# https://atcoder.jp/contests/abc127/submissions/5606400



from functools import reduce





def mod_mul(a, b):

    return (a * b) % MOD





def mod_add(a, b):

    return (a + b) % MOD





def cmb(n, r):

    r = min(r, n - r)

    if r == 0:

        return 1

    if r == 1:

        return n



    f = reduce(mod_mul, list(range(n - r + 1, n + 1)))  # n!/(n-r)!

    d = reduce(mod_mul, list(range(2, r + 1)))  # r!

    return (f * pow(d, MOD - 2, MOD)) % MOD





MOD = 10 ** 9 + 7



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



ans_x = reduce(mod_add, (i * (M - i) for i in range(M))) * N ** 2

ans_y = reduce(mod_add, (i * (N - i) for i in range(N))) * M ** 2

ans = ans_x + ans_y

pat = cmb(N * M - 2, K - 2)

ans = (ans * pat) % MOD



print(ans)

# https://atcoder.jp/contests/abc127/submissions/5606400



from functools import reduce

from operator import add





def mod_mul(a, b):

    return (a * b) % MOD





def cmb(n, r):

    r = min(r, n - r)

    if r == 0:

        return 1

    if r == 1:

        return n

    f = reduce(mod_mul, list(range(n - r + 1, n + 1)))  # n!/(n-r)!

    d = reduce(mod_mul, list(range(2, r + 1)))  # r!

    return (f * pow(d, MOD - 2, MOD)) % MOD





MOD = 10 ** 9 + 7



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



ans_x = reduce(add, (i * (M - i) for i in range(M))) * N ** 2

ans_y = reduce(add, (i * (N - i) for i in range(N))) * M ** 2

ans = (ans_x + ans_y) % MOD

pat = cmb(N * M - 2, K - 2)

ans = (ans * pat) % MOD



print(ans)

# https://atcoder.jp/contests/abc127/submissions/5606400
from functools import reduce


def mod_mul(a, b):
    return (a * b) % MOD


def mod_add(a, b):
    return (a + b) % MOD


def cmb(n, r):
    r = min(r, n - r)
    if r == 0:
        return 1
    if r == 1:
        return n
    f = reduce(mod_mul, list(range(n - r + 1, n + 1)))  # n!/(n-r)!
    d = reduce(mod_mul, list(range(2, r + 1)))  # r!
    return (f * pow(d, MOD - 2, MOD)) % MOD


MOD = 10**9 + 7
N, M, K = list(map(int, input().split()))
ans_x = reduce(mod_add, (i * (M - i) for i in range(M))) * N**2
ans_y = reduce(mod_add, (i * (N - i) for i in range(N))) * M**2
ans = ans_x + ans_y
pat = cmb(N * M - 2, K - 2)
ans = (ans * pat) % MOD
print(ans)

# https://atcoder.jp/contests/abc127/submissions/5606400
from functools import reduce
from operator import add


def mod_mul(a, b):
    return (a * b) % MOD


def cmb(n, r):
    r = min(r, n - r)
    if r == 0:
        return 1
    if r == 1:
        return n
    f = reduce(mod_mul, list(range(n - r + 1, n + 1)))  # n!/(n-r)!
    d = reduce(mod_mul, list(range(2, r + 1)))  # r!
    return (f * pow(d, MOD - 2, MOD)) % MOD


MOD = 10**9 + 7
N, M, K = list(map(int, input().split()))
ans_x = reduce(add, (i * (M - i) for i in range(M))) * N**2
ans_y = reduce(add, (i * (N - i) for i in range(N))) * M**2
ans = (ans_x + ans_y) % MOD
pat = cmb(N * M - 2, K - 2)
ans = (ans * pat) % MOD
print(ans)

+from operator import add - - -def mod_add(a, b): -    return (a + b) % MOD -ans_x = reduce(mod_add, (i * (M - i) for i in range(M))) * N**2 -ans_y = reduce(mod_add, (i * (N - i) for i in range(N))) * M**2 -ans = ans_x + ans_y +ans_x = reduce(add, (i * (M - i) for i in range(M))) * N**2 +ans_y = reduce(add, (i * (N - i) for i in range(N))) * M**2 +ans = (ans_x + ans_y) % MOD