Consider the following problem.

You are given a string $s$, consisting of $n$ lowercase Latin letters, and an integer $k$ ($n$ is not divisible by $k$). Each letter is one of the first $c$ letters of the alphabet.

You apply the following operation until the length of the string is less than $k$: choose a contiguous substring of the string of length exactly $k$, remove it from the string and glue the resulting parts together without changing the order.

Let the resulting string of length smaller than $k$ be $t$. What is lexicographically smallest string $t$ that can obtained?

You are asked the inverse of this problem. Given two integers $n$ and $k$ ($n$ is not divisible by $k$) and a string $t$, consisting of ($n \bmod k$) lowercase Latin letters, count the number of strings $s$ that produce $t$ as the lexicographically smallest solution.

Print that number modulo $998\,244\,353$.