"""
組み合わせ(nCr)計算
https://qiita.com/derodero24/items/91b6468e66923a87f39f#%E7%95%AA%E5%A4%96%E7%B7%A8
逆元の求め方
http://drken1215.hatenablog.com/entry/2018/06/08/210000
解法@公式放送
https://www.youtube.com/watch?v=SS6kW-d-rJ0&feature=youtu.be&t=7376
"""


def cmb(n, r):
    return (fact[n] * finv_t[r] * finv_t[n - r]) % MOD


MOD = 10 ** 9 + 7

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

fact = [1, 1]
inv_t = [0, 1]
finv_t = [1, 1]
for i in range(2, N * M - 2 + 1):
    fact.append((fact[-1] * i) % MOD)
    inv_t.append((-inv_t[MOD % i] * (MOD // i)) % MOD)
    finv_t.append((finv_t[-1] * inv_t[-1]) % MOD)

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

ans = 0

for i in range(M):
    ans += i * (M - i) * N ** 2

for i in range(N):
    ans += i * (N - i) * M ** 2

ans = (ans * pat) % MOD

print(ans) """
組み合わせ(nCr)計算
https://qiita.com/derodero24/items/91b6468e66923a87f39f#%E7%95%AA%E5%A4%96%E7%B7%A8
逆元の求め方
http://drken1215.hatenablog.com/entry/2018/06/08/210000
解法@公式放送
https://www.youtube.com/watch?v=SS6kW-d-rJ0&feature=youtu.be&t=7376
""" def cmb(n, r):
    return (fact[n] * finv_t[r] * finv_t[n - r]) % MOD cmb return (fact[n] * finv_t[r] * finv_t[n - r]) % MOD (fact[n] * finv_t[r] * finv_t[n - r]) % MOD fact[n] * finv_t[r] * finv_t[n - r] fact[n] * finv_t[r] fact[n] fact n finv_t[r] finv_t r finv_t[n - r] finv_t n - r n r 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 fact = [1, 1] fact [1, 1] 1 1 inv_t = [0, 1] inv_t [0, 1] 0 1 finv_t = [1, 1] finv_t [1, 1] 1 1 for i in range(2, N * M - 2 + 1):
    fact.append((fact[-1] * i) % MOD)
    inv_t.append((-inv_t[MOD % i] * (MOD // i)) % MOD)
    finv_t.append((finv_t[-1] * inv_t[-1]) % MOD) i range(2, N * M - 2 + 1) range 2 N * M - 2 + 1 N * M - 2 N * M N M 2 1 fact.append((fact[-1] * i) % MOD) fact.append fact append (fact[-1] * i) % MOD fact[-1] * i fact[-1] fact -1 i MOD inv_t.append((-inv_t[MOD % i] * (MOD // i)) % MOD) inv_t.append inv_t append (-inv_t[MOD % i] * (MOD // i)) % MOD -inv_t[MOD % i] * (MOD // i) -inv_t[MOD % i] inv_t[MOD % i] inv_t MOD % i MOD i MOD // i MOD i MOD finv_t.append((finv_t[-1] * inv_t[-1]) % MOD) finv_t.append finv_t append (finv_t[-1] * inv_t[-1]) % MOD finv_t[-1] * inv_t[-1] finv_t[-1] finv_t -1 inv_t[-1] inv_t -1 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 = 0 ans 0 for i in range(M):
    ans += i * (M - i) * N ** 2 i range(M) range M ans += i * (M - i) * N ** 2 ans i * (M - i) * N ** 2 i * (M - i) i M - i M i N ** 2 N 2 for i in range(N):
    ans += i * (N - i) * M ** 2 i range(N) range N ans += i * (N - i) * M ** 2 ans i * (N - i) * M ** 2 i * (N - i) i N - i N i M ** 2 M 2 ans = (ans * pat) % MOD ans (ans * pat) % MOD ans * pat ans pat MOD print(ans) print ans M, K = map(int, input().split()) map(int, input().split()) M fact = [1, 1] [1, 1] fact inv_t = [0, 1] [0, 1] inv_t K = map(int, input().split()) map(int, input().split()) K ans = (ans * pat) % MOD (ans * pat) % MOD ans ans += i * (M - i) * N ** 2 i * (M - i) * N ** 2 ans ans = 0 0 ans finv_t = [1, 1] [1, 1] finv_t N, M, K = map(int, input().split()) map(int, input().split()) N ans += i * (N - i) * M ** 2 i * (N - i) * M ** 2 ans def cmb(n, r):
    return (fact[n] * finv_t[r] * finv_t[n - r]) % MOD def cmb(n, r):
    return (fact[n] * finv_t[r] * finv_t[n - r]) % MOD cmb MOD = 10 ** 9 + 7 10 ** 9 + 7 MOD pat = cmb(N * M - 2, K - 2) cmb(N * M - 2, K - 2) pat
"""
組み合わせ(nCr)計算
https://qiita.com/derodero24/items/91b6468e66923a87f39f#%E7%95%AA%E5%A4%96%E7%B7%A8
逆元の求め方
http://drken1215.hatenablog.com/entry/2018/06/08/210000
解法@公式放送
https://www.youtube.com/watch?v=SS6kW-d-rJ0&feature=youtu.be&t=7376
"""


def cmb(n, r):
    return (fact[n] * finv_t[r] * finv_t[n - r]) % MOD


MOD = 10 ** 9 + 7

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

fact = [1, 1]
inv_t = [0, 1]
finv_t = [1, 1]
for i in range(2, N * M - 2 + 1):
    fact.append((fact[-1] * i) % MOD)
    inv_t.append((-inv_t[MOD % i] * (MOD // i)) % MOD)
    finv_t.append((finv_t[-1] * inv_t[-1]) % MOD)

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

ans = 0

for i in range(M):
    ans += i * (M - i) * N ** 2

for i in range(N):
    ans += i * (N - i) * M ** 2

ans = (ans * pat) % MOD

print(ans)
