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)

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

mod = 998244353

ans = 0

class Combination:
    def __init__(self, n):
        self.facts = [1 for i in range(N+1)]
        self.invs = [1 for i in range(N+1)]
        
        for i in range(1, N+1):
            self.facts[i] = self.facts[i-1] * i % mod
            self.invs[i] = pow(self.facts[i], mod-2, mod)

    def ncr(self, n, r):
        return self.facts[n] * self.invs[r] * self.invs[n-r] % mod

    def nhr(self, n, r): 
        return self.ncr(n+r-1, n-1)

comb = Combination(N)

for i in range(K+1):
    d = M * pow(M-1, N-i-1, mod) * comb.ncr(N-1, i)
    ans = (ans + d % mod) % mod

print(ans)