International Mathematical Olympiad 2000 Problem 3

$k$ is a positive real. $N$ is an integer greater than 1. $N$ points are placed on a line, not all coincident. A move is carried out as follows. Pick any two points $A$ and $B$ which are not coincident. Suppose that $A$ lies to the right of $B$. Replace $B$ by another point $B'$ to the right of $A$ such that $AB' = kBA$. For what values of $k$ can we move the points arbitrarily far to the right by repeated moves?