Give you a chessboard of n row and m columns. Alice and Bob want to play a game with the following rules:
1) Alice moves first. And they take turns to move. Alice uses black piece and Bob uses white piece.
2) For each move, the player must chose an empty grid (x0, y0) and occupy all grids (x, y) which satisfy x >= x0 and y >= y0.
3) The player who occupies the grid (1, 1) will lose.
Alice and Bob are both clever enough. Please write a program to predict the winner of the game.