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: Time Limit Exceeded)

MAX = 10 ** 5 * 2
mod = 998244353
frac = [1]
for i in range(1,MAX + 1 ):
    frac.append( (frac[-1] * i) % mod )
def pow(a, n):
    if n == 0 : return  1
    elif n == 1 : return a
    tmp = pow(a, n//2)
    tmp = (tmp * tmp) % mod
    if n % 2 == 1 :
        tmp = (tmp * a) % mod
    return tmp
def inv(x):
    return pow(x, mod - 2 )
def comb(n, k):
    if k >= n or k < 0 : return 1
    return (frac[n] * inv(frac[n-k]) * inv(frac[k]))%mod
N,M,K=map(int,input().split())
a=comb(N-1,K)
b=pow(M-1,N-1)
for i in range(1,K+1):
    b+=(pow(M-1,N-1-i)*comb(N-1,i))%mod
    b=b%mod
print((M*b)%mod)