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)

def main():
    N,M,K=map(int,input().split())
    MOD=998244353
    E=0

    n_=1
    for i in range(1,N):
        n_=(n_*i)%MOD

    nr_ = 1
    nr_array=[]
    for i in range(1,N-1):
        nr_ = (nr_ * i) % MOD
        nr_array.append(nr_)

    r_=1
    for i in range(0,K+1):
        if i!=0 and i!=N-1:
            r_ = (r_ * i) % MOD
            nr_=nr_array.pop()
            power_r=pow(r_,MOD-2,MOD)
            power_nr=pow(nr_,MOD-2,MOD)
        Mk=pow(M-1,N-1-i,MOD)

        if i!=0 and i!=N-1:
            E+=(n_*power_r*power_nr*Mk)%MOD
        else:
            E+=Mk%MOD

    res=(M*E)%MOD
    print(res)

if __name__=="__main__":
    main()