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 $$$998\,244\,353$$$.

Input

The first line contains three integers $$$n, k$$$ and $$$c$$$ ($$$1 \le n \le 10^6$$$; $$$2 \le k \le 10^6$$$; $$$1 \le c \le 26$$$; $$$n$$$ is not divisible by $$$k$$$) — the length of string $$$s$$$, the length of the substring that is being removed and the number of first letters from the alphabet.

The second line contains string $$$t$$$, consisting of exactly ($$$n \bmod k$$$) lowercase Latin letters. Each letter is one of the first $$$c$$$ letters of the alphabet.

Output

Print a single integer — the number of strings $$$s$$$ that produce $$$t$$$ as the lexicographically smallest solution.

Note

The strings $$$s$$$ in the first example: "aaa", "aab", "aba", "abb", "baa", "bba".

The strings $$$s$$$ in the second example: "bcabc", "bcacc", "bcbbc", "bcbcc", "bccbc", "bcccc", "caabc", "cabbc", "cacbc", "cbabc", "cbbbc", "cbcbc", "ccabc", "ccbbc", "cccbc".

Inverse Problem

Examples