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)

# ライブラリ改変テスト
class Combi():
    def __init__(self, N, mod):
        self.power = [1 for _ in range(N+1)]
        self.rev = [1 for _ in range(N+1)]
        self.mod = mod
        for i in range(2, N+1):
            self.power[i] = (self.power[i-1]*i) % self.mod
        self.rev[N] = pow(self.power[N], self.mod-2, self.mod)
        for j in range(N, 0, -1):
            self.rev[j-1] = (self.rev[j]*j) % self.mod

    def com(self, K, R):
        if K < R:
            return 0
        else:
            return ((self.power[K])*(self.rev[K-R])*(self.rev[R])) % self.mod

    def pom(self, K, R):
        if K < R:
            return 0
        else:
            return (self.power[K])*(self.rev[K-R]) % self.mod


######################
N, M, K = map(int, input().split())
mod = 998244353
ans = 0
C = Combi(2*10**5, mod)
for i in range(K+1):
    ans += M*C.com(N-1, i)*pow(M-1, N-1-i, mod)
print(ans % mod)
######################