#include <bits/stdc++.h>
using namespace std;
long long MOD = 1000000007;
long long modpow(long long a, long long b){
  long long ans = 1;
  while (b > 0){
    if (b % 2 == 1){
      ans *= a;
      ans %= MOD;
    }
    a *= a;
    a %= MOD;
    b /= 2;
  }
  return ans;
}
long long modinv(long long a){
  return modpow(a, MOD - 2);
}
vector<long long> mf = {1};
long long modfact(int n){
  if (mf.size() > n){
    return mf[n];
  } else {
    for (int i = mf.size(); i <= n; i++){
      long long next = mf.back() * i % MOD;
      mf.push_back(next);
    }
    return mf[n];
  }
}
long long modbinom(int n, int k){
  return modfact(n) * modinv(modfact(k)) % MOD * modinv(modfact(n - k)) % MOD;
}
int main(){
  long long N, M, K;
  cin >> N >> M >> K;
  long long ans1 = 0;
  for (int i = 1; i <= N; i++){
    ans1 += (N - i) * i;
  }
  ans1 %= MOD;
  ans1 *= M;
  ans1 %= MOD;
  ans1 *= M;
  ans1 %= MOD;
  long long ans2 = 0;
  for (int i = 1; i <= M; i++){
    ans2 += (M - i) * i;
  }
  ans2 %= MOD;
  ans2 *= N;
  ans2 %= MOD;
  ans2 *= N;
  ans2 %= MOD;
  long long ans = ans1 + ans2;
  ans %= MOD;
  ans *= modbinom(N * M - 2, K - 2);
  ans %= MOD;
  cout << ans << endl;
}
#include <iostream>
#include <vector>
#include <algorithm>
#include <map>
#include <string>
#include <queue>
#include <fstream>
#include <string>
#include <math.h>
#include <set>
#include <string>
#include <bitset>
#include <fstream>
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
//typedef pair<ll, ll> P;
//typedef pair<ll, P> T;

#define rep(i, n) for (ll i = 0; i < (n); i++)
#define revrep(i, n) for (ll i = (n) - 1; i >= 0; i--)
#define f first
#define s second
#define pb push_back

ll mod = 1000000007;
const ll INF = 100000000000010000;
//const ull B = 998244353;

//ll bit[200010];
//ll kai[3010];
//ll Cnt[10010];

//void pres(double A, ll x = 20) { printf("%.20f\n", x); }

vector<ll> dx = { 0, 1, 0, -1, 1, -1, 1, -1, 0};
vector<ll> dy = { 1, 0, -1, 0, 1, 1, -1, -1, 0};

void chmin(ll& x, ll y) {
	x = min(x, y);
}

void chmax(ll& x, ll y) {
	x = max(x, y);
}


/*ll sum(ll i)
{
	i += 1;
	ll t = 0;
	while (i > 0)
	{
		t += bit[i];
		i -= i & -i;
	}
	return t;
}

void add(ll i, ll x)
{
	i += 1;
	while (i <= 200005)
	{
		bit[i] += x;
		i += i & -i;
	}
}*/

/*`ll SAIKI(ll S) {
	for (ll T = S; ; T = (T - 1) & S) {

	}
}*/



void test() {
	cout << "888888888888888888888888" << endl;
}

ll gcd(ll x, ll y) {
	if (y == 0) return x;
	return gcd(y, x % y);
}

ll pow_mod(ll x, ll k) {
	x %= mod;
	ll res = 1;
	while (k > 0) {
		if (k % 2) {
			res *= x; res %= mod;
		}
		x *= x; x %= mod;
		k /= 2;
	}
	return res;
}

ll div_mod(ll x) {
	return pow_mod(x, mod - 2);
}


vector <ll> par; // 各元の親を表す配列
vector <ll> siz; // 素集合のサイズを表す配列(1 で初期化)

void init_u(ll sz_) {
	par.resize(sz_);
	siz.assign(sz_, 1LL);  // resize だとなぜか初期化されなかった
	for (ll i = 0; i < sz_; ++i) par[i] = i; // 初期では親は自分自身
}

// Member Function
// Find
ll root(ll x) { // 根の検索
	while (par[x] != x) {
		x = par[x] = par[par[x]]; // x の親の親を x の親とする
	}
	return x;
}

// Union(Unite, Merge)
bool merge(ll x, ll y) {
	x = root(x);
	y = root(y);
	if (x == y) return false;
	// merge technique（データ構造をマージするテク．小を大にくっつける）
	if (siz[x] < siz[y]) swap(x, y);
	siz[x] += siz[y];
	par[y] = x;
	return true;
}

bool issame(ll x, ll y) { // 連結判定
	return root(x) == root(y);
}

ll size(ll x) { // 素集合のサイズ
	return siz[root(x)];
}


//コンビネーション
const int MAXcomb = 1000010;
ll fac[MAXcomb], finv[MAXcomb], inv[MAXcomb];
//facはn!,finvは1/n!
//invは逆元
void COMinit() {
	fac[0] = fac[1] = 1;
	finv[0] = finv[1] = 1;
	inv[1] = 1;
	for (int i = 2; i < MAXcomb; i++) {
		fac[i] = fac[i - 1] * i % mod;
		inv[i] = mod - inv[mod%i] * (mod / i) % mod;
		finv[i] = finv[i - 1] * inv[i] % mod;
	}
}
ll comb(int n, int k) {
	if (n < k) return 0;
	if (n < 0 || k < 0) return 0;
	return fac[n] * finv[k] % mod * finv[n - k] % mod;
}


/*map<ll, ll> pres;
ll ct;

void makePrimeList(ll x) {
	ll X = x;
	for (ll j = 2; j * j <= x; j++) {
		ll cnt = 0;
		while (X % j == 0) {
			cnt++;
			X /= j;
		}
		if (cnt) {
			if (pres[j] == 0) {
				ct++;
				pres[j] = ct;
			}
			Cnt[pres[j]] += cnt;
		}
	}
	if (X != 1) {
		if (pres[X] == 0) {
			ct++;
			pres[X] = ct;
		}
		Cnt[pres[X]] += 1;
	}
}*/

ll N, M, K;
ll ans, num;

void solve() {
	cin >> N >> M >> K;
	COMinit();
	rep(i, N) {
		num += i * (i + 1) / 2 % mod;
		num %= mod;
	}
	ans += comb(N * M - 2, K - 2) * M % mod * M % mod * num % mod;
	ans %= mod;
	num = 0;
	rep(i, M) {
		num += i * (i + 1) / 2 % mod;
		num %= mod;
	}
	ans += comb(N * M - 2, K - 2) * N % mod * N % mod * num % mod;
	ans %= mod;
	cout << ans << endl;
}

int main() {
	cin.tie(0);
	ios::sync_with_stdio(false);
	ll T = 1;
	//cin >> T;
	rep(i, T) solve();
	ll N;
	cin >> N;
}