OBM 2007 Problem 4

$2007^2$ unit squares are arranged forming a $2007\times 2007$ table. Arnold and Bernold play the following game: each move by Arnold consists of taking four unit squares that forms a $2\times 2$ square; each move by Bernold consists of taking a single unit square. They play anternatively, Arnold being the first. When Arnold is not able to perform his move, Bernold takes all the remaining unit squares. The person with more unit squares in the end is the winner.

Is it possible to Bernold to win the game, no matter how Arnold play?