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)

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

fac = [0]*(n+1)
per = [0]*(n+1)

fac[0]=1
per[0] = 1
for i in range(1,n+1):
    fac[i] = fac[i-1]*i%mod
    per[i] = pow(fac[i],mod-2,mod)

def nCk(n,k):
    return fac[n]*per[k]%mod*per[n-k]%mod

ans = 0
for i in range(k+1):
    if i == 0:
        ans += m*pow(m-1,n-1-i,mod)%mod
    else:
        ans += m*pow(m-1,n-1-i,mod)%mod * nCk(n-1,i)%mod
    ans %= mod
print(ans)