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: Wrong Answer)

def powmod(b,r,mod)
  a = 1
  while r > 0
    if r%2 == 1
      a = a * b % mod
    end
    b = b * b % mod
    r /= 2
  end
  a
end

def invmod(f, mod)
  powmod(f, mod-2, mod)
end

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

n = N - 1
m = M - 1
m_pow_n = powmod(m, n, Mod)
m_inv = invmod(m, Mod)

ans = 0
comb = m_pow_n
(0..K).each{ |k|
  ans = (ans + comb) % Mod
  comb = comb * m_inv * (n-k) * invmod(k+1, Mod) % Mod
}
puts ans * M % Mod