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 Ruby (2.7.1) (judge verdict: Accepted)

N,M,K = gets.split.map(&:to_i)
Mod = 998244353

D,U = [1,N-1],[1,1]
[K,N/2].min.times{|i| i+=2
	D << D[-1] *(N-i) % Mod
	U << Mod - U[Mod%i] * (Mod/i) % Mod # 謎
}
1.upto(U.size-1){|i|
	U[i] = U[i-1] * U[i] % Mod # 謎
}
Com = lambda{|r| r = [N-1-r,r].min
	D[r] * U[r] % Mod
}

p K.downto(0).inject([0,M*(M-1).pow(N-1-K,Mod)]){|(a,m),k|
	next (a + Com[k] * m) % Mod, m*(M-1)%Mod
}[0]