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)

def choose(n, r, mod)
  return 0 if not (0 <= r and r <= n)
  return 1 if r == 0 or r == n
  fact(n, mod) * inverse(fact(r, mod) * fact(n-r, mod) % mod, mod) % mod
end
@fact = [1]
def fact(n, mod)
  if n > @fact.size then
    f = @fact[-1]
    (@fact.size+1..n).each{|i|
      f = (f * i) % mod
      @fact << f
    }
  end
  @fact[n-1]
end
def inverse(x, mod)
  pow(x, mod-2, mod)
end
def pow(x, n, mod)
  ans = 1
  while n > 0
    ans = ans * x % mod if n.odd?
    x = x * x % mod
    n >>= 1
  end
  ans
end

N, M, K = gets.chomp.split(" ").map(&:to_i)
MOD = 998244353

ans, wk = [0, 1]
(1..N).each{|n|
  wk = (n == 1 ? M : wk * (M-1) % MOD)
  if N - n <= K then
    ans = (ans + wk * choose(N-1, N-n, MOD)) % MOD
  end
}

puts ans