MAX = 2*10**5+100

MOD = 10**9+7

fact = [0]*MAX #fact[i]: i!

inv = [0]*MAX #inv[i]: iの逆元

finv = [0]*MAX #finv[i]: i!の逆元

fact[0] = 1

fact[1] = 1

finv[0] = 1

finv[1] = 1

inv[1] = 1

    

for i in range(2, MAX):

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

    inv[i] = MOD-inv[MOD%i]*(MOD//i)%MOD

    finv[i] = finv[i-1]*inv[i]%MOD



def C(n, r):

    if n<r:

        return 0

    if n<0 or r<0:

        return 0

    return fact[n]*(finv[r]*finv[n-r]%MOD)%MOD



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

ans = 0



for d in range(1, N):

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

    ans %= MOD

    

for d in range(1, M):

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

    ans %= MOD



ans *= C(N*M-2, K-2)

ans %= MOD



print(ans)
MAX = 2*10**5+100

MOD = 10**9+7

fact = [0]*MAX #fact[i]: i!

inv = [0]*MAX #inv[i]: iの逆元

finv = [0]*MAX #finv[i]: i!の逆元

fact[0] = 1

fact[1] = 1

finv[0] = 1

finv[1] = 1

inv[1] = 1

    

for i in range(2, MAX):

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

    inv[i] = MOD-inv[MOD%i]*(MOD//i)%MOD

    finv[i] = finv[i-1]*inv[i]%MOD



def C(n, r):

    if n<r:

        return 0

    if n<0 or r<0:

        return 0

    return fact[n]*(finv[r]*finv[n-r]%MOD)%MOD



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

ans = 0



for i in range(1, N):

    ans += i*(N-i)*M*M*C(N*M-2, K-2)

    ans %= MOD



for i in range(1, M):

    ans += i*(M-i)*N*N*C(N*M-2, K-2)

    ans %= MOD



print(ans)
MAX = 2 * 10**5 + 100
MOD = 10**9 + 7
fact = [0] * MAX  # fact[i]: i!
inv = [0] * MAX  # inv[i]: iの逆元
finv = [0] * MAX  # finv[i]: i!の逆元
fact[0] = 1
fact[1] = 1
finv[0] = 1
finv[1] = 1
inv[1] = 1
for i in range(2, MAX):
    fact[i] = fact[i - 1] * i % MOD
    inv[i] = MOD - inv[MOD % i] * (MOD // i) % MOD
    finv[i] = finv[i - 1] * inv[i] % MOD


def C(n, r):
    if n < r:
        return 0
    if n < 0 or r < 0:
        return 0
    return fact[n] * (finv[r] * finv[n - r] % MOD) % MOD


N, M, K = list(map(int, input().split()))
ans = 0
for d in range(1, N):
    ans += d * (N - d) * M**2
    ans %= MOD
for d in range(1, M):
    ans += d * (M - d) * N**2
    ans %= MOD
ans *= C(N * M - 2, K - 2)
ans %= MOD
print(ans)

MAX = 2 * 10**5 + 100
MOD = 10**9 + 7
fact = [0] * MAX  # fact[i]: i!
inv = [0] * MAX  # inv[i]: iの逆元
finv = [0] * MAX  # finv[i]: i!の逆元
fact[0] = 1
fact[1] = 1
finv[0] = 1
finv[1] = 1
inv[1] = 1
for i in range(2, MAX):
    fact[i] = fact[i - 1] * i % MOD
    inv[i] = MOD - inv[MOD % i] * (MOD // i) % MOD
    finv[i] = finv[i - 1] * inv[i] % MOD


def C(n, r):
    if n < r:
        return 0
    if n < 0 or r < 0:
        return 0
    return fact[n] * (finv[r] * finv[n - r] % MOD) % MOD


N, M, K = list(map(int, input().split()))
ans = 0
for i in range(1, N):
    ans += i * (N - i) * M * M * C(N * M - 2, K - 2)
    ans %= MOD
for i in range(1, M):
    ans += i * (M - i) * N * N * C(N * M - 2, K - 2)
    ans %= MOD
print(ans)

-for d in range(1, N): -    ans += d * (N - d) * M**2 +for i in range(1, N): +    ans += i * (N - i) * M * M * C(N * M - 2, K - 2) -for d in range(1, M): -    ans += d * (M - d) * N**2 +for i in range(1, M): +    ans += i * (M - i) * N * N * C(N * M - 2, K - 2) -ans *= C(N * M - 2, K - 2) -ans %= MOD