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 (GCC 9.2.1) (judge verdict: Wrong Answer)

#include <stdio.h>
#define dr 998244353

int main(){
  int n,m,k,i,j,l[200005]={};
  long mm=0;
  scanf("%d",&n);
  scanf("%d",&m);
  scanf("%d",&k);
  for(i=0;i<n;i++){
    l[0]*=m-1;
    l[0]%=dr;
    for(j=1;j<=k;j++){
      l[j]*=m-1;
      l[j]+=l[j-1];
      l[j]%=dr;
    }
  }
  for(i=0;i<k;i++) mm+=l[i];
  printf("%ld",mm);
  return(0);
}