#include <bits/stdc++.h> //C++の標準ライブラリを一行で一括でインクルードする
#include <math.h> //数学関数と数学定数を利用する
#define rep(i,n) for (int i = 0; i < (n); i++)
#define PI 3.141592653589793
using namespace std;
typedef long long ll;
template<class T> void chmax(T &a,T b) { if (a<b) a=b;}
template<class T> void chmin(T &a,T b) { if (a>b) a=b;}
int gcd(int a, int b){//ユークリッドの互除法
  if (a < b) gcd(b,a); //aの方がbよりでかいのが前提
  if (b == 0) return a; //aをbで割り切れたらreturn
  else gcd(b, a % b);
}
const int INF = 1<<30;
int dx[4] = {0,0,-1,1};
int dy[4] = {-1,1,0,0};
// modint: mod 計算を int を扱うように扱える構造体
template<int MOD> struct Fp {
    long long val;
    constexpr Fp(long long v = 0) noexcept : val(v % MOD) {
        if (val < 0) v += MOD;
    }
    constexpr int getmod() { return MOD; }
    constexpr Fp operator - () const noexcept {
        return val ? MOD - val : 0;
    }
    constexpr Fp operator + (const Fp& r) const noexcept { return Fp(*this) += r; }
    constexpr Fp operator - (const Fp& r) const noexcept { return Fp(*this) -= r; }
    constexpr Fp operator * (const Fp& r) const noexcept { return Fp(*this) *= r; }
    constexpr Fp operator / (const Fp& r) const noexcept { return Fp(*this) /= r; }
    constexpr Fp& operator += (const Fp& r) noexcept {
        val += r.val;
        if (val >= MOD) val -= MOD;
        return *this;
    }
    constexpr Fp& operator -= (const Fp& r) noexcept {
        val -= r.val;
        if (val < 0) val += MOD;
        return *this;
    }
    constexpr Fp& operator *= (const Fp& r) noexcept {
        val = val * r.val % MOD;
        return *this;
    }
    constexpr Fp& operator /= (const Fp& r) noexcept {
        long long a = r.val, b = MOD, u = 1, v = 0;
        while (b) {
            long long t = a / b;
            a -= t * b; swap(a, b);
            u -= t * v; swap(u, v);
        }
        val = val * u % MOD;
        if (val < 0) val += MOD;
        return *this;
    }
    constexpr bool operator == (const Fp& r) const noexcept {
        return this->val == r.val;
    }
    constexpr bool operator != (const Fp& r) const noexcept {
        return this->val != r.val;
    }
    friend constexpr ostream& operator << (ostream &os, const Fp<MOD>& x) noexcept {
        return os << x.val;
    }
    friend constexpr istream& operator >> (istream &is, Fp<MOD>& x) noexcept {
        return is >> x.val;
    }
    friend constexpr Fp<MOD> modpow(const Fp<MOD> &a, long long n) noexcept {
        if (n == 0) return 1;
        auto t = modpow(a, n / 2);
        t = t * t;
        if (n & 1) t = t * a;
        return t;
    }
};
const int MAX = 510000;
const int MOD = 1000000007;
using mint = Fp<MOD>;
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;
}


int main(){
  COMinit();
  mint ans;
  int n,m,k; cin >> n >> m >> k;
  
  rep(i,m){
    ans += mint(i)*mint(m-i)*mint(n*n);
  }
  rep(i,n){
    ans += mint(i)*mint(n-i)*mint(m*m);
  }
  
  mint pat = COM(n*m-2,k-2);
  //printf("ans=%d pat=%d\n",ans,pat);
  ans *= pat;
  
  cout << ans << endl;

  return 0;
}

Measured memory_bytes: 12160