#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
ll mod = 1000000007;
ll pl(ll a, ll b) {
    a %= mod, b %= mod;
    return (a+b) % mod;
}
ll mu(ll a, ll b) {
    a %= mod, b %= mod;
    return (a*b) % mod;
}
ll pow_mod(ll a, ll b) {
    if (b == 0) return 1;
    a %= mod;
    ll k = pow_mod(a, b/2);
    k = mu(k, k);
    if (b & 1) k = mu(k, a);
    return k;
}
ll di(ll a, ll b) {
    a %= mod;
    return mu(a, pow_mod(b, mod-2));
}
ll nCk(ll n, ll k) {
    ll res = 1;
    for (int a = n, b = k; b > 0; a--, b--) {
        res = mu(res, a);
        res = di(res, b);
    }
    return res;
}
int main () {
    ll A[2], K;
    cin >> A[0] >> A[1] >> K;
    ll ans = 0;
    for (int k = 0; k < 2; k++) {
        ll p = A[0], q = A[1];
        for (int i = 1; i <= q-1; i++) {
            ans += mu(mu(mu(p, p), q-i), i);
        }
        swap(A[0], A[1]);
    }
    ans = di(ans, nCk(A[0]*A[1], 2));
    ans = mu(ans, nCk(A[0]*A[1], K));
    ans = mu(ans, nCk(K, 2));
    cout << ans << endl;
}
#include <bits/stdc++.h>

using namespace std;
 
typedef long long ll;
typedef long double ld;
typedef pair<int, int> Pii;
typedef pair<int, ll> Pil;
typedef pair<ll, ll> Pll;
typedef pair<ll, int> Pli;

#define fi first
#define se second

const ll MOD = 1e9 + 7;
const ll MOD2 = 998244353;
const ll MOD3 = 1812447359;
const ll INF = 1ll << 62;
const double PI = 2 * asin(1);

void yes() {printf("yes\n");}
void no() {printf("no\n");}
void Yes() {printf("Yes\n");}
void No() {printf("No\n");}
void YES() {printf("YES\n");}
void NO() {printf("NO\n");}

ll Pow(ll A, ll N){
  if (N ==0) return 1;
  else if (N % 2 == 0) return Pow(A*A%MOD, N/2);
  else return Pow(A*A%MOD, N/2) * A % MOD;
}


int main(){
  ll N, M, K; cin >> N >> M >> K;

  ll cnt1 = 0, cnt2 = 0;
  for (ll i = 0; i <= N - 1; i++){
    cnt1 += i * (N - i); cnt1 %= MOD;
  }
  cnt1 *= M * M % MOD; cnt1 %= MOD;
  for (ll i = 0; i <= M - 1; i++){
    cnt2 += i * (M - i); cnt2 %= MOD;
  }
  cnt2 *= N * N % MOD; cnt2 %= MOD;
  ll ans = (cnt1 + cnt2) % MOD;

  ll nCr = 1;
  for (ll i = 1; i <= K - 2; i++){
    nCr *= N * M - 1 - i; nCr %= MOD;
    nCr *= Pow(i, MOD-2); nCr %= MOD;
  }
  ans *= nCr; ans %= MOD;
  cout << ans << endl;


  return 0;
}
