\begin{problem}{Longest Common Substring}{standard input}{standard output}{5 seconds}{1024 megabytes}

Lisa wrote a program to solve the Longest Common Substring problem. She then used the program to find, for some two strings $s$ and $t$ consisting of characters `\t{0}' and `\t{1}', the longest string $w$ that is a substring of both $s$ and $t$. If there were multiple such longest strings, she found an arbitrary one.

Notably, the length of $w$ Lisa found was very small~--- at most 3.

Lisa remembers $n$ (the length of $s$), $m$ (the length of $t$), and $w$, but she doesn't remember strings $s$ and $t$ themselves. Now she wonders how many pairs of strings $s$ and $t$ exist such that they have lengths $n$ and~$m$, respectively, consist of characters `\t{0}' and `\t{1}', and have $w$ as one of their longest common substrings.

Help Lisa and find this number of pairs modulo $998\,244\,353$. Note that if $n = m$ and $s \ne t$, pairs $(s, t)$ and $(t, s)$ are considered distinct.

\InputFile
The first line contains three integers $n$, $m$, and $k$, denoting the lengths of the strings $s$, $t$, and $w$ ($1 \le n, m \le 100$; $1 \le k \le \min(3, n, m)$).

The second line contains the string $w$ of length $k$ consisting of characters `\t{0}' and `\t{1}'.

\OutputFile
Print the number of pairs of strings $(s, t)$ that have $w$ as one of their longest common substrings, modulo $998\,244\,353$.

\Examples

\begin{example}
\exmpfile{example.01}{example.01.a}%
\exmpfile{example.02}{example.02.a}%
\exmpfile{example.03}{example.03.a}%
\exmpfile{example.04}{example.04.a}%
\end{example}

\Note
Note that a string $a$ is a substring of a string $b$ if $a$ can be obtained from $b$ by deleting zero or more characters from the beginning and zero or more characters from the end.

In the first test, all pairs of strings satisfying the conditions are (``\t{01}'', ``\t{10}''), (``\t{01}'', ``\t{11}''), (``\t{10}'', ``\t{01}''), (``\t{10}'', ``\t{11}''), (``\t{11}'', ``\t{01}''), and (``\t{11}'', ``\t{10}'').

\end{problem}

