#include <bits/stdc++.h>
using namespace std;
#define int long long
#define PI 3.141592653589793
#define rep(i, n) for (int i = 0; i < (n); i++)
#define REP(i, a, n) for (int i = a; i < (n); i++)
#define rrep(i, n, k) for (int i = (n); i >= (k); i--);
#define all(x) (x).begin(), (x).end()
#define vi vector<int>
template<class T> istream &operator>>(istream&is,vector<T>&v){for(auto &elemnt:v)is>>elemnt;return is;}
template<class T,class U> istream &operator>>(istream&is,pair<T,U>&p){is>>p.first>>p.second;return is;}
template<class T>vector<T> make_vector(size_t a){return vector<T>(a);}
template<class T, class... Ts>auto make_vector(size_t a, Ts... ts){return vector<decltype(make_vector<T>(ts...))>(a, make_vector<T>(ts...));}
const int MOD = 1e9 + 7;
const int INF = 2e18;

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 {
    vector< T > _fact, _rfact, _inv;

    Combination(int sz) : _fact(sz + 1), _rfact(sz + 1), _inv(sz + 1) {
        _fact[0] = _rfact[sz] = _inv[0] = 1;
        for(int i = 1; i <= sz; i++) _fact[i] = _fact[i - 1] * i;
        _rfact[sz] /= _fact[sz];
        for(int i = sz - 1; i >= 0; i--) _rfact[i] = _rfact[i + 1] * (i + 1);
        for(int i = 1; i <= sz; i++) _inv[i] = _rfact[i] * _fact[i - 1];
    }

    inline T fact(int k) const { return _fact[k]; }

    inline T rfact(int k) const { return _rfact[k]; }

    inline T inv(int k) const { return _inv[k]; }

    T P(int n, int r) const {
        if(r < 0 || n < r) return 0;
        return fact(n) * rfact(n - r);
    }

    T C(int p, int q) const {
        if(q < 0 || p < q) return 0;
        return fact(p) * rfact(q) * rfact(p - q);
    }

    T H(int n, int r) const {
        if(n < 0 || r < 0) return (0);
        return r == 0 ? 1 : C(n + r - 1, r);
    }
};

signed main() {
    int N, M, K;
    cin >> N >> M >> K;
    vector<modint> beforeN(N + 1), beforeM(M + 1);
    {
        // before calc about N
        beforeN[1] = ((N - 1) * N) / 2;
        int left = 0, right = N - 1;
        for (int i = 2; i <= N; i++) {
            beforeN[i] = beforeN[i - 1];
            beforeN[i] += ++left;
            beforeN[i] -= right--;
        }
    }
    {
        // before calc about M
        beforeM[1] = ((M - 1) * M) / 2;
        int left = 0, right = M - 1;
        for (int i = 2; i <= M; i++) {
            beforeM[i] = beforeM[i - 1];
            beforeM[i] += ++left;
            beforeM[i] -= right--;
        }
    }
    auto comb = Combination<modint>(N * M + 5);
    modint ans = 0;
    modint base = comb.C(N * M - 1, K - 1) * (K - 1) / (N * M - 1);
    for (int i = 1; i <= N; i++) {
        for (int j = 1; j <= M; j++) {
            {
                // about N
                ans += beforeN[i] * M * base;
            }
            {
                // about M
                ans += beforeM[j] * N * base;
            }
        }
    }
    cout << ans / 2 << endl;
}


Measured memory_bytes: 6528