#include <bits/stdc++.h>
using namespace std;

#define lli long long int
#define REP(i,s,n) for(int i=s;i<n;i++)
#define MOD 1000000007
#define NUM 2520
#define INF (1LL<<50)
#define DEBUG 0
#define mp(a,b) make_pair(a,b)
#define SORT(V) sort(V.begin(),V.end())
#define PI (3.141592653589794)

const int MAX = 510000;

long long fac[MAX], finv[MAX], inv[MAX];

// テーブルを作る前処理
void COMinit() {
    fac[0] = fac[1] = 1;
    finv[0] = finv[1] = 1;
    inv[1] = 1;
    for (int i = 2; i < MAX; 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;
    }
}

// 二項係数計算
long long COM(int n, int k){
    if (n < k) return 0;
    if (n < 0 || k < 0) return 0;
    return fac[n] * (finv[k] * finv[n - k] % MOD) % MOD;
}

void func(long long N, long long M, long long K){
    COMinit();
    lli sum = 0;

    REP(i,0,N){
        REP(j,0,M){
            if(i!=0 && j!=0) sum += (2*( N-i)*(M-j)*(i+j))%MOD;
            else sum += ((N-i)*(M-j)*(i+j))%MOD;
            sum%= MOD;
        }
    }

    sum *= COM(N*M-2,K-2);
    sum %= MOD;
    cout<<sum<<endl;

}

int main(){
    // cout << fixed << setprecision(5);

    long long N;
    scanf("%lld",&N);
    long long M;
    scanf("%lld",&M);
    long long K;
    scanf("%lld",&K);
    func(N, M, K);
    return 0;
}

#include <bits/stdc++.h>
#define ll long long int
#define MOD 1000000007
#define INF 1000000000000000000

using namespace std;
ll power(ll n, ll k){
  ll res = 1;
  while(k > 0){
    if (k & 1) 
      res = res * n % MOD;
    n = n * n % MOD;
    k >>= 1;
  }
  return res;
}

ll genfact(ll n, ll k){

  ll res = 1;
  k--;
  while (k >= 0){
    res = (res * (n - k)) % MOD;
    k--;
  }

  return res;
}

ll inv(ll n){
  return power(n, MOD - 2);
}

ll fact(ll n){
  return genfact(n, n - 1);
}

ll nck(ll n, ll k){
  if (k == 0)
    return 1;
  if (n <= 0)
    return 0;

  return ((genfact(n, k) % MOD) * inv(fact(k))) % MOD;
}

int main(void){
  ll n, m, k;
  cin >> n >> m >> k;
  
  ll ans = 0;

  ll t = nck(n*m-2,k-2);
  for (ll j = 1; j < m; j++){
    ans += j*(m-j) % MOD * n % MOD *n % MOD * t % MOD;
    ans = (ans % MOD);
  }
  for (ll i = 1; i < n; i++){
    ans += i*(n-i) % MOD * m % MOD *m % MOD * t % MOD;
    ans = (ans % MOD);
  }
  cout << ans << endl;

  return 0;
}
