Dereck is a linguist tasked on computing the amount of words of a certain length in a new language called "Aionian". A word is considered valid if the sequence of characters does not include the same letter twice in a row or two vowels in a row.

Given the vowels and consonants of the language, calculate the number of words of given lengths.

Input Specification

The first line contains the number of vowels, ~V~ ~(1 \le V \le 10^4)~, with the next ~V~ lines being the vowels.
The next line contains the number of consonants, ~C~ ~(1 \le C \le 10^4)~ with the next ~C~ lines being the consonants.
The next line contains the number of queries, ~L~ ~(1 \le L \le 10^4)~, in which the next ~L~ lines are the lengths Dereck wants you to calculate.

Output Specification

Output the number of words with the length specified, modulo ~10^9+7~.

Sample Input

2
A
E
3
B
C
D
3
10
3
7

Sample Output

564000
66
11640