Space Arrays

Finally, progress reached the Madoka family and she decided to play with her little sister in the sensational game Space Arrays. The rules of the game are as follows: - Initially, a sequence $a_1, a_2, \ldots, a_N$ is given. - The players alternate turns. - In each turn, the current player must choose an index $i$ and increment $a_i$, i.e. change $a_i$ to $a_i + 1$. - Afterwards, if there is no p