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{|i|i.to_i}
P = 998244353
def pow(a, n, p)
    r = 1
    while n > 0
        if n % 2 == 1
            r *= a
        end
        a = a ** 2 % p
        n /= 2
    end
    r % p
end
fa = [1, 1]
inv = [nil, 1]
fi = [1, 1]
(2 .. N).each{|n|
    fa << fa[-1] * n % P
    inv << P - inv[P % n] * (P / n) % P
    fi << fi[-1] * inv[-1] % P
    #fi << pow(fa[-1], P - 2, P)
}
#warn fa.inspect
#warn fi.inspect
r = 0
(0 .. K).each{|k|
    n = N - k
    cp = M * pow(M - 1,  n - 1, P) % P
    #warn cp
    cp *= fa[N - 1] * fi[k] * fi[N - 1 - k] % P
    #warn cp
    r += cp
    r %= P
}
puts r