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 PyPy3 (7.3.0) (judge verdict: Wrong Answer)

# 組み合わせ(N > 10 ** 7 でも可能)
def xgcd(a, b):
    x0, y0, x1, y1 = 1, 0, 0, 1
    while b != 0:
        q, a, b = a // b, b, a % b
        x0, x1 = x1, x0 - q * x1
        y0, y1 = y1, y0 - q * y1
    return a, x0, y0

def modinv(a, m):
    g, x, y = xgcd(a, m)
    if g != 1:
        raise Exception('modular inverse does not exist')
    else:
        return x % m

def comb(n, r, p):
    ret = 1
    while 1:
        if (r == 0):
            break
        N = n % p
        R = r % p
        if N < R:
            return 0
        for i in range(R):
            ret = ret * (N-i) % p
        imul = 1
        for i in range(R):
            imul = imul * (i+1) % p
        ret = ret * modinv(imul, p) % p
        n //= p
        r //= p
    return ret

mod = 998244353

N, M, K = map(int, input().split())


ans = 0
for k in range(K+1):
    tmp_c = comb(N-k, k, mod)
    tmp_pow = pow(M-1, N-1-k, mod)
    ans += (tmp_c * tmp_pow * M) % mod

print(ans%mod)