# 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, range(n - r + 1, n + 1))  # n!/(n-r)!
    d = reduce(mod_mul, range(2, r + 1))  # r!
    return (f * pow(d, MOD - 2, MOD)) % MOD


MOD = 10 ** 9 + 7

N, M, K = 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 functools import reduce from operator import add def mod_mul(a, b):
    return (a * b) % MOD mod_mul return (a * b) % MOD (a * b) % MOD a * b a b MOD a a b b def cmb(n, r):
    r = min(r, n - r)
    if r == 0:
        return 1
    if r == 1:
        return n
    f = reduce(mod_mul, range(n - r + 1, n + 1))  # n!/(n-r)!
    d = reduce(mod_mul, range(2, r + 1))  # r!
    return (f * pow(d, MOD - 2, MOD)) % MOD cmb r = min(r, n - r) r min(r, n - r) min r n - r n r if r == 0:
        return 1
     r == 0 r 0 return 1 1 if r == 1:
        return n
     r == 1 r 1 return n n f = reduce(mod_mul, range(n - r + 1, n + 1)) f reduce(mod_mul, range(n - r + 1, n + 1)) reduce mod_mul range(n - r + 1, n + 1) range n - r + 1 n - r n r 1 n + 1 n 1 d = reduce(mod_mul, range(2, r + 1)) d reduce(mod_mul, range(2, r + 1)) reduce mod_mul range(2, r + 1) range 2 r + 1 r 1 return (f * pow(d, MOD - 2, MOD)) % MOD (f * pow(d, MOD - 2, MOD)) % MOD f * pow(d, MOD - 2, MOD) f pow(d, MOD - 2, MOD) pow d MOD - 2 MOD 2 MOD MOD n n r r MOD = 10 ** 9 + 7 MOD 10 ** 9 + 7 10 ** 9 10 9 7 N, M, K = map(int, input().split()) N map(int, input().split()) map int input().split() ().split () input split M K i * (M - i) for i in range(M) for i in range(M) i range(M) range M for i in range(M) i * (M - i) i M - i M i ans_x = reduce(add, (i * (M - i) for i in range(M))) * N ** 2 ans_x reduce(add, (i * (M - i) for i in range(M))) * N ** 2 reduce(add, (i * (M - i) for i in range(M))) reduce add (i * (M - i) for i in range(M)) N ** 2 N 2 i * (N - i) for i in range(N) for i in range(N) i range(N) range N for i in range(N) i * (N - i) i N - i N i ans_y = reduce(add, (i * (N - i) for i in range(N))) * M ** 2 ans_y reduce(add, (i * (N - i) for i in range(N))) * M ** 2 reduce(add, (i * (N - i) for i in range(N))) reduce add (i * (N - i) for i in range(N)) M ** 2 M 2 ans = (ans_x + ans_y) % MOD ans (ans_x + ans_y) % MOD ans_x + ans_y ans_x ans_y MOD pat = cmb(N * M - 2, K - 2) pat cmb(N * M - 2, K - 2) cmb N * M - 2 N * M N M 2 K - 2 K 2 ans = (ans * pat) % MOD ans (ans * pat) % MOD ans * pat ans pat MOD print(ans) print ans ans = (ans * pat) % MOD (ans * pat) % MOD ans ans = (ans_x + ans_y) % MOD (ans_x + ans_y) % MOD ans MOD = 10 ** 9 + 7 10 ** 9 + 7 MOD N, M, K = map(int, input().split()) map(int, input().split()) N def mod_mul(a, b):
    return (a * b) % MOD def mod_mul(a, b):
    return (a * b) % MOD mod_mul def cmb(n, r):
    r = min(r, n - r)
    if r == 0:
        return 1
    if r == 1:
        return n
    f = reduce(mod_mul, range(n - r + 1, n + 1))  # n!/(n-r)!
    d = reduce(mod_mul, range(2, r + 1))  # r!
    return (f * pow(d, MOD - 2, MOD)) % MOD def cmb(n, r):
    r = min(r, n - r)
    if r == 0:
        return 1
    if r == 1:
        return n
    f = reduce(mod_mul, range(n - r + 1, n + 1))  # n!/(n-r)!
    d = reduce(mod_mul, range(2, r + 1))  # r!
    return (f * pow(d, MOD - 2, MOD)) % MOD cmb K = map(int, input().split()) map(int, input().split()) K ans_x = reduce(add, (i * (M - i) for i in range(M))) * N ** 2 reduce(add, (i * (M - i) for i in range(M))) * N ** 2 ans_x M, K = map(int, input().split()) map(int, input().split()) M ans_y = reduce(add, (i * (N - i) for i in range(N))) * M ** 2 reduce(add, (i * (N - i) for i in range(N))) * M ** 2 ans_y pat = cmb(N * M - 2, K - 2) cmb(N * M - 2, K - 2) pat
# 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, range(n - r + 1, n + 1))  # n!/(n-r)!
    d = reduce(mod_mul, range(2, r + 1))  # r!
    return (f * pow(d, MOD - 2, MOD)) % MOD


MOD = 10 ** 9 + 7

N, M, K = 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)
