from math import factorial as f

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

mod = 10 ** 9 + 7



def combi(n, r):

  return f(n) // (f(n - r) * f(r)) % mod



res = 0

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

for i in range(1, N):

  res += ((N - i + 1) * (N - i) // 2) * c * M * M % mod

  res %= mod



for i in range(1, M):

  res += ((M - i + 1) * (M - i) // 2) * c * N * N % mod

  res %= mod



print((res % mod))



import sys

input = sys.stdin.readline

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

mod = 10 ** 9 + 7

class Factorial:

  def __init__(self, n, mod):

    self.f = [1]

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

      self.f.append(self.f[-1] * i % mod)

    self.i = [pow(self.f[-1], mod - 2, mod)]

    for i in range(1, n + 1)[: : -1]:

      self.i.append(self.i[-1] * i % mod)

    self.i.reverse()

  def factorial(self, i):

    return self.f[i]

  def ifactorial(self, i):

    return self.i[i]

  def combi(self, n, k):

    return self.f[n] * self.i[n - k] % mod * self.i[k] % mod



f = Factorial(N * M, mod)

t = f.combi(N * M - 2, K - 2)



res = 0

for d in range(1, M):

  x = N ** 2 % mod * (M - d) % mod

  res += x * d % mod

  res %= mod

  #print(x)

for d in range(1, N):

  y = M ** 2 % mod * (N - d) % mod

  res += y * d % mod

  res %= mod

#print(res, t)

print((res * t % mod))
from math import factorial as f

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


def combi(n, r):
    return f(n) // (f(n - r) * f(r)) % mod


res = 0
c = combi(N * M - 2, K - 2)
for i in range(1, N):
    res += ((N - i + 1) * (N - i) // 2) * c * M * M % mod
    res %= mod
for i in range(1, M):
    res += ((M - i + 1) * (M - i) // 2) * c * N * N % mod
    res %= mod
print((res % mod))

import sys

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


class Factorial:
    def __init__(self, n, mod):
        self.f = [1]
        for i in range(1, n + 1):
            self.f.append(self.f[-1] * i % mod)
        self.i = [pow(self.f[-1], mod - 2, mod)]
        for i in range(1, n + 1)[::-1]:
            self.i.append(self.i[-1] * i % mod)
        self.i.reverse()

    def factorial(self, i):
        return self.f[i]

    def ifactorial(self, i):
        return self.i[i]

    def combi(self, n, k):
        return self.f[n] * self.i[n - k] % mod * self.i[k] % mod


f = Factorial(N * M, mod)
t = f.combi(N * M - 2, K - 2)
res = 0
for d in range(1, M):
    x = N**2 % mod * (M - d) % mod
    res += x * d % mod
    res %= mod
    # print(x)
for d in range(1, N):
    y = M**2 % mod * (N - d) % mod
    res += y * d % mod
    res %= mod
# print(res, t)
print((res * t % mod))

-from math import factorial as f +import sys +input = sys.stdin.readline -def combi(n, r): -    return f(n) // (f(n - r) * f(r)) % mod +class Factorial: +    def __init__(self, n, mod): +        self.f = [1] +        for i in range(1, n + 1): +            self.f.append(self.f[-1] * i % mod) +        self.i = [pow(self.f[-1], mod - 2, mod)] +        for i in range(1, n + 1)[::-1]: +            self.i.append(self.i[-1] * i % mod) +        self.i.reverse() + +    def factorial(self, i): +        return self.f[i] + +    def ifactorial(self, i): +        return self.i[i] + +    def combi(self, n, k): +        return self.f[n] * self.i[n - k] % mod * self.i[k] % mod +f = Factorial(N * M, mod) +t = f.combi(N * M - 2, K - 2) -c = combi(N * M - 2, K - 2) -for i in range(1, N): -    res += ((N - i + 1) * (N - i) // 2) * c * M * M % mod +for d in range(1, M): +    x = N**2 % mod * (M - d) % mod +    res += x * d % mod -for i in range(1, M): -    res += ((M - i + 1) * (M - i) // 2) * c * N * N % mod +    # print(x) +for d in range(1, N): +    y = M**2 % mod * (N - d) % mod +    res += y * d % mod -print((res % mod)) +# print(res, t) +print((res * t % mod))