SE-SKOLORNAS 2003 Problem 1

If $x, y, z, w$ are nonnegative real numbers satisfying $$\left\{ \begin{array}{l}y = x - 2003 z = 2y - 2003 w = 3z - 2003 \end{array} \right.$$ find the smallest possible value of $x$ and the values of $y, z, w$ corresponding to it.