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 Go (1.14.1) (judge verdict: Time Limit Exceeded)

package main

import "fmt"

const mod = 998244353

func dfs(n, index, m, remain int) int {
	if index == n {
		return 1
	}

	sum := (dfs(n, index+1, m, remain) % mod * (m - 1)) % mod
	if remain > 0 {
		sum += dfs(n, index+1, m, remain-1) % mod
	}
	return sum
}

func main() {
	var n, m, k int
	fmt.Scan(&n, &m, &k)

	ans := m * dfs(n, 1, m, k) % mod
	fmt.Println(ans)
}