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: Runtime Error)

n,m,k = map(int,input().split())
mod = 998244353
ans = 0

def comb(n,k,mod):
    nCk = 1

    for i in range(n-k+1, n+1):
        nCk *= i
        nCk %= mod
 
    for i in range(1,k+1):
        nCk *= pow(i,mod-2,mod)
        nCk %= mod
    return nCk

a1 = pow(m-1, n-k-2, mod)  
b1 = 1  
for i in range(k,-1,-1):
    a = (a1*(m-1))%mod
    b = comb(n-1,i,mod)
    ans += a*b
ans *= m
print(ans%mod)