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: Wrong Answer)

def main():
    n, m, k = map(int, input().split())
    mod = 998244353
    if m == 1:
        print(1)
        return
    ans = 0
    for i in range(k+1):
        ans += m*comb(n-1, i)*pow(m-1, n-i-1, mod)
        ans %= mod
    print(ans)

def comb(a, b):
    numerator = 1
    denominator = 1
    if a-b < 0:
        return None
    b = min(a-b, b)
    for i in range(a-b+1, a+1):
        numerator *= i
    for i in range(1, b+1):
        denominator *= i
    return numerator//denominator

if __name__ == "__main__":
    main()