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G - Computer DJ
Languages: C, C++, Java, Pascal, Haskell, Python, JavaScript, Tiger, C#
Time & Memory limits: (details)
A very famous DJ has been recently invited to play in the closing party of a Computer Science conference. Trying to impress the participants of the event, he decided to use a program in order to choose the songs he would play at this party. However, the result was a disaster, since the way the program chose the songs was quite weird and repetitive.
First of all, the DJ has selected $N$ songs among the set of songs he had available. The program used by the DJ then labels each of the songs using one different character from $\texttt{‘A’}$ to $\texttt{‘Z’}$. The $i^{\text{th}}$ song is labeled using the $i^{\text{th}}$ character of the sequence $\texttt{‘A’} - \texttt{‘Z’}$. The program chooses the songs to be played in the party in the order that their labels appear in the following infinite sequence of characters: first come all the words with one character in lexicographical order; then all the words with two characters in lexicographical order; then all the words with three characters in lexicographical order; and so on. For $N = 3$, this sequence would be $\texttt{ABCAAABACBABBBCCACBCCAAAAABAACABAABBABC}$...
At the end of the party, some people asked the DJ if he remembered which the first song played was. Others would like to know which the $25^{\text{th}}$ was, and so on. The DJ remembers nothing but the strange pattern of repetition of the songs, so he urges you to help him and write a program which answers such queries.
Input
The input contains several test cases. Each test case consists of three lines. The first line of a test case contains two integers $N$ and $Q$ indicating respectively the number of songs chosen by the DJ and the number of queries made by the participants ($1 \leq N \leq 26$ and $1 \leq Q \leq 1000$). In the second line, there will be the N titles of the songs (the title of a song is a chain of alphanumerical characters of at least one and at most $100$ characters) separated by single spaces. The last line of a test case contains a sequence of queries. Each query is a number $k$ $(1 \leq k \leq 100000000)$ corresponding to the $k$-th song played in the party. The end of the input is indicated by $N = Q = 0$.
The input must be read from standard input.
Output
For each query number k in a test case, you shall print a single line containing the name of the $k^{\text{th}}$ song played in the party. A blank line must follow each test case.
The output must be written to standard output.
Sample test(s)
Input
10 3
S0 S1 S2 S3 S4 S5 S6 S7 S8 S9
3 6 10
3 5
Pathethique TurkishMarch Winter
1 2 3 4 16
0 0
Output
S2
S5
S9
Pathethique
TurkishMarch
Winter
Pathethique
Winter