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)

MOD = 998244353

N, M, K = map(int, input().split())

def comb(n, r, mod):
    if r > n-r:
        r = n - r
    
    res_X = 1
    for i in range(n-r+1, n+1):
        res_X = (res_X * i)%mod
    
    res_Y = 1
    for i in range(1, r+1):
        res_Y = (res_Y * i)%mod
    
    return (res_X * pow(res_Y, mod-2, mod))%mod

ans = 0
mm_1 = M
for _ in range(N-K-2):
    mm_1 = (mm_1 * (M-1))%MOD


for k in range(K, -1, -1):
    c = comb(N-1, k, MOD)
    mm_1 = (mm_1 * (M-1)) % MOD
    
    ans += c * mm_1
    ans %= MOD
print(ans)