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: Time Limit Exceeded)

# E - Colorful Blocks

MOD = 998244353
N, M, K = map(int, input().split())

# 予め階乗を計算しておく
f = [1]
for i in range(N):
    f.append(f[i]*(i+1)%MOD)

# 組み合わせ関数
def comb_mod(n, r, p):
    return f[n] * pow(f[r], p-2, p) * pow(f[n-r], p-2, p)

ans = 0
for i in range(K+1):
    ans = (ans + (M*pow(M-1, N-1-i,MOD)) * comb_mod(N-1, i, MOD))%MOD

print(ans)