In the popular game of Minesweeper, some fields of an $a \times b$ board are marked with a mine and on all the remaining fields the number of adjacent fields that contain a mine is recorded. Two fields are considered adjacent if they share a common vertex. For which $k \in \{0, 1, 2, 3, 4, 5, 6, 7, 8\}$ is it possible for some $a$ and $b$ , $ab > 2021$, to create a board whose fields are covered in mines, except for $2021$ fields who are all marked with $k$?