ÖMO 1999 Problem 6

Two players $A$ and $B$ play the following game. An even number of cells are placed on a circle. $A$ begins and $A$ and $B$ play alternately, where each move consists of choosing a free cell and writing either $O$ or $M$ in it. The player after whose move the word $OMO$ (OMO = Osterreichische Mathematik Olympiade) occurs for the first time in three successive cells wins the game. If no such word occurs, then the game is a draw. Prove that if player $B$ plays correctly, then player $A$ cannot win.