IR-MO 2021 Problem 4

Arash and Babak play the following game, taking turns alternatively, on a $1400\times 1401$ table. Arash starts and in his turns he colors $k$ , $L$ -corners (any three cell of a square). Babak in his turn colors one $2\times 2$ square. Neither player is allowed to recolor any cell. Find all positive integers $k$ for which Arash has a winning strategy.