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: Time Limit Exceeded)

//20200510 E
import java.util.*;
public class Main {
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
		int n=sc.nextInt();
		int m=sc.nextInt()%998244353;
		int k=sc.nextInt();
		long[] p=new long[k+1];
		p[0]=m;
		for(int i=0;i<n-1;i++){
			for(int j=k;j>0;j--){
				p[j]=(p[j-1]+p[j]*(m-1))% 998244353;
			}
			p[0]=p[0]*(m-1)%998244353;
		}
		long ans=0;
		for(int i=0;i<k+1;i++){
			ans=(ans+p[i])% 998244353;
		}
		System.out.println(ans);
	}
}