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 <iostream>
using namespace std;
const long long mod = 998244353;
long long qpow(long long a, long long b)
{
	long long res = 1;
	while (b)
	{
		if (b & 1)
		{
			res *= a;
			res %= mod;
		}
		a *= a;
		a %= mod;
		b /= 2;
	}
	return res;
}
int main()
{
	long long n, m, k;
	cin >> n >> m >> k;
	long long ans = 0;
	long long c = 1, temp = 1;
	for (long long i = 0; i <= k; i++)
	{
		temp = ((c % mod) * (m % mod) * (qpow(m - 1, n - 1 - i))) % mod;
		ans += temp;
		ans %= mod;
		c = (c % mod) * ((n - i - 1) % mod) * qpow(i + 1, mod - 2);
	}
	cout << ans << endl;
	return 0;
}