20. N1 (POL) Let \( m \) be a fixed integer greater than 1. The sequence \( x_{0}, x_{1}, x_{2}, \ldots \) is defined as follows:  
\[ x_{i}= \begin{cases}2^{i}, & \text { if } 0 \leq i \leq m-1 \\ \sum_{j=1}^{m} x_{i-j}, & \text { if } i \geq m\end{cases} \]  
Find the greatest \( k \) for which the sequence contains \( k \) consecutive terms divisible by \( m \).