MOD = 10**9+7

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



U = N*M

fact = [1]*(U+1)

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

    fact[i] = (fact[i-1]*i)%MOD



def comb(n,k):

    x = fact[n]

    x *= pow(fact[n-k],MOD-2,MOD)

    x %= MOD

    x *= pow(fact[k],MOD-2,MOD)

    return x



res = 0



for i in range(1,N):

    res += i*M*M*(N-i)%MOD

    res %= MOD



for i in range(1,M):

    res += i*N*N*(M-i)%MOD

    res %= MOD



res *= comb(N*M-2,K-2)

res %= MOD

print(res)
mod = 10**9 + 7

n,m,k = list(map(int,input().split()))

nm = n*m

f = [1]*(nm+1)

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

    f[i] = (f[i-1]*i)%mod

def C(n,k):

    x = f[n]

    x *= pow(f[n-k],mod-2,mod)

    x %= mod

    x *= pow(f[k],mod-2,mod)

    x %= mod

    return x

def F(n):

    x = n*n*(n+1)//2

    y = n*(n+1)*(2*n+1)//6

    return (x-y)%mod

res = (m*m%mod*F(n)%mod + n*n%mod*F(m)%mod)%mod

res *= C(n*m-2,k-2)

print((res%mod))
MOD = 10**9 + 7
N, M, K = list(map(int, input().split()))
U = N * M
fact = [1] * (U + 1)
for i in range(1, U + 1):
    fact[i] = (fact[i - 1] * i) % MOD


def comb(n, k):
    x = fact[n]
    x *= pow(fact[n - k], MOD - 2, MOD)
    x %= MOD
    x *= pow(fact[k], MOD - 2, MOD)
    return x


res = 0
for i in range(1, N):
    res += i * M * M * (N - i) % MOD
    res %= MOD
for i in range(1, M):
    res += i * N * N * (M - i) % MOD
    res %= MOD
res *= comb(N * M - 2, K - 2)
res %= MOD
print(res)

mod = 10**9 + 7
n, m, k = list(map(int, input().split()))
nm = n * m
f = [1] * (nm + 1)
for i in range(1, nm + 1):
    f[i] = (f[i - 1] * i) % mod


def C(n, k):
    x = f[n]
    x *= pow(f[n - k], mod - 2, mod)
    x %= mod
    x *= pow(f[k], mod - 2, mod)
    x %= mod
    return x


def F(n):
    x = n * n * (n + 1) // 2
    y = n * (n + 1) * (2 * n + 1) // 6
    return (x - y) % mod


res = (m * m % mod * F(n) % mod + n * n % mod * F(m) % mod) % mod
res *= C(n * m - 2, k - 2)
print((res % mod))

-MOD = 10**9 + 7 -N, M, K = list(map(int, input().split())) -U = N * M -fact = [1] * (U + 1) -for i in range(1, U + 1): -    fact[i] = (fact[i - 1] * i) % MOD +mod = 10**9 + 7 +n, m, k = list(map(int, input().split())) +nm = n * m +f = [1] * (nm + 1) +for i in range(1, nm + 1): +    f[i] = (f[i - 1] * i) % mod -def comb(n, k): -    x = fact[n] -    x *= pow(fact[n - k], MOD - 2, MOD) -    x %= MOD -    x *= pow(fact[k], MOD - 2, MOD) +def C(n, k): +    x = f[n] +    x *= pow(f[n - k], mod - 2, mod) +    x %= mod +    x *= pow(f[k], mod - 2, mod) +    x %= mod -res = 0 -for i in range(1, N): -    res += i * M * M * (N - i) % MOD -    res %= MOD -for i in range(1, M): -    res += i * N * N * (M - i) % MOD -    res %= MOD -res *= comb(N * M - 2, K - 2) -res %= MOD -print(res) +def F(n): +    x = n * n * (n + 1) // 2 +    y = n * (n + 1) * (2 * n + 1) // 6 +    return (x - y) % mod + + +res = (m * m % mod * F(n) % mod + n * n % mod * F(m) % mod) % mod +res *= C(n * m - 2, k - 2) +print((res % mod))