Question 106
The number $2019$ is written on the board. Katia and Mykola are playing the following game: one by one (starting with Katia) they choose any divisor $d$ of the number $N$ written on the board and change the number on the board $N$ to the number $N - (2d - 1)$, if it is positive integer. Whoever writes number $1$ loses. Who will win in this game and what is the strategy, considering both players want to win?