#include <iostream>
#include <vector>
#include <algorithm>
#include <cmath>
#include <queue>
#include <string>
#include <map>
#include <set>
#include <stack>
#include <tuple>
#include <deque>
#include <numeric>
#include <bitset>
#include <iomanip>
#include <cassert>
#include <chrono>
#include <random>
#include <limits>
#include <iterator>
#include <functional>
#include <sstream>
#include <complex>
using namespace std;

using ll = long long;
using ull = uint64_t;
using P = pair<int, int>;
constexpr double EPS = 1e-9;
constexpr int INF = 1001001001;
constexpr int mod = 1000000007;
// constexpr int mod = 998244353;

template<class T>
inline bool chmax(T& x, T y){
    if(x < y){
        x = y;
        return true;
    }
    return false;
}
template<class T>
inline bool chmin(T& x, T y){
    if(x > y){
        x = y;
        return true;
    }
    return false;
}

template<int mod>
struct ModInt{
    int x;

    ModInt() : x(0) {}
    
    ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}
    
    ModInt &operator+=(const ModInt &p){
        if((x += p.x) >= mod)   x -= mod;
        return *this;
    }
    
    ModInt &operator-=(const ModInt &p){
        if((x += mod - p.x) >= mod) x -= mod;
        return *this;
    }

    ModInt &operator*=(const ModInt &p){
        x = (int)(1LL * x * p.x % mod);
        return *this;
    }

    ModInt &operator/=(const ModInt &p){
        *this *= p.inverse();
        return *this;
    }
    
    ModInt operator-() const {return ModInt(-x);}

    ModInt operator+(const ModInt &p) const {return ModInt(*this) += p;}

    ModInt operator-(const ModInt &p) const {return ModInt(*this) -= p;}

    ModInt operator*(const ModInt &p) const {return ModInt(*this) *= p;}

    ModInt operator/(const ModInt &p) const {return ModInt(*this) /= p;}

    bool operator==(const ModInt &p) const {return x == p.x;}

    bool operator!=(const ModInt &p) const {return x != p.x;}

    ModInt inverse() const{
        int a = x, b = mod, u = 1, v = 0, t;
        while(b > 0){
            t = a / b;
            swap(a -= t * b, b);
            swap(u -= t * v, v);
        }
        return ModInt(u);
    }

    ModInt pow(int64_t n) const{
        ModInt ret(1), mul(x);
        while(n > 0){
            if(n & 1)   ret *= mul;
            mul *= mul;
            n >>= 1;
        }
        return ret;
    }

    friend ostream &operator<<(ostream &os, const ModInt &p){
        return os << p.x;
    }

    friend istream &operator>>(istream &is, ModInt &a){
        int64_t t;
        is >> t;
        a = ModInt<mod>(t);
        return (is);
    }

    static int get_mod() {return mod;}
};

using modint = ModInt<mod>;

template<typename T>
struct Combination{
    int sz;
    vector<T> fact_;
    vector<T> ifact_;
    vector<T> inv_;
    
    Combination(int n = 1e+6) : sz(n) {
        fact_.resize(sz + 1);
        ifact_.resize(sz + 1);
        inv_.resize(sz + 1);

        fact_[0] = ifact_[sz] = inv_[0] = 1;
        for(int i = 1; i <= sz; ++i)    fact_[i] = fact_[i - 1] * i;
        ifact_[sz] /= fact_[sz];
        for(int i = sz; i > 0; --i)     ifact_[i - 1] = ifact_[i] * i;
        for(int i = 1; i <= sz; ++i)    inv_[i] = ifact_[i] * fact_[i - 1];
    }

    inline T fact(int k) const  {return fact_[k];}
    inline T ifact(int k) const {return ifact_[k];}
    inline T inv(int k) const   {return inv_[k];}

    T get_permutation(int n, int k){
        if(n < 0 || k < 0 || n < k)     return 0;
        return fact(n) * ifact(n - k);
    }

    T get_combination(int n, int k){
        if(n < 0 || k < 0 || n < k)     return 0;
        return fact(n) * ifact(k) * ifact(n - k);
    }
};

int main(){
    ios::sync_with_stdio(false);
    cin.tie(nullptr);

    int N, M, K;
    cin >> N >> M >> K;
    Combination<modint> c(N * M);
    modint ans = 0;
    for(int i = 0; i < N; ++i){
        modint X = (ll)(N - i - 1) * (N - i) / 2 * M;
        for(int j = 0; j < M; ++j){
            modint Y = (ll)j * (j + 1) / 2 * (N - i - 1);
            Y += (ll)(M - j - 1) * (M - j) / 2 * (N - i);
            ans += X + Y;
        }
    }
    ans *= c.get_combination(N * M - 2, K - 2);
    cout << ans << endl;
}

Measured memory_bytes: 5556