String concatenation

How many different words of length exactly $\ell$ can you build by concatening $m$ given words? You can use any word as many times as you wish.

Input

Input consists of several cases, each with $\ell$ and $m$ , followed by $m$ different words. Assume that $\ell$ is between 1 and $10^{18}$ , that $m$ is at least 1, that the words only have lowercase letters, and that the sum of their lenghts is at most 50.

Output

For every case, print the result modulo $10^9 + 9$ .

Problem information

Author: Pol Mauri

Generation: 2026-01-25T11:11:19.895Z