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: Accepted)

def cmb(n,r,mod):
    if r<0 or r>n:return 0
    r=min(r,n-r)
    return g1[n]*g2[r]*g2[n-r]%mod


mod=998244353
n,m,k=map(int,input().split())
g1=[1,1]
g2=[1,1]
inverse=[0,1]

for i in range(2,n):
    g1.append((g1[-1]*i)%mod)
    inverse.append((-inverse[mod%i]*(mod//i))%mod)
    g2.append((g2[-1]*inverse[-1]%mod))

ans=m*(m-1)**(n-1)
for i in range(k):
    ans +=(m*pow(m-1,n-2-i,mod))*cmb(n-1,i+1,mod)
    ans %=mod

print(ans%mod)