Clever Title

One day I sat down in my chair and wondered which theorem is the best one. After an hour on my favourite search engine (Ask Jeeves) I found the BEST Theorem. (The BEST Theorem gives a formula for the number of Eulerian circuits in a directed graph, which this problem does not need.) The name comes from the uppercase letters of the authors of the paper: de Bruijn, van Aardenne-Ehrenfest, Smith and Tutte.

A title is clever when you can line the authors up in any order you like, pick one uppercase letter from each author's name, and read the picked letters from left to right to get the title. The title therefore has as many letters as there are authors.

Last year the problem setters of the South Pacific Region proved a theorem about the number of powers modulo a fixed number, and they would like to give it a clever title. Their names are Anderson, Best, Cameron-Jones, Corney, French, Guttmann, Haigh, Lobb, Sergeev, Tran, Ward-Graham and Whalan. The ABCCFGHLSTWW Theorem does take one uppercase letter from each name, but ABCCFGHLSTWW is not a valid word. (In the real world a valid word is an English word. In this problem the list of valid words is part of the input.) No ordering of those names spells a valid word at all. If only Anderson, French, Sergeev and Tran had discovered a theorem, they could call it the FAST Theorem (French, Anderson, Sergeev, Tran), and that is the only ordering of those four names that spells FAST. If the authors were Merlin, Oberon and Othello and they wanted the MOO Theorem, two orderings work: Merlin, Oberon, Othello and Merlin, Othello, Oberon.

The order of the names on a publication usually matters. I already have tenure, so I only care about how many orderings make a title clever. You are given the authors of a theorem and a list of valid titles. For each title, count the orderings of the author names that make it clever.

The first line contains two integers $n$ ($1 \le n \le 10$), the number of authors, and $k$ ($1 \le k \le 1000$), the number of valid words.

Each of the next $n$ lines contains one author name. A name uses only uppercase and lowercase English letters, has between 1 and 20 characters, and contains at least one uppercase letter.

Each of the next $k$ lines contains one valid word. A valid word uses only uppercase English letters and has between 1 and 20 characters.

Print $k$ integers, one per line. Line $i$ holds the number of orderings of the author names that make the $i$-th given word a clever title.