Remove Numbers

Two players are playing a game. They are given an array $A_1, A_2, \ldots, A_N$ as well as an array $B_1, B_2, \ldots, B_M$. The game consists of $M$ rounds. Players are participating in rounds alternatively. During the $i$-th round (for $i$ from $1$ to $M$) the corresponding player (first player, if $i$ is odd, and second if $i$ is even) has to do exactly one of the following: * remove all elem