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 (
	"bufio"
	"fmt"
	"os"
	"sort"
	"strconv"
)

const N = 998244353

func main() {
	sc := NewScanner()

	n := sc.ReadInt()
	m := sc.ReadInt()
	k := sc.ReadInt()

	dp := make([][]int, n+1)

	dp[1] = make([]int, 2)
	dp[1][0] = m % N

	for ni := 2; ni <= n; ni++ {
		kLen := Min(ni, k+1)
		dp[ni] = make([]int, kLen+1)
		dp[ni][0] = dp[ni-1][0] * (m - 1) % N
		for ki := 1; ki < kLen; ki++ {
			dp[ni][ki] =
				(dp[ni-1][ki-1] + dp[ni-1][ki]*(m-1)) % N
		}
	}

	ans := 0
	for ki := 0; ki <= k; ki++ {
		ans = (ans + dp[n][ki]) % N
	}

	fmt.Println(ans)
}

// util
// *   math/simple

func Abs(x int) int {
	if x >= 0 {
		return x
	}
	return -x
}

func Min(values ...int) int {
	if len(values) == 0 {
		panic("no values")
	}
	min := values[0]
	for _, v := range values {
		if v < min {
			min = v
		}
	}
	return min
}

func Max(values ...int) int {
	if len(values) == 0 {
		panic("no values")
	}
	max := values[0]
	for _, v := range values {
		if v > max {
			max = v
		}
	}
	return max
}

func Pow(base int, exponent uint) int {
	answer := 1
	for i := uint(0); i < exponent; i++ {
		answer *= base
	}
	return answer
}

// *   sortutil

func ReverseInts(a []int) {
	sort.Sort(sort.Reverse(sort.IntSlice(a)))
}

func ReverseStrings(a []string) {
	sort.Sort(sort.Reverse(sort.StringSlice(a)))
}

// *   io

type Scanner struct {
	bufScanner *bufio.Scanner
}

func NewScanner() *Scanner {
	bufSc := bufio.NewScanner(os.Stdin)
	bufSc.Split(bufio.ScanWords)
	bufSc.Buffer(nil, 100000000)
	return &Scanner{bufSc}
}

func (sc *Scanner) ReadString() string {
	bufSc := sc.bufScanner
	bufSc.Scan()
	return bufSc.Text()
}

func (sc *Scanner) ReadInt() int {
	bufSc := sc.bufScanner
	bufSc.Scan()
	text := bufSc.Text()

	num, err := strconv.Atoi(text)
	if err != nil {
		panic(err)
	}
	return num
}