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: Accepted)

# https://kmjp.hatenablog.jp/entry/2020/05/10/0900
# 数学的な問題


mod = 998244353

class COM:
    def __init__(self, n, MOD):
        self.n = n
        self.MOD = MOD
        self.fac = [0] * (n+1)
        self.finv = [0] * (n+1)
        self.inv = [0] * (n+1)
        self.fac[0] = self.fac[1] = 1
        self.finv[0] = self.finv[1] = 1
        self.inv[1] = 1
        for i in range(2, n+1):
            self.fac[i] = self.fac[i-1] * i % MOD
            self.inv[i] = MOD - self.inv[MOD % i] * (MOD // i) % MOD
            self.finv[i] = self.finv[i-1] * self.inv[i] % MOD

    def calc(self, k):
        if k < 0:
            return 0
        return self.fac[self.n] * (self.finv[k] * self.finv[self.n-k] % self.MOD) % self.MOD

def main():
    N, M, K = map(int,input().split())

    # 隣り合う組がK以下のパターンを総当たりして解く
    if N > 1:
        cmbclass = COM(N-1, mod)
        cmb = cmbclass.calc
    else:
        cmb = lambda x:1
    res = 0
    for i in range(K+1):
        res += M * cmb(i) % mod * pow(M-1, N-i-1, mod)


    print(res % mod) 


if __name__ == "__main__":
    main()