#include <bits/stdc++.h>
using namespace std;
using lint = long long int;
using pint = pair<int, int>;
using plint = pair<lint, lint>;
struct fast_ios
{
    fast_ios()
    {
        cin.tie(0);
        ios::sync_with_stdio(false);
        cout << fixed << setprecision(20);
    };
} fast_ios_;
#define FOR(i, begin, end) for (int i = (begin), i##_end_ = (end); i < i##_end_; i++)
#define IFOR(i, begin, end) for (int i = (end)-1, i##_begin_ = (begin); i >= i##_begin_; i--)
#define REP(i, n) FOR(i, 0, n)
#define IREP(i, n) IFOR(i, 0, n)
template <typename T>
istream &operator>>(istream &is, vector<T> &vec)
{
    for (auto &v : vec)
        is >> v;
    return is;
}
template <typename T>
ostream &operator<<(ostream &os, const vector<T> &vec)
{
    os << "[";
    for (auto v : vec)
        os << v << ",";
    os << "]";
    return os;
}
template <typename T>
ostream &operator<<(ostream &os, const deque<T> &vec)
{
    os << "deq[";
    for (auto v : vec)
        os << v << ",";
    os << "]";
    return os;
}
template <typename T>
ostream &operator<<(ostream &os, const set<T> &vec)
{
    os << "{";
    for (auto v : vec)
        os << v << ",";
    os << "}";
    return os;
}
template <typename T>
ostream &operator<<(ostream &os, const unordered_set<T> &vec)
{
    os << "{";
    for (auto v : vec)
        os << v << ",";
    os << "}";
    return os;
}
template <typename T>
ostream &operator<<(ostream &os, const multiset<T> &vec)
{
    os << "{";
    for (auto v : vec)
        os << v << ",";
    os << "}";
    return os;
}
template <typename T>
ostream &operator<<(ostream &os, const unordered_multiset<T> &vec)
{
    os << "{";
    for (auto v : vec)
        os << v << ",";
    os << "}";
    return os;
}
template <typename T1, typename T2>
ostream &operator<<(ostream &os, const pair<T1, T2> &pa)
{
    os << "(" << pa.first << "," << pa.second << ")";
    return os;
}
template <typename TK, typename TV>
ostream &operator<<(ostream &os, const map<TK, TV> &mp)
{
    os << "{";
    for (auto v : mp)
        os << v.first << "=>" << v.second << ",";
    os << "}";
    return os;
}
template <typename TK, typename TV>
ostream &operator<<(ostream &os, const unordered_map<TK, TV> &mp)
{
    os << "{";
    for (auto v : mp)
        os << v.first << "=>" << v.second << ",";
    os << "}";
    return os;
}
template <typename T>
void ndarray(vector<T> &vec, int len) { vec.resize(len); }
template <typename T, typename... Args>
void ndarray(vector<T> &vec, int len, Args... args)
{
    vec.resize(len);
    for (auto &v : vec)
        ndarray(v, args...);
}
template <typename T>
bool mmax(T &m, const T q)
{
    if (m < q)
    {
        m = q;
        return true;
    }
    else
        return false;
}
template <typename T>
bool mmin(T &m, const T q)
{
    if (m > q)
    {
        m = q;
        return true;
    }
    else
        return false;
}
template <typename T1, typename T2>
pair<T1, T2> operator+(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first + r.first, l.second + r.second); }
template <typename T1, typename T2>
pair<T1, T2> operator-(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first - r.first, l.second - r.second); }
#define dbg(x) cerr << #x << " = " << (x) << " (L" << __LINE__ << ") " << __FILE__ << endl;
#define FI first
#define SE second
#define ALL(x) (x).begin(), (x).end()
#define SZ(x) ((lint)(x).size())
#define POW2(n) (1LL << (n))

constexpr lint MOD = 1000000007;
// Solve ax+by=gcd(a, b)
lint extgcd(lint a, lint b, lint &x, lint &y)
{
    lint d = a;
    if (b != 0)
        d = extgcd(b, a % b, y, x), y -= (a / b) * x;
    else
        x = 1, y = 0;
    return d;
}
// Calc a^(-1) (MOD m)
lint mod_inverse(lint a, lint m = MOD)
{
    lint x, y;
    extgcd(a, m, x, y);
    return (m + x % m) % m;
}
int main()
{
    lint N, M, K;
    cin >> N >> M >> K;
    lint ret = 0;
    REP(i, N) ret += M * (N - 1 - i) % MOD * (N - i) % MOD * mod_inverse(2) % MOD * M % MOD;
    REP(i, M) ret += N * (M - 1 - i) % MOD * (M - i) % MOD * mod_inverse(2) % MOD * N % MOD;
    ret %= MOD;
    // dbg(ret);
    FOR(i, 1, K - 2 + 1)
    {
        ret = ret * mod_inverse(i) % MOD * ((N * M - 1 - i) % MOD) % MOD;
    }
    cout << ret << endl;
}


Measured memory_bytes: 256