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: Accepted)

#include<bits/stdc++.h>
#define int long long
#define for0(i, n) for(int i = 0; i < (n); i++)
#define puts(x) cout << x << "\n"
constexpr int mod = 998244353;
using namespace std;
int f1(int a, int p) {
	if (p == 1)return a;
	if (p % 2)return f1(a, p - 1) * a % mod;
	else return f1(a * a % mod, p / 2) % mod;
}
signed main() {
	int n, m, k, ans = 0; cin >> n >> m >> k;
	int p1 = m, p2 = 1;
	for0(i, n) {
		if (n - i - 1 <= k)ans += p1 * p2 % mod;
		ans %= mod;
		p1 *= m - 1; p1 %= mod;
		p2 *= n - 1 - i; p2 %= mod;
		p2 *= f1(i + 1, mod - 2); p2 %= mod;
	}
	puts(ans);
}