Problem:
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

Solution in C# (.NET Core 3.1.201) (judge verdict: Runtime Error)

using System;
using System.Collections;
using System.Collections.Generic;

class Program {

    static void Main (string[] args) {
        string[] str = Console.ReadLine ().Split (' ');
        long N = long.Parse (str[0]);
        long M = long.Parse (str[1]);
        long K = long.Parse (str[2]);
        long[, ] dp = new long[N, K + 1];
        dp[0, 0] = M;
        for (long i = 1; i < N; i++) {
            dp[i, 0] = ((M - 1) * dp[i - 1, 0]) % 998244353;
            for (long j = 1; j <= Math.Min (K, i); j++) {
                dp[i, j] = ((((M - 1) * dp[i - 1, j]) % 998244353) + dp[i - 1, j - 1]) % 998244353;
            }
        }
        long total = 0;
        for (long j = 0; j <= K; j++) {
            total = (total + (dp[N - 1, j])) % 998244353;

        }
        Console.WriteLine (total);
        //% 998244353
    }
}
//dotnet run --project test