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
sys.setrecursionlimit(10**9)

n, m, k = map(int, input().split())

def f(nn,mm,kk):
    if nn==1:
        return mm
    if nn==2:#終了条件
        if kk!=0:
            return mm
        else:
            return mm-1

    if kk>0:
        #print(nn,mm,kk,'a')
        return (f(nn-1,mm,kk-1) + ((mm-1)*f(nn-1,mm,kk)))%998244353
    else:
        #print(nn,mm,kk,'b')
        return (mm-1)**(nn-1)%998244353

print((m*f(n,m,k))%998244353)