Fibonacci Nim

Player to play last move wins the Game.

Description of Game:
Objective: Player to play last move wins the Game.
A pile of balls(N) is placed between two players (UUU & CPU).
Step 1: For the first move, one can remove "p" balls such that N > p >1.
Step 2: For the subsequent moves, one can remove "q" balls such that q <= 2p.
Note 1: An alternative turn basis is adopted throughout the game.
Note 2:Always the user need to make a move to remove balls.