N, M, K = map(int, input().split())
mod = int(1e9) + 7
fact = [1 for _ in range(N*M+1)]
invf = [1 for _ in range(N*M+1)]
def inved(a):
  x, y, u, v, k, l = 1, 0, 0, 1, a, mod
  while l != 0:
    x, y, u, v = u, v, x - u * (k // l), y - v * (k // l)
    k, l = l, k % l
  return x % mod
for i in range(N*M):
  fact[i+1] = (fact[i] * (i + 1)) % mod
invf[-1] = inved(fact[-1])
for i in range(N*M, 0, -1):
  invf[i-1] = (invf[i] * i) % mod
Z = (fact[M*N-2] * invf[K-2] * invf[M*N-K]) % mod
X = M * (N + 1) * (N - 1)
X %= mod
Y = N * (M + 1) * (M - 1)
Y %= mod
XY = (inved(6) * M * N * (X + Y)) % mod
print((XY * Z) % mod) N, M, K = map(int, input().split()) N map(int, input().split()) map int input().split() ().split () input split M K mod = int(1e9) + 7 mod int(1e9) + 7 int(1e9) int 1e9 7 1 for _ in range(N*M+1) for _ in range(N*M+1) _ range(N*M+1) range N*M+1 N*M N M 1 for _ in range(N*M+1) 1 fact = [1 for _ in range(N*M+1)] fact [1 for _ in range(N*M+1)] 1 for _ in range(N*M+1) for _ in range(N*M+1) _ range(N*M+1) range N*M+1 N*M N M 1 for _ in range(N*M+1) 1 invf = [1 for _ in range(N*M+1)] invf [1 for _ in range(N*M+1)] def inved(a):
  x, y, u, v, k, l = 1, 0, 0, 1, a, mod
  while l != 0:
    x, y, u, v = u, v, x - u * (k // l), y - v * (k // l)
    k, l = l, k % l
  return x % mod inved x, y, u, v, k, l = 1, 0, 0, 1, a, mod x 1 y 0 u 0 v 1 k a l mod while l != 0:
    x, y, u, v = u, v, x - u * (k // l), y - v * (k // l)
    k, l = l, k % l
   l != 0 l 0 x, y, u, v = u, v, x - u * (k // l), y - v * (k // l) x u y v u x - u * (k // l) x u * (k // l) u k // l k l v y - v * (k // l) y v * (k // l) v k // l k l k, l = l, k % l k l l k % l k l return x % mod x % mod x mod a a for i in range(N*M):
  fact[i+1] = (fact[i] * (i + 1)) % mod i range(N*M) range N*M N M fact[i+1] = (fact[i] * (i + 1)) % mod fact[i+1] fact i+1 i 1 (fact[i] * (i + 1)) % mod fact[i] * (i + 1) fact[i] fact i i + 1 i 1 mod invf[-1] = inved(fact[-1]) invf[-1] invf -1 inved(fact[-1]) inved fact[-1] fact -1 for i in range(N*M, 0, -1):
  invf[i-1] = (invf[i] * i) % mod i range(N*M, 0, -1) range N*M N M 0 -1 invf[i-1] = (invf[i] * i) % mod invf[i-1] invf i-1 i 1 (invf[i] * i) % mod invf[i] * i invf[i] invf i i mod Z = (fact[M*N-2] * invf[K-2] * invf[M*N-K]) % mod Z (fact[M*N-2] * invf[K-2] * invf[M*N-K]) % mod fact[M*N-2] * invf[K-2] * invf[M*N-K] fact[M*N-2] * invf[K-2] fact[M*N-2] fact M*N-2 M*N M N 2 invf[K-2] invf K-2 K 2 invf[M*N-K] invf M*N-K M*N M N K mod X = M * (N + 1) * (N - 1) X M * (N + 1) * (N - 1) M * (N + 1) M N + 1 N 1 N - 1 N 1 X %= mod X mod Y = N * (M + 1) * (M - 1) Y N * (M + 1) * (M - 1) N * (M + 1) N M + 1 M 1 M - 1 M 1 Y %= mod Y mod XY = (inved(6) * M * N * (X + Y)) % mod XY (inved(6) * M * N * (X + Y)) % mod inved(6) * M * N * (X + Y) inved(6) * M * N inved(6) * M inved(6) inved 6 M N X + Y X Y mod print((XY * Z) % mod) print (XY * Z) % mod XY * Z XY Z mod XY = (inved(6) * M * N * (X + Y)) % mod (inved(6) * M * N * (X + Y)) % mod XY K = map(int, input().split()) map(int, input().split()) K Z = (fact[M*N-2] * invf[K-2] * invf[M*N-K]) % mod (fact[M*N-2] * invf[K-2] * invf[M*N-K]) % mod Z def inved(a):
  x, y, u, v, k, l = 1, 0, 0, 1, a, mod
  while l != 0:
    x, y, u, v = u, v, x - u * (k // l), y - v * (k // l)
    k, l = l, k % l
  return x % mod def inved(a):
  x, y, u, v, k, l = 1, 0, 0, 1, a, mod
  while l != 0:
    x, y, u, v = u, v, x - u * (k // l), y - v * (k // l)
    k, l = l, k % l
  return x % mod inved X %= mod mod X M, K = map(int, input().split()) map(int, input().split()) M Y %= mod mod Y X = M * (N + 1) * (N - 1) M * (N + 1) * (N - 1) X fact = [1 for _ in range(N*M+1)] [1 for _ in range(N*M+1)] fact invf = [1 for _ in range(N*M+1)] [1 for _ in range(N*M+1)] invf Y = N * (M + 1) * (M - 1) N * (M + 1) * (M - 1) Y N, M, K = map(int, input().split()) map(int, input().split()) N mod = int(1e9) + 7 int(1e9) + 7 mod
N, M, K = map(int, input().split())
mod = int(1e9) + 7
fact = [1 for _ in range(N*M+1)]
invf = [1 for _ in range(N*M+1)]
def inved(a):
  x, y, u, v, k, l = 1, 0, 0, 1, a, mod
  while l != 0:
    x, y, u, v = u, v, x - u * (k // l), y - v * (k // l)
    k, l = l, k % l
  return x % mod
for i in range(N*M):
  fact[i+1] = (fact[i] * (i + 1)) % mod
invf[-1] = inved(fact[-1])
for i in range(N*M, 0, -1):
  invf[i-1] = (invf[i] * i) % mod
Z = (fact[M*N-2] * invf[K-2] * invf[M*N-K]) % mod
X = M * (N + 1) * (N - 1)
X %= mod
Y = N * (M + 1) * (M - 1)
Y %= mod
XY = (inved(6) * M * N * (X + Y)) % mod
print((XY * Z) % mod)