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: Runtime Error)

#include<stdio.h>

#define mod 998244353
#define ElementType long long
#define str "%lld"

int N, M, K;

ElementType moded(ElementType n)
{
	return n % mod;
}

ElementType f(int total, int start, int pairs)
{
	if (pairs > K)return 0;
	if (total == 1)return M - 1 + (pairs != K);
	if (start)	return moded(moded(f(total - 1, 0, pairs)) * moded(M));
	return moded(moded(f(total - 1, 0, pairs) * moded(M - 1)) + moded(f(total - 1, 0, pairs+1)));
}

int main()
{
	freopen("in.txt", "r", stdin);

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

	printf(str, f(N, 1, 0));

	return 0;
}