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)

N,M,K = map(int,input().split())
mod = 998244353
ans = (M**N)%mod
def combination(n,k):
    bunbo,bunsi = 1,1
    for i in range(k):
        bunsi = bunsi*(n-i)%mod
        bunbo = bunbo*(i+1)%mod
    return bunsi*pow(bunbo,mod-2,mod)%mod

for t in range(K+1,N):
    tmp = combination(N-1,t)
    ans = (ans - (tmp*M%mod)*pow(M-1,N-1-t,mod)%mod)%mod
print(ans)