Vasya has a set of $4*n*$ 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 $4*n*$ 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 $10^{9} + 7$.

Input

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.

Output

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

Note

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.