Two Set Game

There are two arrays $S_1$ and $S_2$ of size $N_1$ and $N_2$, respectively. Let $A$ and $B$ denote Alice and Bob's score where both $A$ and $B$ are $0$ initially. Alice and Bob take turns choosing a number to add to their score, with Alice starting first. In their turn, a player can do **exactly one** of the following two things: - If $S_1$ is not empty, choose the **minimum** element from $S