Tic Tac Toe

Two drunken players Alice and Bob are playing a modified version of Tic-Tac-Toe. Initially, there is a $N \times M$ empty grid. Alice and Bob take alternate turns **starting with Alice**. In her turn, Alice chooses an empty cell on the board and puts a `"A"` on the chosen cell. In Bob's turn, he chooses an empty cell and puts a `"B"` on the chosen cell. The player who first gets any $K\times K$