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.Linq;
using System.Collections.Generic;
using static System.Console;
using System.Text;
using System.IO;
using static System.Math;
namespace AtCoder
{
    class Program
    {
        static StreamReader sr;

        static public long[] Sarray() { return ReadLine().Split().Select(long.Parse).ToArray(); }
        static public List<long> Slist() { return ReadLine().Split().Select(long.Parse).ToList(); }
        static long Mod = (long)998244353;
        static void Main(string[] args)
        {
            //SetOut(new StreamWriter(OpenStandardOutput()) { AutoFlush = false });
            var NMK = Sarray();
            var N = NMK[0];
            var M = NMK[1];
            var K = NMK[2];
            var cmb = new Combination(N, Mod);
            var ans = 0L;
            for (var i = 0; i <= K; ++i)
            {
                var t = cmb.nCk((int)N - 1, i) * modpow(M - 1, N - 1 - i, Mod) % Mod;
                t = M * t % Mod;
                ans = (ans + t) % Mod;
            }
            WriteLine(ans);
            //Out.Flush();
        }
        static long modpow(long a, long n, long mod)
        {
            var res = 1L;
            while (0 < n)
            {
                if (n % 2 != 0) res = res * a % mod;
                a = a * a % mod;
                n >>= 1;
            }
            return res;
        }
        public class Combination
        {
            readonly long mod;
            readonly long[] fac, finv, inv;
            public Combination(long n, long mod = 1000000007)
            {
                long max = n + 1;
                this.mod = mod;
                fac = new long[max];
                finv = new long[max];
                inv = new long[max];
                fac[0] = fac[1] = 1;
                finv[0] = finv[1] = 1;
                inv[1] = 1;
                for (int i = 2; i < max; ++i)
                {
                    fac[i] = fac[i - 1] * i % mod;
                    inv[i] = mod - inv[mod % i] * (mod / i) % mod;
                    finv[i] = finv[i - 1] * inv[i] % mod;
                }
            }
            public long nCk(int n, int k)
            {
                if (n < k) return 0;
                if (n < 0 | k < 0) return 0;
                return fac[n] * (finv[k] * finv[n - k] % mod) % mod;
            }
        }
    }
}