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: Runtime Error)

DELIM = 998244353

def kaijo(n, x):
    double = (n**2) % DELIM
    if(x==1):
        return n
    if(x%2==0):
        return kaijo(double, x//2) % DELIM
    else:
        return (kaijo(double, x//2) * (n % DELIM)) % DELIM


def calc(N, M, x):
    m = M % DELIM
    m2 = (M-1) % DELIM
    nx = (N-x) % DELIM
    if(x == 0):
        return (m * kaijo(m2, N-1)) % DELIM
    return (nx * m * kaijo(m2, N-1-x)) % DELIM

def main():
    N, M, K = map(int, input().split())
    ans = 0
    for x in range(0, K+1, 1):
        ans = (ans + calc(N, M, x)) % DELIM
    print(ans)


main()