# -*- coding: utf-8 -*-
import sys
# sys.setrecursionlimit(10**6)
# buff_readline = sys.stdin.buffer.readline
buff_readline = sys.stdin.readline
readline = sys.stdin.readline

INF = 2**62-1


def read_int():
    return int(buff_readline())


def read_int_n():
    return list(map(int, buff_readline().split()))


def read_float():
    return float(buff_readline())


def read_float_n():
    return list(map(float, buff_readline().split()))


def read_str():
    return readline().strip()


def read_str_n():
    return readline().strip().split()


def error_print(*args):
    print(*args, file=sys.stderr)


def mt(f):
    import time

    def wrap(*args, **kwargs):
        s = time.time()
        ret = f(*args, **kwargs)
        e = time.time()

        error_print(e - s, 'sec')
        return ret

    return wrap


class Combination:
    def __init__(self, n, mod):

        g1 = [1, 1]
        g2 = [1, 1]
        inverse = [0, 1]
        for i in range(2, n + 1):
            g1.append((g1[-1] * i) % mod)
            inverse.append((-inverse[mod % i] * (mod//i)) % mod)
            g2.append((g2[-1] * inverse[-1]) % mod)
        self.MOD = mod
        self.N = n
        self.g1 = g1
        self.g2 = g2
        self.inverse = inverse

    def __call__(self, n, r):
        if (r < 0 or r > n):
            return 0
        r = min(r, n-r)
        return self.g1[n] * self.g2[r] * self.g2[n-r] % self.MOD


@mt
def slv(N, M, K):
    mod = 10**9+7
    C = Combination(N*M, mod)
    b = C(N*M-2, K-2)
    ans = 0
    m = M**2
    for d in range(1, N):
        ans += (N-d) * b * d * m
        ans %= mod
    m = N**2
    for d in range(1, M):
        ans += (M-d) * b * d * m
        ans %= mod



    return ans



def main():
    N, M, K = read_int_n()
    print(slv(N, M, K))


if __name__ == '__main__':
    main() import sys sys buff_readline = sys.stdin.readline buff_readline sys.stdin.readline sys.stdin sys stdin readline readline = sys.stdin.readline readline sys.stdin.readline sys.stdin sys stdin readline INF = 2**62-1 INF 2**62-1 2**62 2 62 1 def read_int():
    return int(buff_readline()) read_int return int(buff_readline()) int(buff_readline()) int buff_readline() buff_readline def read_int_n():
    return list(map(int, buff_readline().split())) read_int_n return list(map(int, buff_readline().split())) list(map(int, buff_readline().split())) list map(int, buff_readline().split()) map int buff_readline().split() ().split () buff_readline split def read_float():
    return float(buff_readline()) read_float return float(buff_readline()) float(buff_readline()) float buff_readline() buff_readline def read_float_n():
    return list(map(float, buff_readline().split())) read_float_n return list(map(float, buff_readline().split())) list(map(float, buff_readline().split())) list map(float, buff_readline().split()) map float buff_readline().split() ().split () buff_readline split def read_str():
    return readline().strip() read_str return readline().strip() readline().strip() ().strip () readline strip def read_str_n():
    return readline().strip().split() read_str_n return readline().strip().split() readline().strip().split() ().strip().split ().strip() ().strip () readline strip split def error_print(*args):
    print(*args, file=sys.stderr) error_print print(*args, file=sys.stderr) print *args args file=sys.stderr file sys.stderr sys stderr *args def mt(f):
    import time

    def wrap(*args, **kwargs):
        s = time.time()
        ret = f(*args, **kwargs)
        e = time.time()

        error_print(e - s, 'sec')
        return ret

    return wrap mt import time time def wrap(*args, **kwargs):
        s = time.time()
        ret = f(*args, **kwargs)
        e = time.time()

        error_print(e - s, 'sec')
        return ret

     wrap s = time.time() s time.time() time.time time time ret = f(*args, **kwargs) ret f(*args, **kwargs) f *args args **kwargs kwargs e = time.time() e time.time() time.time time time error_print(e - s, 'sec') error_print e - s e s 'sec' return ret ret *args **kwargs return wrap wrap f f class Combination:
    def __init__(self, n, mod):

        g1 = [1, 1]
        g2 = [1, 1]
        inverse = [0, 1]
        for i in range(2, n + 1):
            g1.append((g1[-1] * i) % mod)
            inverse.append((-inverse[mod % i] * (mod//i)) % mod)
            g2.append((g2[-1] * inverse[-1]) % mod)
        self.MOD = mod
        self.N = n
        self.g1 = g1
        self.g2 = g2
        self.inverse = inverse

    def __call__(self, n, r):
        if (r < 0 or r > n):
            return 0
        r = min(r, n-r)
        return self.g1[n] * self.g2[r] * self.g2[n-r] % self.MOD Combination def __init__(self, n, mod):

        g1 = [1, 1]
        g2 = [1, 1]
        inverse = [0, 1]
        for i in range(2, n + 1):
            g1.append((g1[-1] * i) % mod)
            inverse.append((-inverse[mod % i] * (mod//i)) % mod)
            g2.append((g2[-1] * inverse[-1]) % mod)
        self.MOD = mod
        self.N = n
        self.g1 = g1
        self.g2 = g2
        self.inverse = inverse

