Buggy python submission (verdict: Time Limit Exceeded):
def comb(n, k, mod=10**9 + 7):
    from functools import reduce
    from operator import mul
    k = min(k, n - k)
    x = reduce(mul, range(n - k + 1, n + 1), 1) % mod
    y = reduce(mul, range(1, k + 1), 1) % mod
    return x * pow(y, mod - 2, mod) % mod


def solve(string):
    n, m, k = map(int, string.split())
    mod = 10**9 + 7
    base = n * m * (n + m) * (n * m - 1) // 6 % mod
    return str(base * comb(n * m - 2, k - 2) % mod)


if __name__ == '__main__':
    print(solve(input()))


Fixed submission:
mod = 10**9 + 7


def comb(n, k):
    x, y = 1, 1
    k = min(k, n - k)
    for i in range(k):
        x *= n - i
        x %= mod
        y *= i + 1
        y %= mod
    return x * pow(y, mod - 2, mod) % mod


def solve(string):
    n, m, k = map(int, string.split())
    base = n * m * ((n + 1) * (m + 1) * (n + m - 2) - n**2 - m**2 + 2) // 6 % mod
    return str(base * comb(n * m - 2, k - 2) % mod)


if __name__ == '__main__':
    print(solve(input()))

Buggy python submission (verdict: Time Limit Exceeded):
from scipy.misc import comb


def solve(string):
    n, m, k = map(int, string.split())
    p = 10**9 + 7
    base = n * m * ((n + 1) * (m + 1) * (n + m - 2) - n**2 - m**2 + 2) // 6 % p
    return str(base * (comb(n * m - 2, min(k - 2, n * m - k), exact=True) % p) % p)


if __name__ == '__main__':
    print(solve(input()))


Fixed submission:
mod = 10**9 + 7


def comb(n, k):
    x, y = 1, 1
    k = min(k, n - k)
    for i in range(k):
        x *= n - i
        x %= mod
        y *= i + 1
        y %= mod
    return x * pow(y, mod - 2, mod) % mod


def solve(string):
    n, m, k = map(int, string.split())
    base = n * m * ((n + 1) * (m + 1) * (n + m - 2) - n**2 - m**2 + 2) // 6 % mod
    return str(base * comb(n * m - 2, k - 2) % mod)


if __name__ == '__main__':
    print(solve(input()))

Buggy python submission (verdict: Time Limit Exceeded):
from scipy.misc import comb


def solve(string):
    n, m, k = map(int, string.split())
    base = n * m * ((n + 1) * (m + 1) * (n + m - 2) - n**2 - m**2 + 2) // 6 % (10**9 + 7)
    return str(base * comb(n * m - 2, min(k - 2, n * m - k), exact=True) % (10**9 + 7))


if __name__ == '__main__':
    print(solve(input()))


Fixed submission:
mod = 10**9 + 7


def comb(n, k):
    x, y = 1, 1
    k = min(k, n - k)
    for i in range(k):
        x *= n - i
        x %= mod
        y *= i + 1
        y %= mod
    return x * pow(y, mod - 2, mod) % mod


def solve(string):
    n, m, k = map(int, string.split())
    base = n * m * ((n + 1) * (m + 1) * (n + m - 2) - n**2 - m**2 + 2) // 6 % mod
    return str(base * comb(n * m - 2, k - 2) % mod)


if __name__ == '__main__':
    print(solve(input()))

Buggy python submission (verdict: Time Limit Exceeded):
from scipy.misc import comb


def solve(string):
    n, m, k = map(int, string.split())
    base = n * m * ((n + 1) * (m + 1) * (n + m - 2) - n**2 - m**2 + 2) // 6 % (10**9 + 7)
    return str(base * comb(n * m - 2, k - 2, exact=True) % (10**9 + 7))


if __name__ == '__main__':
    print(solve(input()))


Fixed submission:
mod = 10**9 + 7


def comb(n, k):
    x, y = 1, 1
    k = min(k, n - k)
    for i in range(k):
        x *= n - i
        x %= mod
        y *= i + 1
        y %= mod
    return x * pow(y, mod - 2, mod) % mod


def solve(string):
    n, m, k = map(int, string.split())
    base = n * m * ((n + 1) * (m + 1) * (n + m - 2) - n**2 - m**2 + 2) // 6 % mod
    return str(base * comb(n * m - 2, k - 2) % mod)


if __name__ == '__main__':
    print(solve(input()))

Buggy python submission (verdict: Time Limit Exceeded):
import operator as op
from functools import reduce


def ncr(n, r):
    r = min(r, n - r)
    numer = reduce(op.mul, range(n, n - r, -1), 1)
    denom = reduce(op.mul, range(1, r + 1), 1)
    return numer // denom


def solve(string):
    n, m, k = map(int, string.split())
    base = n * m * ((n + 1) * (m + 1) * (n + m - 2) - n**2 - m**2 + 2) // 6 % (10**9 + 7)
    return str(base * ncr(m * n - 2, k - 2) % (10**9 + 7))


if __name__ == '__main__':
    print(solve(input()))


