Rick, Morty and Dice Game

Rick and Morty wanted to start the day by playing a game. Both of them have their own polyhedral dice. Rick’s dice has $n_1$ faces with numbers 1 to $n_1$ while Morty’s dice has $n_2$ faces with numbers 1 to $n_2$. In the $k_{th}$ round of the game: - Rick wins, if his dice shows an even number when $k$ is odd or shows an odd number when $k$ is even. - Morty wins, if his dice shows an odd number