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: Accepted)

using static System.Math;
using static System.Console;
using System.Collections.Generic;
using System.Linq;
using System;

class Program
{
    #region Reader
    static string ReadStr => Console.ReadLine();
    static string[] ReadStrs => Console.ReadLine().Split(' ');
    static int ReadInt => Convert.ToInt32(Console.ReadLine().Trim());
    static int[] ReadInts => Console.ReadLine().Trim().Split(' ').Select(s => Convert.ToInt32(s)).ToArray();
    static long ReadLong => Convert.ToInt64(Console.ReadLine().Trim());
    static long[] ReadLongs => Console.ReadLine().Trim().Split(' ').Select(s => Convert.ToInt64(s)).ToArray();
    static List<int[]> ReadPairs(int N)
    {
        List<int[]> ans = new List<int[]>();
        for (int i = 0; i < N; i++) { ans.Add(ReadInts); }
        return ans;
    }
    static List<long[]> ReadPairsLong(int N)
    {
        List<long[]> ans = new List<long[]>();
        for (int i = 0; i < N; i++) { ans.Add(ReadLongs); }
        return ans;
    }
    #endregion
    #region Method
    const int mod = 1000000007;
    public static int Mod(int a, int mod) { return a % mod >= 0 ? a % mod : a % mod + mod; }
    public static long Mod(long a, long mod = mod) { return a % mod >= 0 ? a % mod : a % mod + mod; }
    bool eq<T, U>() => typeof(T).Equals(typeof(U));
    T ct<T, U>(U a) => (T)Convert.ChangeType(a, typeof(T));
    T cv<T>(string s) => eq<T, int>() ? ct<T, int>(int.Parse(s))
                       : eq<T, long>() ? ct<T, long>(long.Parse(s))
                       : eq<T, double>() ? ct<T, double>(double.Parse(s))
                       : eq<T, char>() ? ct<T, char>(s[0])
                                         : ct<T, string>(s);
    void Multi<T>(out T a) => a = cv<T>(ReadStr);
    void Multi<T, U>(out (T,U) ans)
    {
        var ar = ReadStrs;
        ans =(cv<T>(ar[0]), cv<U>(ar[1]));
    }
    void Multi<T, U, V>(out (T,U,V) ans)
    {
        var ar = ReadStrs; 
        ans =(cv<T>(ar[0]), cv<U>(ar[1]),cv<V>(ar[2]));
    }
    void Multi<T,U>(out T a,out U b)
    {
        var ar = ReadStrs; 
        a = cv<T>(ar[0]);  b = cv<U>(ar[1]);
    }
    void Multi<T, U, V>(out T a,out U b,out V c)
    {
        var ar = ReadStrs;
        a = cv<T>(ar[0]);  b = cv<U>(ar[1]);  c = cv<V>(ar[2]);
    }
    #endregion

    public static Dictionary<int, int> PrimeFactors(int n)
    {
        int i = 2;
        int tmp = n;
        Dictionary<int, int> d = new Dictionary<int, int>();

        while (i * i <= n) //※1
        {
            if (tmp % i == 0)
            {
                tmp /= i;
                if (d.ContainsKey(i)) d[i]++;
                else d.Add(i, 1);
            }
            else
            {
                i++;
            }
        }
        if (tmp != 1)
        {
            if (d.ContainsKey(tmp)) d[tmp]++;
            else d.Add(tmp, 1);
        }
        return d;
    }

    static List<long> Divisor(long N)
    {
        List<long> ans = new List<long>();
        int max = (int)Math.Sqrt(N);
        for (int i = 1; i < max; i++)
        {
            if (N % i == 0)
            {
                ans.Add(i);
                ans.Add(N / i);
            }
        }

        if (N % max == 0)
        {
            if (N / max == max) ans.Add(max);
            else
            {
                ans.Add(max);
                ans.Add(N / max);
            }
        }
        return ans;
    }
    #region Mod
    public static long GetInv(long a, long mod = 1000000007)
    {
        return PowerMod(a, mod - 2, mod);
    }
    public static long Combination(long a, long b, long mod = 1000000007)
    {
        if (b < 0 || b > a) return 0;
        if (b > a / 2) b = a - b;
        long numerator = Factorial(a, mod);
        long denominator = (Factorial(b, mod) * Factorial(a - b, mod)) % mod;

        return (numerator * GetInv(denominator, mod)) % mod;
    }
    public static long Factorial(long n, long mod = 1000000007)
    {
        if (n == 0) return 1;
        if (n == 1) return 1;
        long ans = n;
        for (int i = 2; i < n; i++)
        {
            ans = (ans * i) % mod;
        }

        return ans;
    }
    private static long PowerMod(long a, long n, long mod = 1000000007)
    {
        if (n == 0) return 1;
        if (n == 1) return a;

        long p = PowerMod(a, n / 2, mod);
        if (n % 2 == 1) return ((p * p) % mod * a) % mod;
        else return (p * p) % mod;
    }
    #endregion

    static HashSet<int> Primes(int limit)
    {
        bool[] done = new bool[limit+1];

        var ans = new HashSet<int>();
        for (int i = 2; i <= limit; i++)
        {
            if (done[i]) continue;
            ans.Add(i);
            int index = i;
            while (index<=limit)
            {
                done[index] = true;
                index += i;
            }
        }
        return ans;
    }




    static void Main()
    {
        int[] NMD = ReadInts;
        long box_num = NMD[0];
        long c_num = NMD[1];
        long K = NMD[2];

        long ans = 0;

        long[] comb = new long[box_num];
        comb[0] = 1;

        for (int i = 1; i < box_num; i++)
        {
            comb[i] = comb[i-1] * (box_num - i);
            comb[i] = Mod(comb[i], 998244353);
            comb[i] *= GetInv(i, 998244353);
            comb[i] = Mod(comb[i], 998244353);
        }


        for (int k = 0; k <= K; k++)
        {
            long temp = c_num * PowerMod(c_num - 1, box_num - 1-k, 998244353);
            temp = Mod(temp, 998244353);

            temp *= comb[box_num-k-1];
            temp = Mod(temp, 998244353);

            ans += temp;
            ans = Mod(ans, 998244353);
        }



        WriteLine(ans);
    }



}