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: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Text.RegularExpressions;
using static System.Console;
using static System.Math;
using static MyIO;
using static MyUtil;

public class E { public static void Main() => (new Solver()).Solve(); }

public class Solver
{
	public void Solve()
	{
		long N = GetLong();
		long M = GetLong();
		long K = GetLong();

		if(N == 1)
		{
			WriteLine(M);
			return;
		}
		if(M == 1)
		{
			WriteLine(0);
			return;
		}

		MInt.InitTable(N);
		var ans = new MInt(0);
		for(long k = 0; k <= K; k++)
			ans += MInt.MComb(N - 1, N - 1 - k) * M * MInt.MPow((M - 1), N - 1 - k);

		WriteLine(ans.Val);
	}
}

public struct MInt
{
	private const long MOD = 998244353;
	private static MInt[] f = null;
	private static MInt[] g = null;
	public long Val { get; private set; }

	public MInt(long v)
	{
		Val = (v + MOD) % MOD;
	}

	public static void InitTable(int N) => InitTable((long)N);
	public static void InitTable(long N)
	{
		f = new MInt[N + 1];
		f[0] = new MInt(1);
		for(long i = 1; i <= N; i++)
			f[i] = f[i - 1] * i;

		g = new MInt[N + 1];
		g[N] = MPow(f[N], MOD - 2);
		for(long i = N; i > 0; i--)
			g[i - 1] = g[i] * i;
	}

	public static MInt MComb(long n, long k)
	{
		if(n < 0 || n < k)
			return new MInt(0);
			
		return f[n] * g[k] * g[n - k];
	}

	public static MInt operator+(MInt x, long y) => x + new MInt(y);	
	public static MInt operator+(long x, MInt y) => new MInt(x) + y;
	public static MInt operator+(MInt x, MInt y)
	{
		long tmp = x.Val + y.Val;
		if(tmp >= MOD)
			tmp -= MOD;
		return new MInt(tmp);
	}

	public static MInt operator-(MInt x, long y) => x - new MInt(y);
	public static MInt operator-(long x, MInt y) => new MInt(x) - y;
	public static MInt operator-(MInt x, MInt y)
	{
		long tmp = x.Val;
		if(tmp < y.Val)
			tmp += MOD;
		tmp -= y.Val;
		return new MInt(tmp);
	}

	public static MInt operator*(MInt x, MInt y) => new MInt((x.Val * y.Val) % MOD);
	public static MInt operator*(MInt x, long y) => x * new MInt(y);
	public static MInt operator*(long x, MInt y) => new MInt(x) * y;

	public static MInt operator/(MInt x, MInt y) => x * MPow(y, MOD - 2);
	public static MInt operator/(MInt x, long y) => x * MPow(y, MOD - 2);
	public static MInt operator/(long x, MInt y) => x * MPow(y, MOD - 2);

	public static MInt MPow(MInt x, MInt y) => MPow(x.Val, y.Val);
	public static MInt MPow(MInt x, long y) => MPow(x.Val, y);
	public static MInt MPow(long x, MInt y) => MPow(x, y.Val);
	public static MInt MPow(long x, long y)
	{
		long exp = y;
		long xx = x;
		long res = 1;
		while(exp > 0)
		{
			if((exp & 1) == 1)
				res = (res * xx) % MOD;

			xx = (xx * xx) % MOD;
			exp >>= 1;
		}
		return new MInt(res);
	}
}

public static class MyIO
{
	private static string[] args = new string[0];
	private static int cnt = 0;
	private static IEnumerable<string> getArgs(long N) => Range(0, N).Select(_ => getArg());
	private static string getArg()
	{
		if(cnt == args.Length) { args = Console.ReadLine().Split(); cnt = 0; }
		return args[cnt++];
	}

	public static int GetInt() => int.Parse(getArg());
	public static long GetLong() => long.Parse(getArg());
	public static double GetDouble() => double.Parse(getArg());
	public static decimal GetDecimal() => decimal.Parse(getArg());
	public static string GetString() => getArg();
	public static char GetChar() => getArg()[0];
	public static int[] GetInts(long N) => getArgs(N).Select(int.Parse).ToArray();
	public static long[] GetLongs(long N) => getArgs(N).Select(long.Parse).ToArray();
	public static double[] GetDoubles(long N) => getArgs(N).Select(double.Parse).ToArray();
	public static decimal[] GetDecimals(long N) => getArgs(N).Select(decimal.Parse).ToArray();
	public static string[] GetStrings(long N) => getArgs(N).ToArray();
}

public static class MyUtil
{
	public static void chmax<T>(ref T x, T y) where T : IComparable<T> { if(x.CompareTo(y) < 0) x = y; }
	public static void chmin<T>(ref T x, T y) where T : IComparable<T> { if(x.CompareTo(y) > 0)	x = y; }
	public static void swap<T>(ref T x, ref T y) { T tmp = x; x = y; y = tmp; }
	public static long rightShift(long x, long y) => (x >> (int)y);
	public static long leftShift(long x, long y) => (x << (int)y);
	public static bool contains(long s, long x) => (rightShift(s, x) & 1L) == 1L;
	public static long gcd(long x, long y) => (y == 0) ? x : gcd(y, x % y);
	public static long lcm(long x, long y) => (x / gcd(x,y)) * y;	
	public static IEnumerable<int> Range(long start, long count) => Enumerable.Range((int)start, (int)count);
	public static void Sort(this List<string> source) => source.Sort(StringComparer.Ordinal);
}