OMCC 2001 Problem 1

Two players $A$ , $B$ and another 2001 people form a circle, such that $A$ and $B$ are not in consecutive positions. $A$ and $B$ play in alternating turns, starting with $A$ . A play consists of touching one of the people neighboring you, which such person once touched leaves the circle. The winner is the last man standing.

Show that one of the two players has a winning strategy, and give such strategy.

Note: A player has a winning strategy if he/she is able to win no matter what the opponent does.