Mafia

A mafia has infiltrated the city <insert name here>. This has made the police force of <insert name here> very confused, with accusations of corruption being made in every direction. The city's $N$ cops (which are numbered between $0$ and $N - 1$) has made a number of accusations about other policemen. Each accusation is either:

1. Police number $i$ is an honest cop.
2. Police number $i$ is a corrupt cop.

An honest cop always tells the truth, while a corrupt cop always lies. In total, there has been $M$ accusations.

The chief of police is now trying to fix the situation, starting with determining how many of her police men are corrupt. She has $G$ different guesses about the number of corrupt cops, and for each such number $C$, she wants to know how many different sets of size $C$ can be corrupt (where all the remaining cops are honest), given that all accusations are consistent.

The sample judge reads input in the following format:

• line $1$: N M
• line $2$: A[0] ... A[M - 1]
• line $3$: B[0] ... B[M - 1]
• line $4$: T[0] ... T[M - 1]
• line $5$: G: the number of calls made to guess(C).
• line $6$ C1 ... CG: the parameters of the $G$ calls to guess(C).

The sample judge will write $G$ lines with the return values of guess(C).

Let $G$ be the number of calls to guess(C).

• $N \le 2\\,000$
• $M \le 70\\,000$
• $G \le 2\\,000$