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: Accepted)

package main

import (
	"bufio"
	. "fmt"
	"io"
	"os"
)

// github.com/EndlessCheng/codeforces-go
func run(_r io.Reader, _w io.Writer) {
	in := bufio.NewReader(_r)
	out := bufio.NewWriter(_w)
	defer out.Flush()
	const mod = 998244353

	pow := func(x, n int) int {
		x %= mod
		res := 1
		for ; n > 0; n >>= 1 {
			if n&1 == 1 {
				res = res * x % mod
			}
			x = x * x % mod
		}
		return res
	}
	inv := func(a int) int { return pow(a, mod-2) }
	const mx int = 3e5
	F := [mx + 1]int{1}
	invF := [mx + 1]int{inv(1)}
	for i := 1; i <= mx; i++ {
		F[i] = F[i-1] * i % mod
		invF[i] = inv(F[i])
	}
	comb := func(n, k int) int { return F[n] * invF[k] % mod * invF[n-k] % mod }

	var n, m, k, ans int
	Fscan(in, &n, &m, &k)
	for i := 0; i <= k; i++ {
		v := m
		v = v * comb(n-1, i) % mod
		v = v * pow(m-1, n-1-i) % mod
		ans = (ans +v) % mod
	}
	Fprint(out, ans)
}

func main() { run(os.Stdin, os.Stdout) }