Palindrome Counter

时间限制：C/C++/Rust/Pascal 4秒，其他语言8秒
空间限制：C/C++/Rust/Pascal 256 M，其他语言512 M
64bit IO Format: %lld

题目描述

Define the palindrome value of a string $s$ as the number of non-empty strings $t$ such that:

$t$ is a palindrome, that is, it reads the same forwards and backwards.
$t$ is a contiguous substring of $s$ .

For example, if $s$ is " $\texttt{aba}$ ", then string $t$ can be " $\texttt{a}$ ", " $\texttt{b}$ ", or " $\texttt{aba}$ ", so the palindrome value of $s$ is $3$ .

Find the sum of palindrome values of all strings with length $n$ and character set size $k$ . Since the answer may be too large, output it modulo $998\,244\,353$ .

输入描述:

The first line contains two integers  (), denoting the length of the string and the character set size.

输出描述:

Output a single integer, representing the answer, modulo .

示例1

输入

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4 2

输出

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示例2

输入

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5 3

输出

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