PL-OM 2004 Problem 6

An integer $m > 1$ is given. The infinite sequence $(x_n)_{n\ge 0}$ is defined by $x_i=2^i$ for $i<m$ and $x_i=x_{i-1}+x_{i-2}+\cdots +x_{i-m}$ for $i\ge m$ . Find the greatest natural number $k$ such that there exist $k$ successive terms of this sequence which are divisible by $m$ .