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 109 + 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 109 + 7.
[samples]
## 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.
**Definitions**
Let $ n, m \in \mathbb{Z}^+ $, with $ 1 \leq n, m \leq 500 $.
Let $ \Sigma = \{a, b, c, d, e\} $, identified with $ \mathbb{Z}_5 = \{0, 1, 2, 3, 4\} $ via $ a \mapsto 0, b \mapsto 1, c \mapsto 2, d \mapsto 3, e \mapsto 4 $.
Let $ A = (0, 0, \dots, 0) \in \mathbb{Z}_5^m $ be the initial string (all 'a').
Let $ S = \{s_1, s_2, \dots, s_n\} \subseteq \mathbb{Z}_5^m $ be the set of $ n $ distinct string templates, each representing a group of 4 identical strings.
For each $ s_k \in S $, define its *effect vector* $ v_k \in \mathbb{Z}_5^m $ by $ v_k[i] = \text{value of } s_k[i] \in \mathbb{Z}_5 $.
Let $ q \in \mathbb{Z}^+ $, $ 1 \leq q \leq 300 $, be the number of target strings.
For each query $ j \in \{1, \dots, q\} $, let $ b_j \in \mathbb{Z}_5^m $ be the target string, and define the *required shift vector* $ d_j = (d_{j,1}, \dots, d_{j,m}) \in \mathbb{Z}_5^m $ by $ d_j = b_j - A = b_j \pmod{5} $.
**Constraints**
1. For each group $ k \in \{1, \dots, n\} $, we may choose any number $ x_k \in \{0, 1, 2, 3, 4\} $ of strings from its group of 4.
2. The total effect of the chosen strings must satisfy:
$$
\sum_{k=1}^n x_k \cdot v_k \equiv d_j \pmod{5}, \quad \text{for each query } j.
$$
**Objective**
For each query $ j \in \{1, \dots, q\} $, compute the number of integer solutions $ (x_1, \dots, x_n) \in \{0,1,2,3,4\}^n $ to the system:
$$
\sum_{k=1}^n x_k v_k \equiv d_j \pmod{5}
$$
Output the result modulo $ 10^9 + 7 $.