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 <cstdio>

long long dp[1000000];

int main() {
  int N, M, K;

  scanf("%d %d %d", &N, &M, &K);

  dp[0] = M;
  for (int i = 2; i <= N; i++) {
    for (int j = K; j >= 0; j--) {
      dp[j] = dp[j] * (M - 1);
      if (j != 0) dp[j] += dp[j-1];
      dp[j] = dp[j] % 998244353;
    }
  }

  long long ans = 0;
  for (int i = 0; i <= K; i++) {
    printf("%d\n", dp[i]);
    ans += dp[i];
  }
  ans = ans % 998244353;

  printf("%lld\n", ans);
}