And-Or Game

Chef is playing a game with two sequences of non-negative integers $A_1, A_2, \ldots, A_N$ and $B_1, B_2, \ldots, B_M$. He has an integer $V$, which is initially equal to $0$. Chef will play for a number of turns he chooses (possibly zero); he stops playing when he gets bored. In each turn of the game, Chef must perform one of the following operations: - Choose an integer $X$ from $A$ and change