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: Wrong Answer)

import sys
def S(): return sys.stdin.readline().rstrip()
def I(): return int(sys.stdin.readline().rstrip())
def MI(): return map(int,sys.stdin.readline().rstrip().split())
def LI(): return list(map(int,sys.stdin.readline().rstrip().split()))
def LS(): return list(sys.stdin.readline().rstrip().split())

MOD = 998244353
n,m,k = MI()

s = [1]
for i in range(2, n):
    s.append(s[-1]*i%MOD)
if m == 1 and k < n-1:
    print(0)
    exit(0)
elif m == 1 and k == n-1:
    print(1)
    exit(0)
elif k == n-1:
    print(pow(m, n, MOD))
ans = m*pow(m-1, n-1, MOD)%MOD
for i in range(1, k+1):
    tmp = m*pow(m-1, n-1-i, MOD)*s[n-2]*pow(s[n-2-i], MOD-2, MOD)*pow(s[i-1], MOD-2, MOD)
    ans += tmp
    ans %= MOD
print(ans)