#pragma region header
#include <bits/stdc++.h>
#define int long long
#define all(a) begin(a), end(a)
#define rall(a) rbegin(a), rend(a)
#define mp make_pair
#define mt make_tuple
#define rep1(i, n) for (decltype(+n) i = 0; i < (n); i++)
#define rrep1(i, n) for (auto i = n - 1; i > static_cast<decltype(i)>(-1); i--)
#define rep2(i, a, b) for (auto i = (a); i < (b); i++)
#define rrep2(i, a, b) for (auto i = b - 1; i >= a; i--)
#define GET_MACRO(_1, _2, _3, NAME, ...) NAME
#define rep(...) GET_MACRO(__VA_ARGS__, rep2, rep1) (__VA_ARGS__)
#define rrep(...) GET_MACRO(__VA_ARGS__, rrep2, rrep1) (__VA_ARGS__)
#define each(i, a) for (auto &&i : (a))
using namespace std;

using ld = long double;
using vi = vector<int>;
using vvi = vector<vi>;
using vs = vector<string>;
using vvs = vector<vs>;
using vd = vector<ld>;
using vvd = vector<vd>;
using vb = vector<bool>;
using vvb = vector<vb>;
using pii = pair<int, int>;
using vp = vector<pii>;
using vvp = vector<vp>;
using mii = map<int, int>;
using vm = vector<mii>;
using vvm = vector<vm>;
template <class T, class U>
using umap = unordered_map<T, U>;
using umii = umap<int, int>;
using seti = set<int>;
template <class T>
using uset = unordered_set<T>;
using useti = uset<int>;
template <class T>
using less_queue = priority_queue<T>;
template <class T>
using greater_queue = priority_queue<T, vector<T>, greater<T>>;

constexpr int INF = 1e18;

template <int MOD>
struct Fp {
  long long val;
  constexpr Fp(long long v = 0) noexcept : val(v % MOD) {
    if (val < 0) val += 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>& a) noexcept {
    long long t;
    is >> t;
    a = Fp<MOD>(t);
    return is;
  }
  constexpr Fp pow(long long n) const noexcept {
    if (n == 0) return 1;
    auto t = pow(n / 2);
    t = t * t;
    if (n & 1) t = t * val;
    return t;
  }
  constexpr Fp inv() const noexcept {
    return pow(MOD - 2);
  }
};
const int MOD = 1000000007;
using mint = Fp<MOD>;

template <class T>
void SORT(T &a) { stable_sort(all(a)); }
template <class T>
void RSORT(T &a) { stable_sort(rall(a)); }
template <class T>
void rev(T &a) { reverse(rall(a)); }
template <class T>
void uniq(T &a) { a.erase(unique(all(a)), end(a)); }
template <class T>
auto min_of(T a) { return *min_element(all(a)); }
template <class T>
auto max_of(T a) { return *max_element(all(a)); }
template <class T>
int sum_of(T a) { return accumulate(all(a), 0ll); }
template <class T, class U>
auto sum_of(T a, U init) { return accumulate(all(a), init); }
template <class T, class U>
int count_of(T a, U i) { return count(all(a), i); }
template <class T, class U>
bool has(T a, U i) { return find(all(a), i) != end(a); }
template <class T>
int sz(T a) { return a.size(); };

template <class T>
void COUT(T x) { cout << x << endl; }
template <class T, class U>
void COUT(T x, U y) { cout << x << ' ' << y << endl; }
template <class T, class U, class V>
void COUT(T x, U y, V z) { cout << x << ' ' << y << ' ' << z << endl; }
template <class T>
void CSP(T x) { cout << x << ' '; }
template <class T>
void CVEC(T v) {
  int c = v.size() - 1;
  for (size_t i = 0; i < c; i++) cout << v[i] << ' ';
  if (c > -1) cout << v[c];
  cout << endl;
}

template <class T>
bool amin(T &a, const T &b) {
  if (a > b) {
    a = b;
    return true;
  }
  return false;
}
template <class T>
bool amax(T &a, const T &b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}

constexpr int lshift(int x) noexcept { return 1ll << x; }
constexpr int popcount(unsigned int x) noexcept { return __builtin_popcountll(x); }
constexpr int least1(unsigned int x) noexcept { return __builtin_ffsll(x); }
constexpr int ceil_div(int x, int y) noexcept { return (x - 1) / y + 1; }

#pragma endregion header

// MOD = 1000000007;
struct combination {
  vector<mint> fact, ifact;
  combination(int n): fact(n + 1), ifact(n + 1) {
    assert(n < MOD);
    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) {
    if (k < 0 || k > n) return 0;
    return fact[n] * ifact[k] * ifact[n - k];
  }
} comb(200000);

void solve(int n, int m, int k) {
  mint ans(0);
  rep(i, 1, n)ans += mint(i) * (n - i) * m * m;
  rep(i, 1, m)ans += mint(i) * (m - i) * n * n;
  ans *= comb(n * m - 2, k - 2);
  COUT(ans);
}


#pragma region main
signed main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  cout << fixed << setprecision(15);

  int n;
  cin >> n;
  int m;
  cin >> m;
  int k;
  cin >> k;
  solve(n, m, k);
}
#pragma endregion main


Measured memory_bytes: 6216