     __init__ g1 = [1, 1] g1 [1, 1] 1 1 g2 = [1, 1] g2 [1, 1] 1 1 inverse = [0, 1] inverse [0, 1] 0 1 for i in range(2, n + 1):
            g1.append((g1[-1] * i) % mod)
            inverse.append((-inverse[mod % i] * (mod//i)) % mod)
            g2.append((g2[-1] * inverse[-1]) % mod)
         i range(2, n + 1) range 2 n + 1 n 1 g1.append((g1[-1] * i) % mod) g1.append g1 append (g1[-1] * i) % mod g1[-1] * i g1[-1] g1 -1 i mod inverse.append((-inverse[mod % i] * (mod//i)) % mod) inverse.append inverse append (-inverse[mod % i] * (mod//i)) % mod -inverse[mod % i] * (mod//i) -inverse[mod % i] inverse[mod % i] inverse mod % i mod i mod//i mod i mod g2.append((g2[-1] * inverse[-1]) % mod) g2.append g2 append (g2[-1] * inverse[-1]) % mod g2[-1] * inverse[-1] g2[-1] g2 -1 inverse[-1] inverse -1 mod self.MOD = mod self.MOD self MOD mod self.N = n self.N self N n self.g1 = g1 self.g1 self g1 g1 self.g2 = g2 self.g2 self g2 g2 self.inverse = inverse self.inverse self inverse inverse self self n n mod mod def __call__(self, n, r):
        if (r < 0 or r > n):
            return 0
        r = min(r, n-r)
        return self.g1[n] * self.g2[r] * self.g2[n-r] % self.MOD __call__ if (r < 0 or r > n):
            return 0
         r < 0 or r > n r < 0 r 0 r > n r n return 0 0 r = min(r, n-r) r min(r, n-r) min r n-r n r return self.g1[n] * self.g2[r] * self.g2[n-r] % self.MOD self.g1[n] * self.g2[r] * self.g2[n-r] % self.MOD self.g1[n] * self.g2[r] * self.g2[n-r] self.g1[n] * self.g2[r] self.g1[n] self.g1 self g1 n self.g2[r] self.g2 self g2 r self.g2[n-r] self.g2 self g2 n-r n r self.MOD self MOD self self n n r r def slv(N, M, K):
    mod = 10**9+7
    C = Combination(N*M, mod)
    b = C(N*M-2, K-2)
    ans = 0
    m = M**2
    for d in range(1, N):
        ans += (N-d) * b * d * m
        ans %= mod
    m = N**2
    for d in range(1, M):
        ans += (M-d) * b * d * m
        ans %= mod



    return ans slv mod = 10**9+7 mod 10**9+7 10**9 10 9 7 C = Combination(N*M, mod) C Combination(N*M, mod) Combination N*M N M mod b = C(N*M-2, K-2) b C(N*M-2, K-2) C N*M-2 N*M N M 2 K-2 K 2 ans = 0 ans 0 m = M**2 m M**2 M 2 for d in range(1, N):
        ans += (N-d) * b * d * m
        ans %= mod
     d range(1, N) range 1 N ans += (N-d) * b * d * m ans (N-d) * b * d * m (N-d) * b * d (N-d) * b N-d N d b d m ans %= mod ans mod m = N**2 m N**2 N 2 for d in range(1, M):
        ans += (M-d) * b * d * m
        ans %= mod



     d range(1, M) range 1 M ans += (M-d) * b * d * m ans (M-d) * b * d * m (M-d) * b * d (M-d) * b M-d M d b d m ans %= mod ans mod return ans ans N N M M K K @mt slv mt slv def main():
    N, M, K = read_int_n()
    print(slv(N, M, K)) main N, M, K = read_int_n() N read_int_n() read_int_n M K print(slv(N, M, K)) print slv(N, M, K) slv N M K if __name__ == '__main__':
    main() __name__ == '__main__' __name__ '__main__' main() main def mt(f):
    import time

    def wrap(*args, **kwargs):
        s = time.time()
        ret = f(*args, **kwargs)
        e = time.time()

        error_print(e - s, 'sec')
        return ret

    return wrap def mt(f):
    import time

    def wrap(*args, **kwargs):
        s = time.time()
        ret = f(*args, **kwargs)
        e = time.time()

        error_print(e - s, 'sec')
        return ret

    return wrap mt def read_int_n():
    return list(map(int, buff_readline().split())) def read_int_n():
    return list(map(int, buff_readline().split())) read_int_n def slv(N, M, K):
    mod = 10**9+7
    C = Combination(N*M, mod)
    b = C(N*M-2, K-2)
    ans = 0
    m = M**2
    for d in range(1, N):
        ans += (N-d) * b * d * m
        ans %= mod
    m = N**2
    for d in range(1, M):
        ans += (M-d) * b * d * m
        ans %= mod