Fixed submission:
mod = 10**9 + 7


def comb(n, k):
    x, y = 1, 1
    k = min(k, n - k)
    for i in range(k):
        x *= n - i
        x %= mod
        y *= i + 1
        y %= mod
    return x * pow(y, mod - 2, mod) % mod


def solve(string):
    n, m, k = map(int, string.split())
    base = n * m * ((n + 1) * (m + 1) * (n + m - 2) - n**2 - m**2 + 2) // 6 % mod
    return str(base * comb(n * m - 2, k - 2) % mod)


if __name__ == '__main__':
    print(solve(input()))

Buggy python submission (verdict: Time Limit Exceeded):
from scipy.misc import comb


def solve(string):
    n, m, k = map(int, string.split())
    base = n * m * ((n + 1) * (m + 1) * (n + m - 2) - n**2 - m**2 + 2) // 6 % (10**9 + 7)
    return str(base * (comb(n * m - 2, k - 2, exact=True) % (10**9 + 7)) % (10**9 + 7))


if __name__ == '__main__':
    print(solve(input()))


Fixed submission:
mod = 10**9 + 7


def comb(n, k):
    x, y = 1, 1
    k = min(k, n - k)
    for i in range(k):
        x *= n - i
        x %= mod
        y *= i + 1
        y %= mod
    return x * pow(y, mod - 2, mod) % mod


def solve(string):
    n, m, k = map(int, string.split())
    base = n * m * ((n + 1) * (m + 1) * (n + m - 2) - n**2 - m**2 + 2) // 6 % mod
    return str(base * comb(n * m - 2, k - 2) % mod)


if __name__ == '__main__':
    print(solve(input()))

Buggy python submission (verdict: Time Limit Exceeded):
from scipy.misc import comb


def solve(string):
    n, m, k = map(int, string.split())
    base = n * m * ((n + 1) * (m + 1) * (n + m - 2) - n**2 - m**2 + 2) // 6 % (10**9 + 7)
    return str(base * comb(n * m - 2, k - 2, exact=True) % (10**9 + 7))


if __name__ == '__main__':
    print(solve(input()))


Fixed submission:
mod = 10**9 + 7


def comb(n, k):
    x, y = 1, 1
    k = min(k, n - k)
    for i in range(k):
        x *= n - i
        x %= mod
        y *= i + 1
        y %= mod
    return x * pow(y, mod - 2, mod) % mod


def solve(string):
    n, m, k = map(int, string.split())
    base = n * m * ((n + 1) * (m + 1) * (n + m - 2) - n**2 - m**2 + 2) // 6 % mod
    return str(base * comb(n * m - 2, k - 2) % mod)


if __name__ == '__main__':
    print(solve(input()))

Buggy python submission (verdict: Time Limit Exceeded):
from operator import mul
from functools import reduce


def solve(string):
    n, m, k = map(int, string.split())
    base = n * m * ((n + 1) * (m + 1) * (n + m - 2) - n**2 - m**2 + 2) // 6 % (10**9 + 7)
    return str(base * reduce(mul, range(n * m - k + 1, n * m - 1)) //
               reduce(mul, range(1, k - 1)) % (10**9 + 7) if k > 2 else base)


if __name__ == '__main__':
    print(solve(input()))


Fixed submission:
mod = 10**9 + 7


def comb(n, k):
    x, y = 1, 1
    k = min(k, n - k)
    for i in range(k):
        x *= n - i
        x %= mod
        y *= i + 1
        y %= mod
    return x * pow(y, mod - 2, mod) % mod


def solve(string):
    n, m, k = map(int, string.split())
    base = n * m * ((n + 1) * (m + 1) * (n + m - 2) - n**2 - m**2 + 2) // 6 % mod
    return str(base * comb(n * m - 2, k - 2) % mod)


if __name__ == '__main__':
    print(solve(input()))

Buggy python submission (verdict: Time Limit Exceeded):
from scipy.misc import comb


def solve(string):
    n, m, k = map(int, string.split())
    return str(n * m * ((n + 1) * (m + 1) * (n + m - 2) - n**2 - m**2 + 2) // 6 *
               comb(n * m - 2, k - 2, exact=True) % (10**9 + 7))


if __name__ == '__main__':
    print(solve(input()))


Fixed submission:
mod = 10**9 + 7


def comb(n, k):
    x, y = 1, 1
    k = min(k, n - k)
    for i in range(k):
        x *= n - i
        x %= mod
        y *= i + 1
        y %= mod
    return x * pow(y, mod - 2, mod) % mod


def solve(string):
    n, m, k = map(int, string.split())
    base = n * m * ((n + 1) * (m + 1) * (n + m - 2) - n**2 - m**2 + 2) // 6 % mod
    return str(base * comb(n * m - 2, k - 2) % mod)


if __name__ == '__main__':
    print(solve(input()))