#include <algorithm>
#include <bitset>
#include <cassert>
#include <cmath>
#include <functional>
#include <iomanip>
#include <iostream>
#include <map>
#include <queue>
#include <unordered_map>
#include <vector>
#include <string.h>
#include <set>

using namespace std;

#define COUT(x) cout << #x << " = " << (x) << " (L" << __LINE__ << ")" << endl

#define rep(i, n) for(int i = 0; i < n; ++i)
#define all(s) s.begin(), s.end()

typedef long long ll;
typedef unsigned long long ull;
typedef pair<ll, ll> P;
typedef tuple<ll, ll, ll> triple;
typedef double D;

const ll INF = 1e9;
const ll MOD = 1000000007;  // 1e9 + 7

// Mod int
// cf. https://www.youtube.com/watch?v=1Z6ofKN03_Y
struct mint {
  ll x;
  mint(ll x = 0) : x((x + MOD) % MOD) {}
  mint& operator+= (const mint a) {
    if ((x += a.x) >= MOD) x %= MOD;
    return *this;
  }
  mint operator+ (const mint a) const {
    mint res(*this);
    return res += a;
  }
  mint& operator-= (const mint a) {
    if ((x += MOD - a.x) >= MOD) x %= MOD;
    return *this;
  }
  mint operator- (const mint a) const {
    mint res(*this);
    return res -= a;
  }
  mint& operator*= (const mint a) {
    (x *= a.x) %= MOD;
    return *this;
  }
  mint operator* (const mint a) const {
    mint res(*this);
    return res *= a;
  }
  mint pow(ll t) const {
    if (!t) { return 1; }
    mint a = pow(t >> 1);
    a *= a;
    if (t & 1) a *= *this;
    return a;
  }

  // for prime mod
  mint inv() const {
    return pow(MOD-2);
  }
  mint& operator/= (const mint a) {
    return (*this) *= a.inv();
  }
  mint operator/ (const mint a) const {
    mint res(*this);
    return res /= a;
  }
};

// Combination mod prime.
// cf. https://www.youtube.com/watch?v=1Z6ofKN03_Y
struct Combination {
  vector<mint> fact, ifact;
  Combination(int n) { init(n); }
  void init(int n) {
    assert(n < MOD); // n must be lower than MOD.

    fact.resize(n + 1);
    ifact.resize(n + 1);

    fact[0] = 1;
    for (int i = 1; i <= n; ++i) { fact[i] = fact[i-1] * i; }
    ifact[n] = fact[n].inv();
    for (int i = n; i >= 1; --i) { ifact[i-1] = ifact[i] * i; }
  }
  mint operator() (int n, int k) const {
    if (k < 0 || k > n) { return 0; }
    return fact[n] * ifact[k] * ifact[n-k];
  }
  mint perm(int n, int k) const {
    if (k < 0 || k > n) { return 0; }
    return fact[n] * ifact[n-k];
  }
};

// int main(int argc, char** argv) {
//   MOD = 13;
//
//   Combination c(12);
//   cout << c(12, 0).x << endl;  // 1  = 1 % 13
//   cout << c(12, 1).x << endl;  // 12 = 12 % 13
//   cout << c(12, 2).x << endl;  // 1  = 66 % 13 = (12 * 11 / 2) % 13
//   cout << c(12, 3).x << endl;  // 12 = 220 % 13 = (12 * 11 * 10 / (3 * 2 * 1)) % 13
//   cout << c(12, 11).x << endl; // 12 = 12 % 13
//   cout << c(12, 12).x << endl; // 1  = 12 % 13
//
//   cout << c.perm(12, 3).x << endl; // 7 = 12 * 11 * 10 % 13
// }

// - answer
//   - x
//     - factor: (N-2)C(K-2)
//     - each d: (N-d) * M*2
//       - d: [1, N)
//   - y
//     - factor: (N-2)C(K-2)
//     - each d: (M-d) * N*2
//       - d: [1, M)

int main(int argc, char** argv) {
  ll N, M, K;
  cin >> N >> M >> K;

  mint x(0);
  for (ll d = 1; d < N; ++d) { // d: |xi-xj|
    x += mint(d) * mint(N-d) * mint(M) * mint(M);
  }
  mint y(0);
  for (ll d = 1; d < M; ++d) { // d: |yi-yj|
    y += mint(d) * mint(M-d) * mint(N) * mint(N);
  }

  Combination c(N * M);
  mint ans = (x + y) * c(N * M-2, K-2);

  cout << ans.x << endl;
}


Measured memory_bytes: 3328