Here's another cutting game, which is also joyful.

The game uses  rectangular paper and the -th paper among them consists of  grids. Two players should choose one paper and cut this paper into two new pieces of rectangular paper in turn. Note that the player can also choose this new paper for cut.

In each turn the player can cut either horizontally or vertically, keeping every grids unbroken. Therefore, you can't do anything on a  paper. What's more, players can't skip their turns.

The player who can't move lose this game and his opponent win this game.

Now, given the initial  paper, you're asked to determine who will win this game eventually if both players play optimally.