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 1.8.0) (judge verdict: Wrong Answer)

import java.util.*;

class Main{
    static long mod = 998244353L;
    static Long n;
    static Long m;
    static Long k;
    static int max = 200000;
    static long[] dp = new long[max+1];
    public static void main(String args[]) {
        Scanner sc = new Scanner(System.in);
        n = sc.nextLong();
        m = sc.nextLong();
        k = sc.nextLong();

        dp[0] = 1;
        for(int i=1;i<=max;i++){
            dp[i] = dp[i-1]*i;
            dp[i] %= mod;
        }

        Long result = 0L;
        for(long i=0;i<=k;i++){
            Long nuri = nurikata(n-i)%mod;
            Long com = combi(n-1, i)%mod;
            // System.out.println(nuri + " " + com);
            result += (nuri*com)%mod;
        }
        System.out.println(result);
    }

    private static Long combi(long n, long k) {
        if(k==0 || k==n)return 1L;
        int ni = (int)n;
        int ki = (int)k;
        long res = mod + dp[ni];
        res /= dp[ki];
        res += mod;
        res /= dp[ni-ki];
        return res%mod;
    }

    private static Long nurikata(Long x) {
        Long tmp = m%mod;
        for(long i=0;i<x-1;i++){
            tmp *= (m-1);
            tmp %= mod;
        }
        return tmp;
    }
}