Buggy python submission (verdict: Time Limit Exceeded):
import sys
from math import factorial
input = sys.stdin.readline
N, M, K = map(int, input().split())
MOD = 998244353
inv = [1] * N
FAC = factorial(N - 1) % MOD
if M == 1:
    print(1 if K == N - 1 else 0)
else:
    res = 0
    for i in range(1, N):
        inv[i] = pow(factorial(i), MOD - 2, MOD)
    for k in range(K + 1):
        # k個の○とN-k-1個の|を並べる順列
        # punc = (N-1)!/k!/(N-k-1)!
        # punc = factorial(
        #     k + (N - k - 1)) // factorial(k) // factorial(N - k - 1)
        punc = FAC
        # punc *= pow(factorial(k), MOD - 2, MOD)
        punc *= inv[k]
        punc = punc % MOD
        # punc *= pow(factorial(N - k - 1), MOD - 2, MOD)
        punc *= inv[N - k - 1]
        punc = punc % MOD
        color = M * pow(M - 1, N - k - 1, MOD)
        res += ((punc % MOD) * color) % MOD
        res = res % MOD
    print(res % MOD)


Fixed submission:
import sys
from math import factorial
input = sys.stdin.readline
N, M, K = map(int, input().split())
MOD = 998244353
inv = [1] * N
FAC = factorial(N - 1) % MOD
if M == 1:
    print(1 if K == N - 1 else 0)
else:
    res = 0
    for i in range(1, N):
        inv[i] = (inv[i - 1] * pow(i, MOD - 2, MOD)) % MOD
    for k in range(K + 1):
        # k個の○とN-k-1個の|を並べる順列
        # punc = (N-1)!/k!/(N-k-1)!
        # punc = factorial(
        #     k + (N - k - 1)) // factorial(k) // factorial(N - k - 1)
        punc = FAC
        # punc *= pow(factorial(k), MOD - 2, MOD)
        punc *= inv[k]
        punc = punc % MOD
        # punc *= pow(factorial(N - k - 1), MOD - 2, MOD)
        punc *= inv[N - k - 1]
        punc = punc % MOD
        color = M * pow(M - 1, N - k - 1, MOD)
        res += ((punc % MOD) * color) % MOD
        res = res % MOD
    print(res % MOD)

Buggy python submission (verdict: Time Limit Exceeded):
import sys
from math import factorial
input = sys.stdin.readline
N, M, K = map(int, input().split())
MOD = 998244353
if M == 1:
    print(1 if K == N - 1 else 0)
else:
    res = 0
    for k in range(K + 1):
        # k個の○とN-k-1個の|を並べる順列
        # punc = (N-1)!/k!/(N-k-1)!
        # punc = factorial(
        #     k + (N - k - 1)) // factorial(k) // factorial(N - k - 1)
        punc = factorial(N - 1) % MOD
        punc *= pow(factorial(k), MOD - 2, MOD)
        punc = punc % MOD
        punc *= pow(factorial(N - k - 1), MOD - 2, MOD)
        punc = punc % MOD
        color = M * pow(M - 1, N - k - 1, MOD)
        res += ((punc % MOD) * color) % MOD
        res = res % MOD
    print(res % MOD)

Fixed submission:
import sys
from math import factorial
input = sys.stdin.readline
N, M, K = map(int, input().split())
MOD = 998244353
inv = [1] * N
FAC = factorial(N - 1) % MOD
if M == 1:
    print(1 if K == N - 1 else 0)
else:
    res = 0
    for i in range(1, N):
        inv[i] = (inv[i - 1] * pow(i, MOD - 2, MOD)) % MOD
    for k in range(K + 1):
        # k個の○とN-k-1個の|を並べる順列
        # punc = (N-1)!/k!/(N-k-1)!
        # punc = factorial(
        #     k + (N - k - 1)) // factorial(k) // factorial(N - k - 1)
        punc = FAC
        # punc *= pow(factorial(k), MOD - 2, MOD)
        punc *= inv[k]
        punc = punc % MOD
        # punc *= pow(factorial(N - k - 1), MOD - 2, MOD)
        punc *= inv[N - k - 1]
        punc = punc % MOD
        color = M * pow(M - 1, N - k - 1, MOD)
        res += ((punc % MOD) * color) % MOD
        res = res % MOD
    print(res % MOD)

