P15757 [JAG 2025 Summer Camp #1] Inversion of Suffix Array

You are given positive integers $N$, $K$ and a string $S$ of length $N$ consisting of lowercase English letters. Let $T$ be the string obtained by concatenating $K$ copies of $S$. Find the inversion number of the Suffix Array of $T$, modulo $998244353$. For a string $s$ of length $n$, the suffix array of $s$ is a permutation of integers from $1$ to $n$ that represents the starting positions of all non-empty suffixes of $s$, sorted in lexicographical order.

The input is given in the following format: $$\begin{aligned} &N \ K \\ &S \end{aligned}$$ - $1 \leq N \leq 200\,000$ - $1 \leq K \leq 10^{12}$ - $S$ is a string of length $N$ consisting of lowercase English letters. - $N$ and $K$ are integers.

Output the answer in a single line.