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: Runtime Error)

using System;

namespace E
{
    class Program
    {
        static void Main(string[] args)
        {
            var NMK = Array.ConvertAll(Console.ReadLine().Split(' '), int.Parse);
            var N = NMK[0]; var M = NMK[1]; var K = NMK[2];
            long MOD = 998244353;
            Combination.combInit(100000, MOD);
            long result = 0;
            for (int i = 0; i <= K; i++)
            {
                long subtotal = M;
                subtotal *= modpow(M - 1, N - i - 1, MOD);
                subtotal %= MOD;
                subtotal *= Combination.combination(N - 1, i);
                subtotal %= MOD;
                result += subtotal;
                result %= MOD;
            }
            Console.WriteLine(result);
        }
        static long modpow(long a, long n, long mod)
        {
            long result = 1;
            while (n > 0)
            {
                if ((n & 1) > 0) result = (result * a) % mod;
                a = (a * a) % mod;
                n >>= 1;
            }
            return result;
        }
    }
    static class Combination
    {
        static long combMax;
        static long combMOD;

        static long[] factorial;
        static long[] inverse;
        static long[] factInv;

        public static void combInit(long _max, long _mod)
        {
            combMax = _max;
            combMOD = _mod;
            factorial = new long[combMax];
            inverse = new long[combMax];
            factInv = new long[combMax];

            factorial[0] = factorial[1] = 1;
            factInv[0] = factInv[1] = 1;
            inverse[1] = 1;

            for (int i = 2; i < combMax; i++)
            {
                factorial[i] = factorial[i - 1] * i % combMOD;
                inverse[i] = combMOD - inverse[combMOD % i] * (combMOD / i) % combMOD;
                factInv[i] = factInv[i - 1] * inverse[i] % combMOD;
            }
        }

        public static long combination(int n, int k)
        {
            if (n < k) return 0;
            if (n < 0 || k < 0) return 0;
            return factorial[n] * (factInv[k] * factInv[n - k] % combMOD) % combMOD;
        }
    }
}