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# (Mono-mcs 6.8.0.105) (judge verdict: Wrong Answer)

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

namespace ABC167E
{
    class Program
    {
        static void Main(string[] args)
        {
            var NMK = ReadInt();
            int N = NMK[0];
            int M = NMK[1];
            int K = NMK[2];

            long mod = 998244353;

            long[] dp = new long[N];

            //初期化
            dp[0] = (M * Calc.ModPow(M - 1, N - 1, mod)) % mod;

            long ans = dp[0];
            for (int k = 1; k <= K; k++)
            {
                long a = (dp[k - 1] * (N - k)) % mod;

                a = (a * Calc.ModPow(k, mod - 2, mod)) % mod;
                a = (a * Calc.ModPow(M - 1, mod - 2, mod)) % mod;

                dp[k] = a;
                ans = (ans + a) % mod;
            }

            Console.WriteLine(ans);
            Console.ReadKey();
        }

        static int[] ReadInt()
        {
            int[] ret = Console.ReadLine().Split().Select(int.Parse).ToArray();
            return ret;
        }
        static long[] ReadLong()
        {
            long[] ret = Console.ReadLine().Split().Select(long.Parse).ToArray();
            return ret;
        }
    }

    static class Calc
    {
        /// <summary>
        /// a^n (mod p)
        /// nが非常に大きい時に有効
        /// </summary>
        /// <param name="a"></param>
        /// <param name="n"></param>
        /// <param name="mod"></param>
        /// <returns></returns>
        public static long ModPow(long a, long n, long p)
        {
            if (n == 1) return a % p;
            if (n % 2 == 1) return (a * ModPow(a, n - 1, p)) % p;

            long t = ModPow(a, n / 2, p);
            return (t * t) % p;
        }

        /// <summary>
        /// 組み合わせ個数
        /// </summary>
        /// <param name="n"></param>
        /// <param name="k"></param>
        /// <param name="p"></param>
        /// <returns></returns>
        public static long nCk(long n, long k, long p)
        {
            long ans = 1;
            k = Math.Min(k, n - k);
            for (long i = n; i > n - k; i--)
            {
                ans = (ans * i) % p;
            }

            for (long i = 1; i <= k; i++)
            {
                ans = (ans * ModPow(i, p - 2, p)) % p;
            }

            return ans;
        }
    }

}