# DNA Sequence

Time Limit: 1000MS

Memory Limit: 65536K

## Description

It's well known that DNA Sequence is a sequence only contains A, C, T and G, and it's very useful to analyze a segment of DNA Sequence，For example, if a animal's DNA sequence contains segment ATC then it may mean that the animal may have a genetic disease. Until now scientists have found several those segments, the problem is how many kinds of DNA sequences of a species don't contain those segments. Suppose that DNA sequences of a species is a sequence that consist of A, C, T and G，and the length of sequences is a given integer n.

## Input

First line contains two integer m (0 <= m <= 10), n (1 <= n <=2000000000). Here, m is the number of genetic disease segment, and n is the length of sequences. Next m lines each line contain a DNA genetic disease segment, and length of these segments is not larger than 10.

## Output

An integer, the number of DNA sequences, mod 100000.

## Sample Input

4 3
AT
AC
AG
AA


## Sample Output

36

N/A