MOD = 10**9+7
MAX = 2*10**5
n, m, k = map(int, input().split())

fact = [1]*(MAX+1)
for i in range(1, MAX+1):
    fact[i] = (fact[i-1]*i)%MOD
finv = [1]*MAX + [pow(fact[-1], MOD-2, MOD)]
for i in range(MAX, 0, -1):
    finv[i-1] = (finv[i]*i)%MOD

def comb(n, r):
    return ((fact[n]*finv[n-r])%MOD*finv[r])%MOD

cumsum = [0]*(MAX+1)
for i in range(1, max(n, m)+1):
    cumsum[i] = cumsum[i-1]+i

ans = 0
for i in range(n):
    ans += (cumsum[i] + cumsum[n-i-1])*(m**2)
for i in range(m):
    ans += (cumsum[i] + cumsum[m-i-1])*(n**2)

ans //= 2
ans = (ans*comb(n*m-2, k-2))%MOD
print(ans)

e373f645d6e9240421ddf593cc61f4399344591f
<mask token>

<mask token>


def comb(n, r):
    return fact[n] * finv[n - r] % MOD * finv[r] % MOD


<mask token>

<mask token>
for i in range(1, MAX + 1):
    fact[i] = fact[i - 1] * i % MOD
<mask token>
for i in range(MAX, 0, -1):
    finv[i - 1] = finv[i] * i % MOD


def comb(n, r):
    return fact[n] * finv[n - r] % MOD * finv[r] % MOD


<mask token>
for i in range(1, max(n, m) + 1):
    cumsum[i] = cumsum[i - 1] + i
<mask token>
for i in range(n):
    ans += (cumsum[i] + cumsum[n - i - 1]) * m ** 2
for i in range(m):
    ans += (cumsum[i] + cumsum[m - i - 1]) * n ** 2
ans //= 2
<mask token>
print(ans)

MOD = 10 ** 9 + 7
MAX = 2 * 10 ** 5
n, m, k = map(int, input().split())
fact = [1] * (MAX + 1)
for i in range(1, MAX + 1):
    fact[i] = fact[i - 1] * i % MOD
finv = [1] * MAX + [pow(fact[-1], MOD - 2, MOD)]
for i in range(MAX, 0, -1):
    finv[i - 1] = finv[i] * i % MOD


def comb(n, r):
    return fact[n] * finv[n - r] % MOD * finv[r] % MOD


cumsum = [0] * (MAX + 1)
for i in range(1, max(n, m) + 1):
    cumsum[i] = cumsum[i - 1] + i
ans = 0
for i in range(n):
    ans += (cumsum[i] + cumsum[n - i - 1]) * m ** 2
for i in range(m):
    ans += (cumsum[i] + cumsum[m - i - 1]) * n ** 2
ans //= 2
ans = ans * comb(n * m - 2, k - 2) % MOD
print(ans)

MOD = 10**9+7
MAX = 2*10**5
n, m, k = map(int, input().split())

fact = [1]*(MAX+1)
for i in range(1, MAX+1):
    fact[i] = (fact[i-1]*i)%MOD
finv = [1]*MAX + [pow(fact[-1], MOD-2, MOD)]
for i in range(MAX, 0, -1):
    finv[i-1] = (finv[i]*i)%MOD

def comb(n, r):
    return ((fact[n]*finv[n-r])%MOD*finv[r])%MOD

cumsum = [0]*(MAX+1)
for i in range(1, max(n, m)+1):
    cumsum[i] = cumsum[i-1]+i

ans = 0
for i in range(n):
    ans += (cumsum[i] + cumsum[n-i-1])*(m**2)
for i in range(m):
    ans += (cumsum[i] + cumsum[m-i-1])*(n**2)

ans //= 2
ans = (ans*comb(n*m-2, k-2))%MOD
print(ans)
