BALTIC-WAY 2011 Problem 10

Two persons play the following game with integers. The initial number is $2011^{2011}$ . The players move in turns. Each move consists of subtraction of an integer between $1$ and $2010$ inclusive, or division by $2011$ , rounding down to the closest integer when necessary. The player who first obtains a non-positive integer wins. Which player has a winning strategy?