Remove Stones

**This is an interactive problem.** Alice and Bob are going to play a game, whose rules are as follows: They have a pile of $N$ stones, and an integer $K$. Alice and Bob take turns playing, with Alice going first. On their turn, a player must do the following: - Choose an integer $x$ such that $\gcd(x, K) = 1$, and there are at least $x$ stones remaining in the pile. Then, remove $x$ stones