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: Wrong Answer)

import sys
readline = sys.stdin.readline
MOD = 998244353

def comb(n, r, mod=MOD):
    r = min(n - r, r)
    res = 1
    fac = 1
    for i in range(r):
        res *= n - i
        res %= mod
        fac *= i + 1
        fac %= mod
    return res * pow(fac, mod-2, mod) % mod

def main():
    N, M, K = map(int, readline().rstrip().split())
    res = 0
    power = pow(M-1, N-K-1, MOD)
    c = comb(N-1, K, MOD)
    for k in range(K, -1, -1):
        n = N - k
        res += c * power * M
        res %= MOD
        power = (power * (M-1)) % MOD
        c = c * k // (N-1 - K + 1)
    
    print(res)


if __name__ == '__main__':
    main()