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: Wrong Answer)

import sys
n, m, k = map(int, input().split())
mod = 998244353

# 隣り合ったブロックを異なる色で塗ると何通りあるか
# 隣り合ったブロック通しで同じ色にする場所をn-1箇所から選ぶ(combination)

# combinationを計算する
def combination(n, r, p):
    if r < 0 or r > n:
        return 0
    r = min(r, n-r)
    return (f[n]*f_inverse[r]*f_inverse[n-r])%p

f = [1, 1] # n!を計算する
f_inverse = [1, 1]# n!の逆元を計算する
n_inverse = [0, 1] # nの逆元
for i in range(2, n+1):
    f.append((f[i-1]*i)%mod)
    n_inverse.append( (-1*(mod//i)*n_inverse[mod%i])%mod )
    f_inverse.append((f_inverse[i-1]*n_inverse[i])%mod)

c = (m * ((m-1)**(n-1-k)))%mod
count = 0
for i in range(k+1):
    # print(count, c, combination(n-1, i, mod))
    count += combination(n-1, i, mod) * c
    c = ( c * (m-1) )% mod
    count %= mod
    
print(count)

# for i in range(1, k):
#     count += t * s
#     t = t//(m-1)
#     s = ((s * (n-1-i))// (i+1))%998244353
#     print(count, t, s)