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 System;
using System.Text;
using System.Collections.Generic;
using System.Collections;
using System.Linq;
using E = System.Linq.Enumerable;
class Program
{

    static void Main(string[] args)
    {

        //var NX = Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToArray();
        var NMK = Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToArray();
        var N = NMK[0];
        var M = NMK[1];
        var K = NMK[2];
        Modular ans = new Modular(0);
        for (int i = 0; i <= K; i++)
        {
            ans += M * Modular.Pow(M - 1, (int)N - 1 - i)*Modular.Ncr((int)N -1,i);
        }

        Console.WriteLine(ans.value);
    }
}

class Modular
{
    private const int M = 998244353;
    public long value;
    public Modular(long value) { this.value = value; }
    public static implicit operator Modular(long a)
    {
        var m = a % M;
        return new Modular((m < 0) ? m + M : m);
    }
    public static Modular operator +(Modular a, Modular b)
    {
        return (a.value + b.value) % M;
    }
    public static Modular operator -(Modular a, Modular b)
    {
        return a.value - b.value;
    }
    public static Modular operator *(Modular a, Modular b)
    {
        return a.value * b.value;
    }
    public static Modular Pow(Modular a, int n)
    {
        switch (n)
        {
            case 0:
                return 1;
            case 1:
                return a;
            default:
                var p = Pow(a, n / 2);
                return p * p * Pow(a, n % 2);
        }
    }
    public static Modular operator /(Modular a, Modular b)
    {
        return a * Pow(b, M - 2);
    }
    private static readonly List<int> facs = new List<int> { 1 };
    private static Modular Fac(int n)
    {
        for (int i = facs.Count; i <= n; ++i)
        {
            facs.Add((int)(Math.BigMul(facs.Last(), i) % M));
        }
        return facs[n];
    }
    public static Modular Ncr(int n, int r)
    {
        return (n < r) ? 0
             : (n == r) ? 1
                        : Fac(n) / (Fac(r) * Fac(n - r));
    }
    public static explicit operator int(Modular a)
    {
        return (int)a.value;
    }

    public static Modular Lcm(Modular a, Modular b)
    {
        var tmp = Gcdl(a.value, b.value);
        return ((a * b) / new Modular(tmp));
    }
    static Modular Gcd(Modular m, Modular n)
    {
        if (n.value > m.value) return Gcd(n, m);
        if (n.value == 0) return m;
        var r = new Modular(m.value % n.value);
        return Gcd(n, r);
    }

    static long Gcdl(long m, long n)
    {
        if (n > m) return Gcdl(n, m);
        if (n == 0) return m;
        return Gcdl(n, m % n);
    }
}