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: Accepted)

def modpow(a, x, mod):
    if x == 0:
        return 1
    elif x % 2 == 0:
        return modpow((a * a) % mod, x // 2, mod)
    else:
        return (modpow((a * a) % mod, x // 2, mod) * a) % mod


N, M, K = map(int, input().split(' '))
max_K = 3 * 10 ** 5
mod = 998244353

inv = [0 for i in range(max_K + 1)]
inv[0] = 1
inv[1] = 1
for i in range(2, K + 1):
    inv[i] = modpow(i, mod - 2, mod)
choose = [0 for i in range(K + 1)]
choose[0] = 1
for i in range(1, K + 1):
    choose[i] = choose[i - 1] * (((N - i) * inv[i]) % mod)
    choose[i] %= mod

ans = 0
for i in range(N - 1 - K, N):
    ans += modpow((M - 1), i, mod) * choose[N - i - 1]
    ans %= mod
print((ans * M) % mod)