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 Python (3.8.2) (judge verdict: Time Limit Exceeded)

#!/usr/bin/env python

def main():
    n, m, k = map(int, input().split())
    div = 998244353

    ret = 0
    comb = 1
    x = m * ((m-1) ** (n-k-1))
    comb_list = [comb]
    x_list = [x]
    for i in range(1, k+1):
        comb = comb * (n-i) // i
        x = x * (m-1) % div
        comb_list.append(comb)
        x_list.append(x)

    x_list.reverse()
    for i in range(k+1):
        ret += comb_list[i] * x_list[i] % div
        ret %= div

    print(ret)


if __name__ == '__main__':
    main()