MathDB

There is a board with

2010

rows and

2001

columns, on it there is a token located in the upper left box that can perform one of the following operations:
(A) Walk 3 steps horizontally or vertically. (B) Walk 2 steps to the right and 3 steps down. (C) Walk 2 steps to the left and 2 steps up.
With the condition that immediately after carrying out an operation on (B) or (C) it is mandatory to take a step to the right before perform the following operation. It is possible to exit the board, so count the number of steps necessary, entering through the other end of the row or column from which it exits, as if the board outside circular (example: from the beginning you can walk to the square located in row

1

and column

1999

). Will it be possible that after

2011

operations allowed the checker to land exactly on the bottom square right?

Problem Statement