles: Tile 1 - A square $2 \times 2$ . Tile 2 - A L-shaped tile with five cells, in other words, the square $3 \times 3$ without the upper right square $2 \times 2$ . Each tile 1 covers exactly $4$ cells and each tile 2 covers exactly $5$ cells. Rotation is allowed. Determine all pairs $(m,n)$ , such that the covering is possible.