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 PyPy3 (7.3.0) (judge verdict: Time Limit Exceeded)

from sys import stdin, setrecursionlimit
from math import factorial

setrecursionlimit(10 ** 9)
INF = 1 << 60


def input():
    return stdin.readline().strip()


def main():
    N, M, K = map(int, input().split())
    MOD = 998244353
    fac = [0] * (N + 10)
    finv = [0] * (N + 10)
    inv = [0] * (N + 10)
    fac[0] = fac[1] = 1
    finv[0] = finv[1] = 1
    inv[1] = 1
    for i in range(2, N + 2):
        fac[i] = fac[i - 1] * i % MOD
        inv[i] = MOD - inv[MOD % i] * (MOD // i) % MOD
        finv[i] = finv[i - 1] * inv[i] % MOD

    def COM(n, k):
        if n < k:
            return 0
        if n < 0 or k < 0:
            return 0
        return fac[n] * (finv[k] * finv[n - k] % MOD) % MOD

    ans = 0
    for k in range(K + 1):
        ans += COM(N - 1, k) * ((M % MOD) * ((M - 1) % MOD) ** (N - k - 1)) % MOD

    print(ans % MOD)

    return


if __name__ == '__main__':
    main()