#include <iostream>
#include <algorithm>
#include <string>
#include <string.h>
#include <stdlib.h>
#include <math.h>
#include <vector>
#include <queue>
#include <stack>
#include <cmath>
#include <map>
#include <iomanip>
#include <set>
#include <ctime>
#include <tuple>
#include <bitset>
#include <assert.h>
#include <deque>
using namespace std;
typedef long long ll;

#define fi first
#define se second
#define rep(i, n) for (ll i = 0; i < n; i++)
#define debugA cerr << "AAAAA" << endl
#define debug_ cerr << "-------------" << endl
#define debug(x) cerr << #x << ": " << x << endl
#define debug_vec(v)                   \
    cout << #v << endl;                \
    for (int i = 0; i < v.size(); i++) \
    {                                  \
        cout << v[i] << " ";           \
    }                                  \
    cout << endl;
#define debug_vec2(v)                         \
    cout << #v << endl;                       \
    for (int i = 0; i < v.size(); i++)        \
    {                                         \
        for (int j = 0; j < v[i].size(); j++) \
        {                                     \
            cout << v[i][j] << " ";           \
        }                                     \
        cout << endl;                         \
    }

template <typename T>
bool chmax(T &a, const T &b)
{
    if (a < b)
    {
        a = b;
        return true;
    }
    return false;
}

template <typename T>
bool chmin(T &a, const T &b)
{
    if (a > b)
    {
        a = b;
        return true;
    }
    return false;
}

using Graph = vector<vector<int>>;
using P = pair<int, int>;
using P1 = pair<int, pair<int, int>>; // クラスカル法とかで、{cost, {from, to}}的に使う。
const ll INF = 1001001001001001001;
const double pi = acos(-1);

// auto mod int
// https://youtu.be/L8grWxBlIZ4?t=9858
// https://youtu.be/ERZuLAxZffQ?t=4807 : optimize
// https://youtu.be/8uowVvQ_-Mo?t=1329 : division
const int mod = 1000000007;
struct mint
{
    ll x; // typedef long long ll;
    mint(ll x = 0) : x((x % mod + mod) % mod) {}
    mint operator-() const { return mint(-x); }
    mint &operator+=(const mint a)
    {
        if ((x += a.x) >= mod)
            x -= mod;
        return *this;
    }
    mint &operator-=(const mint a)
    {
        if ((x += mod - a.x) >= mod)
            x -= mod;
        return *this;
    }
    mint &operator*=(const mint a)
    {
        (x *= a.x) %= mod;
        return *this;
    }
    mint operator+(const mint a) const { return mint(*this) += a; }
    mint operator-(const mint a) const { return mint(*this) -= a; }
    mint operator*(const mint a) const { return mint(*this) *= a; }
    mint pow(ll t) const
    {
        if (!t)
            return 1;
        mint a = pow(t >> 1);
        a *= a;
        if (t & 1)
            a *= *this;
        return a;
    }

    // for prime mod
    mint inv() const { return pow(mod - 2); }
    mint &operator/=(const mint a) { return *this *= a.inv(); }
    mint operator/(const mint a) const { return mint(*this) /= a; }
};
istream &operator>>(istream &is, const mint &a) { return is >> a.x; }
ostream &operator<<(ostream &os, const mint &a) { return os << a.x; }

struct combination
{
    vector<mint> fact, ifact;
    combination(int n) : fact(n + 1), ifact(n + 1)
    {
        assert(n < mod);
        fact[0] = 1;
        for (int i = 1; i <= n; ++i)
            fact[i] = fact[i - 1] * i;
        ifact[n] = fact[n].inv();
        for (int i = n; i >= 1; --i)
            ifact[i - 1] = ifact[i] * i;
    }
    mint operator()(int n, int k)
    {
        if (k < 0 || k > n)
            return 0;
        return fact[n] * ifact[k] * ifact[n - k];
    }
} c(200005);

int main()
{
    ll n, m, k;
    cin >> n >> m >> k;
    mint ans = 0;
    for (int i = 1; i <= m - 1; i++)
    {
        ans += i * (m - i) * n * n;
    }
    for (int i = 1; i <= n - 1; i++)
    {
        ans += i * (n - i) * m * m;
    }
    mint com = c(int((n * m - 2) % mod), int(k - 2));
    ans *= com;
    // mint ans = c(int((n * m - 2) % mod), int(k - 2)) * ((m - 1) * m * n + (n - 1) * n * m) / 2;
    cout << ans << endl;

    return 0;
}


Measured memory_bytes: 3328