Buggy python submission (verdict: Time Limit Exceeded):
import sys
from math import factorial
input = sys.stdin.readline
N, M, K = map(int, input().split())
if M == 1:
    print(1 if K == N - 1 else 0)
else:
    res = 0
    for k in range(K + 1):
        # k個の○とN-k-1個の|を並べる順列
        punc = factorial(
            k + (N - k - 1)) // factorial(k) // factorial(N - k - 1)
        # color = M * ((M - 1)**(N - k - 1))
        color = M
        for _ in range(N - k - 1):
            color *= M - 1
            color = color % 998244353
        res += ((punc % 998244353) * (color % 998244353)) % 998244353
        res = res % 998244353
    print((res) % 998244353)

Fixed submission:
import sys
from math import factorial
input = sys.stdin.readline
N, M, K = map(int, input().split())
MOD = 998244353
inv = [1] * N
FAC = factorial(N - 1) % MOD
if M == 1:
    print(1 if K == N - 1 else 0)
else:
    res = 0
    for i in range(1, N):
        inv[i] = (inv[i - 1] * pow(i, MOD - 2, MOD)) % MOD
    for k in range(K + 1):
        # k個の○とN-k-1個の|を並べる順列
        # punc = (N-1)!/k!/(N-k-1)!
        # punc = factorial(
        #     k + (N - k - 1)) // factorial(k) // factorial(N - k - 1)
        punc = FAC
        # punc *= pow(factorial(k), MOD - 2, MOD)
        punc *= inv[k]
        punc = punc % MOD
        # punc *= pow(factorial(N - k - 1), MOD - 2, MOD)
        punc *= inv[N - k - 1]
        punc = punc % MOD
        color = M * pow(M - 1, N - k - 1, MOD)
        res += ((punc % MOD) * color) % MOD
        res = res % MOD
    print(res % MOD)

Buggy python submission (verdict: Time Limit Exceeded):
import sys
from math import factorial
input = sys.stdin.readline
N, M, K = map(int, input().split())
if M == 1:
    print(1 if K == N - 1 else 0)
else:
    res = 0
    for k in range(K + 1):
        # k個の○とN-k-1個の|を並べる順列
        punc = factorial(k + (N - k - 1)) // (factorial(k)
                                              * factorial(N - k - 1))
        color = M * ((M - 1)**(N - k - 1))
        res += punc * color
    print((res) % 998244353)

Fixed submission:
import sys
from math import factorial
input = sys.stdin.readline
N, M, K = map(int, input().split())
MOD = 998244353
inv = [1] * N
FAC = factorial(N - 1) % MOD
if M == 1:
    print(1 if K == N - 1 else 0)
else:
    res = 0
    for i in range(1, N):
        inv[i] = (inv[i - 1] * pow(i, MOD - 2, MOD)) % MOD
    for k in range(K + 1):
        # k個の○とN-k-1個の|を並べる順列
        # punc = (N-1)!/k!/(N-k-1)!
        # punc = factorial(
        #     k + (N - k - 1)) // factorial(k) // factorial(N - k - 1)
        punc = FAC
        # punc *= pow(factorial(k), MOD - 2, MOD)
        punc *= inv[k]
        punc = punc % MOD
        # punc *= pow(factorial(N - k - 1), MOD - 2, MOD)
        punc *= inv[N - k - 1]
        punc = punc % MOD
        color = M * pow(M - 1, N - k - 1, MOD)
        res += ((punc % MOD) * color) % MOD
        res = res % MOD
    print(res % MOD)