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: Accepted)

N, M, K = map(int, input().split())
MOD = 998244353
modinv = lambda a, mod=MOD: pow(a, mod - 2, mod)

comb = [M] * (K + 1)
for i in range(1, K + 1):
    comb[i] = comb[i - 1] * (N - i) % MOD
    comb[i] = comb[i] * modinv(i) % MOD

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