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 Java (OpenJDK 11.0.6) (judge verdict: Accepted)

import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Scanner;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author silviase
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Scanner in = new Scanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        EColorfulBlocks solver = new EColorfulBlocks();
        solver.solve(1, in, out);
        out.close();
    }

    static class EColorfulBlocks {
        public void solve(int testNumber, Scanner in, PrintWriter out) {

            int n = in.nextInt();
            int m = in.nextInt();
            int k = in.nextInt();

            ModInt res = new ModInt(0);
            ModComb mc = new ModComb(n);

            for (int i = 0; i <= k; i++) {
                res = res.add(new ModInt(m).mul(new ModInt(m - 1).pow(n - i - 1)).mul(mc.combination(n - 1, i)));
            }

            out.println(res.getVal());
        }

    }

    static class ModComb {
        private int size;
        private ModInt[] fac;
        private ModInt[] inv;

        public ModComb(int n) {
            size = n;
            fac = new ModInt[n + 1];
            inv = new ModInt[n + 1];
            makeFac();
        }

        private void makeFac() {
            for (int i = 0; i <= size; i++) {
                if (i == 0) {
                    fac[i] = new ModInt(1);
                } else {
                    fac[i] = fac[i - 1].mul(i);
                }
                inv[i] = fac[i].inv();
            }
        }

        public ModInt combination(int n, int k) {
            if (n < k || k < 0) return new ModInt(0);
            return fac[n].mul(inv[k].getVal()).mul(inv[n - k].getVal());
        }

    }

    static class ModInt {
        public long val;
        final int MOD = (int) 998244353;

        public ModInt(long i) {
            this.val = (i + MOD) % MOD;
        }

        public ModInt mul(long l) {
            return new ModInt(this.val * l);
        }

        public ModInt add(ModInt m) {
            return new ModInt(this.val + m.val);
        }

        public ModInt mul(ModInt m) {
            return new ModInt(this.val * m.val);
        }

        public ModInt inv() {
            return this.pow(MOD - 2);
        }

        public ModInt pow(long l) {
            ModInt res = new ModInt(1);
            ModInt v = new ModInt(this.val);
            while (l > 0) {
                if (l % 2 != 0) {
                    res = res.mul(v.val);
                }
                v = v.mul(v.val);
                l /= 2;
            }
            return res;
        }

        public long getVal() {
            return val;
        }

        public String toString() {
            return Long.toString(val);
        }

    }
}