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: Runtime Error)

MOD = 998244353
FACT = Array.new(100100, 1)
FINV = Array.new(100100, 1)
INV = Array.new(100100, 1)

def powmod(n, r, mod)
  if r.zero?
    1
  elsif r.odd?
    (n * powmod(n, r - 1, mod)) % mod
  else
    (powmod(n, r / 2, mod) ** 2) % mod
  end
end


FACT[0] = FACT[1] = 1
FINV[0] = FINV[1] = 1
INV[1] = 1
(2 ... 100100).each do |i|
  FACT[i] = FACT[i - 1] * i % MOD;
  INV[i] = MOD - INV[MOD%i] * (MOD / i) % MOD;
  FINV[i] = FINV[i - 1] * INV[i] % MOD;
end

def combination(n, k)
  return 0 if n < k
  return 0 if n < 0 || k < 0
  return FACT[n] * (FINV[k] * FINV[n - k] % MOD) % MOD;
end


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

all = powmod(M, N, MOD)
upK = (K + 1 .. N - 1).inject(0){|s, k| (s + combination(N - 1, k) * M * powmod(M - 1, N - 1 - k, MOD)) % MOD }

puts  (all - upK) % MOD