2001 OIM Problems/Problem 5

Problem

On a $2000 \times 2001$ board the squares have coordinates $(x, y)$ with $x, y$ integers, $0 \le x le 1999$ and $0 \le y \le 2000$ . A ship on the board moves as follows: Before each movement, the ship is in a position $(x, y)$ and has a speed $(h, v)$ where $h$ and $v$ are integers. The ship chooses a new speed $(h',b'} such that$ (Error compiling LaTeX. Unknown error_msg)h'-h $be equal to$ −1, 0 $or$ 1 $and$ v'-v $be equal to$ −1, 0 $or$ 1 $. The new position of the ship will be$ (x',y') $where$ x' $is the reminder of the division of$ x+h' $by 2000, and$ y' $is the reminder of the division of$ y+v' $by 2001. There are two ships on the board: the Martian one and the Earth one that wants to catch the Martian one. Initially each ship is on a square on the board and has speed$ (0, 0)$. First moves Earth ship and continue moving alternately. Is there a strategy that always allows the Earth ship to catch the Martian ship, whatever the initial positions are?