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
```

## Comments