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 . 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