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*modinv(y) % MOD



def modinv(a):

    b=MOD

    (x, lastx) = (0, 1)

    (y, lasty) = (1, 0)

    while b != 0:

        q = a // b

        (a, b) = (b, a % b)

        (x, lastx) = (lastx - q * x, x)

        (y, lasty) = (lasty - q * y, y)

    return lastx%MOD



MOD=10**9+7

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





x=0

for i in range(1,N):

   x=x+i*(N-i)

x=(x*M*M)%MOD



y=0

for j in range(1,M):

    y=y+j*(M-j)

y=(y*N*N)%MOD

    

ans=comb(N*M-2,K-2)*(x+y)%MOD

print(ans)
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*modinv(y) % MOD



def modinv(a):

    b=MOD

    (x, lastx) = (0, 1)

    (y, lasty) = (1, 0)

    while b != 0:

        q = a // b

        (a, b) = (b, a % b)

        (x, lastx) = (lastx - q * x, x)

        (y, lasty) = (lasty - q * y, y)

    return lastx%MOD



MOD=10**9+7

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





x=0

for i in range(1,N//2+1):

   x+=2*i*(N-i)

if N%2==0: x-=N*N//4



y=0

for j in range(1,M//2+1):

    y+=2*j*(M-j)

if M%2==0: y-=M*M//4 



ans=comb(N*M-2,K-2)*(x*M*M+y*N*N)%MOD

print(ans)
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 * modinv(y) % MOD


def modinv(a):
    b = MOD
    (x, lastx) = (0, 1)
    (y, lasty) = (1, 0)
    while b != 0:
        q = a // b
        (a, b) = (b, a % b)
        (x, lastx) = (lastx - q * x, x)
        (y, lasty) = (lasty - q * y, y)
    return lastx % MOD


MOD = 10**9 + 7
N, M, K = list(map(int, input().split()))
x = 0
for i in range(1, N):
    x = x + i * (N - i)
x = (x * M * M) % MOD
y = 0
for j in range(1, M):
    y = y + j * (M - j)
y = (y * N * N) % MOD
ans = comb(N * M - 2, K - 2) * (x + y) % MOD
print(ans)

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 * modinv(y) % MOD


def modinv(a):
    b = MOD
    (x, lastx) = (0, 1)
    (y, lasty) = (1, 0)
    while b != 0:
        q = a // b
        (a, b) = (b, a % b)
        (x, lastx) = (lastx - q * x, x)
        (y, lasty) = (lasty - q * y, y)
    return lastx % MOD


MOD = 10**9 + 7
N, M, K = list(map(int, input().split()))
x = 0
for i in range(1, N // 2 + 1):
    x += 2 * i * (N - i)
if N % 2 == 0:
    x -= N * N // 4
y = 0
for j in range(1, M // 2 + 1):
    y += 2 * j * (M - j)
if M % 2 == 0:
    y -= M * M // 4
ans = comb(N * M - 2, K - 2) * (x * M * M + y * N * N) % MOD
print(ans)

-for i in range(1, N): -    x = x + i * (N - i) -x = (x * M * M) % MOD +for i in range(1, N // 2 + 1): +    x += 2 * i * (N - i) +if N % 2 == 0: +    x -= N * N // 4 -for j in range(1, M): -    y = y + j * (M - j) -y = (y * N * N) % MOD -ans = comb(N * M - 2, K - 2) * (x + y) % MOD +for j in range(1, M // 2 + 1): +    y += 2 * j * (M - j) +if M % 2 == 0: +    y -= M * M // 4 +ans = comb(N * M - 2, K - 2) * (x * M * M + y * N * N) % MOD