from math import factorial



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

mod = 10 ** 9 + 7



def Comb(N, K):

    a = factorial(N) % mod

    b = factorial(K) % mod

    c = factorial(N-K) % mod

    return (a * pow(b, mod-2, mod) * pow(c, mod-2, mod)) % mod





c = Comb(N*M-2, K-2)



ans = 0



for d in range(M):

    ans += d * (M - d) * (N ** 2)

    ans %= mod



for d in range(N):

    ans += d * (N - d) * (M ** 2)

    ans %= mod



ans *= c

ans %= mod



print(ans)
from math import factorial



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

mod = 10 ** 9 + 7



def f(N):

    a = 1

    for i in range(1, N+1):

        a *= i

        a %= mod

    return a % mod



def Comb(N, K):

    a = f(N)

    b = f(K)

    c = f(N-K)

    return (a * pow(b, mod-2, mod) * pow(c, mod-2, mod)) % mod





c = Comb(N*M-2, K-2)



ans = 0



for d in range(M):

    ans += d * (M - d) * (N ** 2)

    ans %= mod



for d in range(N):

    ans += d * (N - d) * (M ** 2)

    ans %= mod



ans *= c

ans %= mod



print(ans)
from math import factorial

N, M, K = list(map(int, input().split()))
mod = 10**9 + 7


def Comb(N, K):
    a = factorial(N) % mod
    b = factorial(K) % mod
    c = factorial(N - K) % mod
    return (a * pow(b, mod - 2, mod) * pow(c, mod - 2, mod)) % mod


c = Comb(N * M - 2, K - 2)
ans = 0
for d in range(M):
    ans += d * (M - d) * (N**2)
    ans %= mod
for d in range(N):
    ans += d * (N - d) * (M**2)
    ans %= mod
ans *= c
ans %= mod
print(ans)

from math import factorial

N, M, K = list(map(int, input().split()))
mod = 10**9 + 7


def f(N):
    a = 1
    for i in range(1, N + 1):
        a *= i
        a %= mod
    return a % mod


def Comb(N, K):
    a = f(N)
    b = f(K)
    c = f(N - K)
    return (a * pow(b, mod - 2, mod) * pow(c, mod - 2, mod)) % mod


c = Comb(N * M - 2, K - 2)
ans = 0
for d in range(M):
    ans += d * (M - d) * (N**2)
    ans %= mod
for d in range(N):
    ans += d * (N - d) * (M**2)
    ans %= mod
ans *= c
ans %= mod
print(ans)

+def f(N): +    a = 1 +    for i in range(1, N + 1): +        a *= i +        a %= mod +    return a % mod + + -    a = factorial(N) % mod -    b = factorial(K) % mod -    c = factorial(N - K) % mod +    a = f(N) +    b = f(K) +    c = f(N - K)