// template version 1.12
using namespace std;
#include <iostream>
#include <bits/stdc++.h>

// varibable settings
#define infile "../test/sample-1.in"
#define int long long //{{{
const int INF=1e18;
const int MOD=1e9+7; //}}}

// define basic macro {{{
#define _overload3(_1,_2,_3,name,...) name
#define _rep(i,n) repi(i,0,n)
#define repi(i,a,b) for(int i=(int)(a);i<(int)(b);++i)
#define rep(...) _overload3(__VA_ARGS__,repi,_rep,)(__VA_ARGS__)
#define _rrep(i,n) rrepi(i,0,n)
#define rrepi(i,a,b) for(int i=(int)((b)-1);i>=(int)(a);--i)
#define rrep(...) _overload3(__VA_ARGS__,rrepi,_rrep,)(__VA_ARGS__)
#define each(i,a) for (auto&& i : a)
#define all(x) (x).begin(),(x).end()
#define sz(x) ((int)(x).size())
#define pb(a) push_back(a)
#define mp(a, b) make_pair(a, b)
#define ceil(a,b) ((a)+(b)-1)/(b)
#define uni(x) sort(all(x));x.erase(unique(all(x)),x.end())
#define ub upper_bound
#define lb lower_bound
#define posl(A, x) (lower_bound(all(A), x)-A.begin())
#define posu(A, x) (upper_bound(all(A),x)-A.begin())
template<class T> inline void chmax(T &a, const T &b) { if((a) < (b)) (a) = (b); }
template<class T> inline void chmin(T &a, const T &b) { if((a) > (b)) (a) = (b); }

typedef long long ll;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef long double ld;
typedef pair<int,int> pii;
typedef tuple<int,int,int> iii;

template<typename T> using PQ = priority_queue<T, vector<T>, greater<T>>;
struct Fast { Fast(){ std::cin.tie(0); ios::sync_with_stdio(false); } } fast;

#if defined(PCM) || defined(LOCAL)
  #include "lib/dump.hpp"
#else
  #define dump(...) 42
  #define dump_1d(...) 42
  #define dump_2d(...) 42
#endif
//}}}

int mod = 1e9+7;
struct mint { //逆元などを使いたければmint2{{{
  int x;
  mint(int x=0):x((x%mod+mod)%mod){}
  mint& operator+=(const mint a) {
    (x += a.x) %= mod;
    return *this;
  }
  mint& operator-=(const mint a) {
    (x += mod-a.x) %= mod;
    return *this;
  }
  mint& operator*=(const mint a) {
    (x *= a.x) %= mod;
    return *this;
  }
  mint operator+(const mint a) const {
    mint res(*this);
    return res+=a;
  }
  mint operator-(const mint a) const {
    mint res(*this);
    return res-=a;
  }
  mint operator*(const mint a) const {
    mint res(*this);
    return res*=a;
  }
};
ostream& operator<<(ostream& os, const mint& a){
  os << a.x;
  return os;
} //}}}

const int MAX = 510000;
// Calculate COM(MAX, k) for k<=MAX by O(1) after COMinit() by O(MAX)
// {{{
ll fac[MAX], finv[MAX], inv[MAX];

// 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
ll 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;
}
//}}}

int solve(){
  int n,m,k;cin>>n>>m>>k;
  COMinit();

  mint ans = 0;
  rep(d, 1, m){
    ans += mint(d)*(n*n)*(m-d)*COM(n*m-2, k-2);
  }

  rep(d, 1, n){
    ans += mint(d)*(m*m)*(n-d)*COM(n*m-2, k-2);
  }
  cout << ans << endl;

  return 0;
}

signed main() { //{{{
#ifdef INPUT_FROM_FILE
  std::ifstream in(infile);
  std::cin.rdbuf(in.rdbuf());
#endif
  solve();
  return 0;
} //}}}


Measured memory_bytes: 12160