    return ans def slv(N, M, K):
    mod = 10**9+7
    C = Combination(N*M, mod)
    b = C(N*M-2, K-2)
    ans = 0
    m = M**2
    for d in range(1, N):
        ans += (N-d) * b * d * m
        ans %= mod
    m = N**2
    for d in range(1, M):
        ans += (M-d) * b * d * m
        ans %= mod



    return ans slv def error_print(*args):
    print(*args, file=sys.stderr) def error_print(*args):
    print(*args, file=sys.stderr) error_print def read_str_n():
    return readline().strip().split() def read_str_n():
    return readline().strip().split() read_str_n def main():
    N, M, K = read_int_n()
    print(slv(N, M, K)) def main():
    N, M, K = read_int_n()
    print(slv(N, M, K)) main class Combination:
    def __init__(self, n, mod):

        g1 = [1, 1]
        g2 = [1, 1]
        inverse = [0, 1]
        for i in range(2, n + 1):
            g1.append((g1[-1] * i) % mod)
            inverse.append((-inverse[mod % i] * (mod//i)) % mod)
            g2.append((g2[-1] * inverse[-1]) % mod)
        self.MOD = mod
        self.N = n
        self.g1 = g1
        self.g2 = g2
        self.inverse = inverse

    def __call__(self, n, r):
        if (r < 0 or r > n):
            return 0
        r = min(r, n-r)
        return self.g1[n] * self.g2[r] * self.g2[n-r] % self.MOD class Combination:
    def __init__(self, n, mod):

        g1 = [1, 1]
        g2 = [1, 1]
        inverse = [0, 1]
        for i in range(2, n + 1):
            g1.append((g1[-1] * i) % mod)
            inverse.append((-inverse[mod % i] * (mod//i)) % mod)
            g2.append((g2[-1] * inverse[-1]) % mod)
        self.MOD = mod
        self.N = n
        self.g1 = g1
        self.g2 = g2
        self.inverse = inverse

    def __call__(self, n, r):
        if (r < 0 or r > n):
            return 0
        r = min(r, n-r)
        return self.g1[n] * self.g2[r] * self.g2[n-r] % self.MOD Combination buff_readline = sys.stdin.readline sys.stdin.readline buff_readline INF = 2**62-1 2**62-1 INF def read_float_n():
    return list(map(float, buff_readline().split())) def read_float_n():
    return list(map(float, buff_readline().split())) read_float_n readline = sys.stdin.readline sys.stdin.readline readline def read_int():
    return int(buff_readline()) def read_int():
    return int(buff_readline()) read_int def read_str():
    return readline().strip() def read_str():
    return readline().strip() read_str def read_float():
    return float(buff_readline()) def read_float():
    return float(buff_readline()) read_float
# -*- coding: utf-8 -*-
import sys
# sys.setrecursionlimit(10**6)
# buff_readline = sys.stdin.buffer.readline
buff_readline = sys.stdin.readline
readline = sys.stdin.readline

INF = 2**62-1


def read_int():
    return int(buff_readline())


def read_int_n():
    return list(map(int, buff_readline().split()))


def read_float():
    return float(buff_readline())


def read_float_n():
    return list(map(float, buff_readline().split()))


def read_str():
    return readline().strip()


def read_str_n():
    return readline().strip().split()


def error_print(*args):
    print(*args, file=sys.stderr)


def mt(f):
    import time

    def wrap(*args, **kwargs):
        s = time.time()
        ret = f(*args, **kwargs)
        e = time.time()

        error_print(e - s, 'sec')
        return ret

    return wrap


class Combination:
    def __init__(self, n, mod):

        g1 = [1, 1]
        g2 = [1, 1]
        inverse = [0, 1]
        for i in range(2, n + 1):
            g1.append((g1[-1] * i) % mod)
            inverse.append((-inverse[mod % i] * (mod//i)) % mod)
            g2.append((g2[-1] * inverse[-1]) % mod)
        self.MOD = mod
        self.N = n
        self.g1 = g1
        self.g2 = g2
        self.inverse = inverse

    def __call__(self, n, r):
        if (r < 0 or r > n):
            return 0
        r = min(r, n-r)
        return self.g1[n] * self.g2[r] * self.g2[n-r] % self.MOD


@mt
def slv(N, M, K):
    mod = 10**9+7
    C = Combination(N*M, mod)
    b = C(N*M-2, K-2)
    ans = 0
    m = M**2
    for d in range(1, N):
        ans += (N-d) * b * d * m
        ans %= mod
    m = N**2
    for d in range(1, M):
        ans += (M-d) * b * d * m
        ans %= mod



    return ans



def main():
    N, M, K = read_int_n()
    print(slv(N, M, K))


if __name__ == '__main__':
    main()
