Given is $2022\times 2022$ cells table. We can select $4$ cells, such that they make the figure $L$ (rotations, symmetric still count) (left one) and put a ball in each of them, or select $4$ cell which makes up the right figure (rotations, symmetric still count) and get one ball from each of them. For which $k$ is it possible in a given moment to be exactly $k$ points in each of the cells
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