#include <bits/stdc++.h>
#define FOR(i, a, b) for(int i=(a); i<(b); i++)
#define REP(i, n) FOR(i, 0, n)
#define all(x) (x).begin(), (x).end()
#define bit(x) (1L << (x))
using ll = long long;
using namespace std;

template<typename T>
vector<T> make_v(size_t a,T b){return vector<T>(a,b);}
 
template<typename... Ts>
auto make_v(size_t a,Ts... ts){
  return vector<decltype(make_v(ts...))>(a,make_v(ts...));
}

template <int Mod, bool IsPrime = false>
class mod_int {
    using ll = long long;

public:
    constexpr mod_int() : n(0) {}
    constexpr mod_int(int n_) : n(n_) {
        if(n >= Mod)     n %= Mod;
        else if(n < 0) n = (n % Mod + Mod) % Mod;
    }
    constexpr mod_int(ll n_) : n(n_) { n = (n + Mod) % Mod; }

    constexpr operator int() const { return n; }
    constexpr operator ll() const  { return n; }

    constexpr bool operator==(mod_int const& other) const { return n == other.n; }
    constexpr mod_int& operator+=(mod_int const& other) {
        if((n += other.n) >= Mod) n -= Mod;
        return *this;
    }
    constexpr mod_int& operator-=(mod_int const& other) {
        if((n += Mod - other.n) >= Mod) n -= Mod;
        return *this;
    }
    constexpr mod_int& operator*=(mod_int const& other) {
        n = (unsigned long long)n * other.n % Mod;
        return *this;
    }
    constexpr typename std::enable_if<IsPrime, mod_int>::type& operator/=(mod_int const& other) {
        return *this *= other.inverse();
    }
    constexpr mod_int operator+(mod_int other) const { return mod_int(*this) += other; }
    constexpr mod_int operator-(mod_int other) const { return mod_int(*this) -= other; }
    constexpr mod_int operator*(mod_int other) const { return mod_int(*this) *= other; }
    constexpr mod_int operator/(mod_int other) const { return mod_int(*this) /= other; }

    constexpr typename std::enable_if<IsPrime, mod_int>::type inverse() const {
        ll a = n, b = Mod, u = 1, v = 0;
        while(b) {
            ll t = a / b;
            a -= t * b; std::swap(a, b);
            u -= t * v; std::swap(u, v);
        }
        return mod_int(u);
    }

private:
    ll n;
};

template <int Mod, bool IsPrime>
std::ostream& operator<<(std::ostream& os, mod_int<Mod, IsPrime> const& n) {
    os << (int)n;
    return os;
}

constexpr int default_mod = 1000000007;

template <int Mod = default_mod>
mod_int<Mod, true> fact(int n) {
    static std::vector<mod_int<Mod, true>> v = {1};
    if(n >= static_cast<int>(v.size())) {
        const int from = v.size(), to = n + 1024;
        v.reserve(to);
        for(int i = from; i < to; ++i) {
            v.push_back(v.back() * mod_int<Mod, true>(i));
        }
    }
    return v[n];
}

template <int Mod = default_mod>
mod_int<Mod, true> comb(int n, int r) { // nCr
    if(r < 0 || r > n) return 0;
    return fact<Mod>(n) / fact<Mod>(r) / fact<Mod>(n - r);
}

using mint = mod_int<default_mod, true>; // default

int main() {
  int n, m, k; cin >> n >> m >> k;
  
  function<mint(int, int, int)> calc = [](int n, int m, int k){
    mint ret;

    REP(d, n){
      ret += mint(d) * mint(n-d) * mint(m * m) * comb(n*m-2, k-2);
    }

    return ret;
  };

  cout << calc(n, m, k) + calc(m, n, k) << endl;

  return 0;
}


Measured memory_bytes: 3328