CF832E.Vasya and Shifts

Vasya has a set of $4n$ strings of equal length, consisting of lowercase English letters "a", "b", "c", "d" and "e". Moreover, the set is split into $n$ groups of $4$ equal strings each. Vasya also has one special string $a$ of the same length, consisting of letters "a" only.

Vasya wants to obtain from string $a$ some fixed string $b$ , in order to do this, he can use the strings from his set in any order. When he uses some string $x$ , each of the letters in string $a$ replaces with the next letter in alphabet as many times as the alphabet position, counting from zero, of the corresponding letter in string $x$ . Within this process the next letter in alphabet after "e" is "a".

For example, if some letter in $a$ equals "b", and the letter on the same position in $x$ equals "c", then the letter in $a$ becomes equal "d", because "c" is the second alphabet letter, counting from zero. If some letter in $a$ equals "e", and on the same position in $x$ is "d", then the letter in $a$ becomes "c". For example, if the string $a$ equals "abcde", and string $x$ equals "baddc", then $a$ becomes "bbabb".

A used string disappears, but Vasya can use equal strings several times.

Vasya wants to know for $q$ given strings $b$ , how many ways there are to obtain from the string $a$ string $b$ using the given set of $4n$ strings? Two ways are different if the number of strings used from some group of $4$ strings is different. Help Vasya compute the answers for these questions modulo $10^{9}+7$ .

The first line contains two integers $n$ and $m$ ( $1<=n,m<=500$ ) — the number of groups of four strings in the set, and the length of all strings.

Each of the next $n$ lines contains a string $s$ of length $m$ , consisting of lowercase English letters "a", "b", "c", "d" and "e". This means that there is a group of four strings equal to $s$ .

The next line contains single integer $q$ ( $1<=q<=300$ ) — the number of strings $b$ Vasya is interested in.

Each of the next $q$ strings contains a string $b$ of length $m$ , consisting of lowercase English letters "a", "b", "c", "d" and "e" — a string Vasya is interested in.

For each string Vasya is interested in print the number of ways to obtain it from string $a$ , modulo $10^{9}+7$ .

In the first example, we have $4$ strings "b". Then we have the only way for each string $b$ : select $0$ strings "b" to get "a" and select $4$ strings "b" to get "e", respectively. So, we have $1$ way for each request.

In the second example, note that the choice of the string "aaaa" does not change anything, that is we can choose any amount of it (from $0$ to $4$ , it's $5$ different ways) and we have to select the line "bbbb" $2$ times, since other variants do not fit. We get that we have $5$ ways for the request.