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

mod=10**9+7

f=[1]

for i in range(2*10**5+7):f+=[f[-1]*(i+1)%mod]

def comb(a,b):return f[a]*pow(f[b],mod-2,mod)*pow(f[a-b],mod-2,mod)%mod

ans=0

for i in range(1,n):

  ans+=(i*(n-i)*m**2)*(comb(n*m-2,k-2))

  ans%=mod

for i in range(1,m):

  ans+=(i*(m-i)*n**2)*(comb(n*m-2,k-2))

  ans%=mod

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



mod = 10**9+7

f = [1]

for i in range(n*m):

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

def comb(a, b):

  return f[a]*pow(f[b], mod-2, mod)*pow(f[a-b], mod-2, mod) % mod



ans=0

for dist in range(1,n):

  c=n-dist

  p=(c*m*m)%mod

  ans+=p*dist

for dist in range(1,m):

  c=m-dist

  p=(c*n*n)%mod

  ans+=p*dist

ans%=mod

print((ans*comb(n*m-2,k-2)%mod))
n, m, k = list(map(int, input().split()))
mod = 10**9 + 7
f = [1]
for i in range(2 * 10**5 + 7):
    f += [f[-1] * (i + 1) % mod]


def comb(a, b):
    return f[a] * pow(f[b], mod - 2, mod) * pow(f[a - b], mod - 2, mod) % mod


ans = 0
for i in range(1, n):
    ans += (i * (n - i) * m**2) * (comb(n * m - 2, k - 2))
    ans %= mod
for i in range(1, m):
    ans += (i * (m - i) * n**2) * (comb(n * m - 2, k - 2))
    ans %= mod
print(ans)

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


def comb(a, b):
    return f[a] * pow(f[b], mod - 2, mod) * pow(f[a - b], mod - 2, mod) % mod


ans = 0
for dist in range(1, n):
    c = n - dist
    p = (c * m * m) % mod
    ans += p * dist
for dist in range(1, m):
    c = m - dist
    p = (c * n * n) % mod
    ans += p * dist
ans %= mod
print((ans * comb(n * m - 2, k - 2) % mod))

-for i in range(2 * 10**5 + 7): +for i in range(n * m): -for i in range(1, n): -    ans += (i * (n - i) * m**2) * (comb(n * m - 2, k - 2)) -    ans %= mod -for i in range(1, m): -    ans += (i * (m - i) * n**2) * (comb(n * m - 2, k - 2)) -    ans %= mod -print(ans) +for dist in range(1, n): +    c = n - dist +    p = (c * m * m) % mod +    ans += p * dist +for dist in range(1, m): +    c = m - dist +    p = (c * n * n) % mod +    ans += p * dist +ans %= mod +print((ans * comb(n * m - 2, k - 2) % mod))