Lockdown Game-4

Alice and Bob are playing a game. They have an integer $N$. Alice has $l$ distinct intgers and Bob has $m$ distinct integers each of which is between $1$ to $N-1$ (both inclusive). The Game starts with a starting integer $X$. In each turn each player can pick any number from his set of distinct integers and add it to $X$. If $X$ becomes greater than $N$, $X$ is assigned the value $X-N$ i.e The int