101674: [AtCoder]ABC167 E - Colorful Blocks

Memory Limit：256 MB Time Limit：2 S
Judge Style：Text Compare Creator：
Submit：0 Solved：0

Description

Score : $500$ points

Problem Statement

There are $N$ blocks arranged in a row. Let us paint these blocks.

We will consider two ways to paint the blocks different if and only if there is a block painted in different colors in those two ways.

Find the number of ways to paint the blocks under the following conditions:

  • For each block, use one of the $M$ colors, Color $1$ through Color $M$, to paint it. It is not mandatory to use all the colors.
  • There may be at most $K$ pairs of adjacent blocks that are painted in the same color.

Since the count may be enormous, print it modulo $998244353$.

Constraints

  • All values in input are integers.
  • $1 \leq N, M \leq 2 \times 10^5$
  • $0 \leq K \leq N - 1$

Input

Input is given from Standard Input in the following format:

$N$ $M$ $K$

Output

Print the answer.

Sample Input 1

3 2 1

Sample Output 1

6

The following ways to paint the blocks satisfy the conditions: 112, 121, 122, 211, 212, and 221. Here, digits represent the colors of the blocks.

Sample Input 2

100 100 0

Sample Output 2

73074801

Sample Input 3

60522 114575 7559

Sample Output 3

479519525

Input

题意翻译

有 $n$ 个方格排成一排，你需要给这些方格染色。 你有 $m$ 种颜色给方格染色，每一个方格只可以染一种颜色，且这 $n$ 个方格都需要染色。注意，一种染色方式不一定需要使用所有的颜色。 请问有多少种染色方式，使得**最多**可能有 $k$ 对相邻颜色的方格。由于答案可能很大，所以请你输出答案模 $998244353$ 的值。 样例一解释：共有六种方法，分别是：```112```、```121```、```122```、```211```、```212```、```221``` 。 Translate by Chancylaser.

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