The Wave

Chef is stuck in the wavey world of polynomials. You are given all $N$ roots of a polynomial $P(x) = \prod_{i=1}^N (x - a_i)$. The roots are pairwise distinct integers, but they are not given in any particular order. To help Chef escape, you should answer $Q$ queries (numbered $1$ through $Q$). For each valid $i$, in the $i$-th query, you are given an integer $x_i$ and you have to determine wheth