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)

n, m, k = map(int, input().strip().split())

ways = [0] * n

for i in range(n):
    if i == 0:
        ways[i] = m
    else:
        way = ways[i - 1] * (m - 1)
        way %= 998244353
        ways[i] = way

total = 0
nCr = 1
for i in range(k + 1):
    nCr *= (n - i) // (i + 1) if i > 0 else 1
    total += ways[-(i + 1)] * nCr
    total %= 998244353

print(total % 998244353)