Mafia

문제

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 $NN$ cops (which are numbered between $00$ and $N-1N\; -\; 1$) has made a number of accusations about other policemen. Each accusation is either:

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

An honest cop always tells the truth, while a corrupt cop always lies. In total, there has been $MM$ 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 $GG$ different guesses about the number of corrupt cops, and for each such number $CC$, she wants to know how many different sets of size $CC$ can be corrupt (where all the remaining cops are honest), given that all accusations are consistent.

입력

The sample judge reads input in the following format:

• line $11$: N M
• line $22$: A[0] ... A[M - 1]
• line $33$: B[0] ... B[M - 1]
• line $44$: T[0] ... T[M - 1]
• line $55$: G: the number of calls made to guess(C).
• line $66$ C1 ... CG: the parameters of the $GG$ calls to guess(C).

출력

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

3 2
1 2
0 1
2 2
4
0 1 2 3

0 1 1 0