
def xgcd(a, b):
    x0, y0, x1, y1 = 1, 0, 0, 1
    while b != 0:
        q, a, b = a // b, b, a % b
        x0, x1 = x1, x0 - q * x1
        y0, y1 = y1, y0 - q * y1
    return x0

def modinv(a, m):
    x = xgcd(a, m)
    return x % m


max_num = 10 ** 9 + 7
res = 0
n, m, k = map(int, input().strip().split())

for d in range(1, n):
    res += (n - d) * d * m * m
    res %= max_num
for d in range(1, m):
    res += (m - d) * d * n * n
    res %= max_num

r = min(n*m-2, k-2)
for i in range(1, r+1):
    res *= n * m - 1 - i
    res %= max_num
for i in range(1, r+1):
    res *= modinv(i, max_num)
    res %= max_num

print(res) def xgcd(a, b):
    x0, y0, x1, y1 = 1, 0, 0, 1
    while b != 0:
        q, a, b = a // b, b, a % b
        x0, x1 = x1, x0 - q * x1
        y0, y1 = y1, y0 - q * y1
    return x0 xgcd x0, y0, x1, y1 = 1, 0, 0, 1 x0 1 y0 0 x1 0 y1 1 while b != 0:
        q, a, b = a // b, b, a % b
        x0, x1 = x1, x0 - q * x1
        y0, y1 = y1, y0 - q * y1
     b != 0 b 0 q, a, b = a // b, b, a % b q a // b a b a b b a % b a b x0, x1 = x1, x0 - q * x1 x0 x1 x1 x0 - q * x1 x0 q * x1 q x1 y0, y1 = y1, y0 - q * y1 y0 y1 y1 y0 - q * y1 y0 q * y1 q y1 return x0 x0 a a b b def modinv(a, m):
    x = xgcd(a, m)
    return x % m modinv x = xgcd(a, m) x xgcd(a, m) xgcd a m return x % m x % m x m a a m m max_num = 10 ** 9 + 7 max_num 10 ** 9 + 7 10 ** 9 10 9 7 res = 0 res 0 n, m, k = map(int, input().strip().split()) n map(int, input().strip().split()) map int input().strip().split() ().strip().split ().strip() ().strip () input strip split m k for d in range(1, n):
    res += (n - d) * d * m * m
    res %= max_num d range(1, n) range 1 n res += (n - d) * d * m * m res (n - d) * d * m * m (n - d) * d * m (n - d) * d n - d n d d m m res %= max_num res max_num for d in range(1, m):
    res += (m - d) * d * n * n
    res %= max_num d range(1, m) range 1 m res += (m - d) * d * n * n res (m - d) * d * n * n (m - d) * d * n (m - d) * d m - d m d d n n res %= max_num res max_num r = min(n*m-2, k-2) r min(n*m-2, k-2) min n*m-2 n*m n m 2 k-2 k 2 for i in range(1, r+1):
    res *= n * m - 1 - i
    res %= max_num i range(1, r+1) range 1 r+1 r 1 res *= n * m - 1 - i res n * m - 1 - i n * m - 1 n * m n m 1 i res %= max_num res max_num for i in range(1, r+1):
    res *= modinv(i, max_num)
    res %= max_num i range(1, r+1) range 1 r+1 r 1 res *= modinv(i, max_num) res modinv(i, max_num) modinv i max_num res %= max_num res max_num print(res) print res r = min(n*m-2, k-2) min(n*m-2, k-2) r res = 0 0 res res += (m - d) * d * n * n (m - d) * d * n * n res res %= max_num max_num res k = map(int, input().strip().split()) map(int, input().strip().split()) k def xgcd(a, b):
    x0, y0, x1, y1 = 1, 0, 0, 1
    while b != 0:
        q, a, b = a // b, b, a % b
        x0, x1 = x1, x0 - q * x1
        y0, y1 = y1, y0 - q * y1
    return x0 def xgcd(a, b):
    x0, y0, x1, y1 = 1, 0, 0, 1
    while b != 0:
        q, a, b = a // b, b, a % b
        x0, x1 = x1, x0 - q * x1
        y0, y1 = y1, y0 - q * y1
    return x0 xgcd n, m, k = map(int, input().strip().split()) map(int, input().strip().split()) n m, k = map(int, input().strip().split()) map(int, input().strip().split()) m res %= max_num max_num res res %= max_num max_num res res *= n * m - 1 - i n * m - 1 - i res res *= modinv(i, max_num) modinv(i, max_num) res res += (n - d) * d * m * m (n - d) * d * m * m res res %= max_num max_num res def modinv(a, m):
    x = xgcd(a, m)
    return x % m def modinv(a, m):
    x = xgcd(a, m)
    return x % m modinv max_num = 10 ** 9 + 7 10 ** 9 + 7 max_num

def xgcd(a, b):
    x0, y0, x1, y1 = 1, 0, 0, 1
    while b != 0:
        q, a, b = a // b, b, a % b
        x0, x1 = x1, x0 - q * x1
        y0, y1 = y1, y0 - q * y1
    return x0

def modinv(a, m):
    x = xgcd(a, m)
    return x % m


max_num = 10 ** 9 + 7
res = 0
n, m, k = map(int, input().strip().split())

for d in range(1, n):
    res += (n - d) * d * m * m
    res %= max_num
for d in range(1, m):
    res += (m - d) * d * n * n
    res %= max_num

r = min(n*m-2, k-2)
for i in range(1, r+1):
    res *= n * m - 1 - i
    res %= max_num
for i in range(1, r+1):
    res *= modinv(i, max_num)
    res %= max_num

print(res)
