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: Runtime Error)

import java.util.*;
import java.io.PrintWriter;
public class Main{
	static long mod=998244353;
	public static void main(String[] args){
		Scanner sc=new Scanner(System.in);
		int n=sc.nextInt();
		int m=sc.nextInt();
		int k=sc.nextInt();
		
		long[] pow=new long[n+1];
		long[] ppp=new long[n+1];
		ppp[1]=1;
		for(int i=2; i<=n; i++){
			ppp[i]=(ppp[i-1]*i)%mod;
		}
		pow[1]=m;
		for(int i=2; i<=n; i++){
			pow[i]=(pow[i-1]*(m-1))%mod;
		}
		long ans=0;
		for(int i=0; i<=k; i++){
			ans+=pow[n-i]*((ppp[n-i]*((pow1(ppp[i],mod-2)*pow1(ppp[n-2*i],mod-2))%mod))%mod)%mod;
			ans%=mod;
		}
		System.out.println(ans);
	}
	static long pow1(long p,long q){
		if(p==0){
			return 1;
		}
		long res=1;
		while(q>0){
			if((q & 1)==1){
				res*=p;
				res%=mod;
			}
			q>>=1;
			p*=p;
			p%=mod;
		}
		return res;
	}
}