#include <bits/stdc++.h>

using namespace std;

typedef long long ll;
typedef pair<ll, ll> P;
typedef vector<ll> vl;
typedef vector<vl> vvl;
template<typename T> using v = vector<T>;
template<typename T> using pq = priority_queue<T>;
template<typename T> using minpq = priority_queue<T, vector<T>, greater<T>>;
template<typename T, typename K> using ump = unordered_map<T, K>;
const ll dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1};
const ll mod = 1000000007;
const ll inf = ll(1e9);
const ll e5 = ll(1e5);
const ll ll_inf = ll(1e9) * ll(1e9);

#define rep(i, n) for(ll i = 0; i < (ll)(n); i++)
#define repr(i, n) for(ll i = n - 1; i >= 0; i--)
#define repone(i, n) for(ll i = 1; i <= (ll)(n); i++)
#define each(i, mp) for(auto& i:mp)
#define eb emplace_back
#define F first
#define S second
#define all(obj) (obj).begin(), (obj).end()

template<class T>
void dump_debug(T list) {
#ifdef MY_DEBUG
    each(e, list) cout << e << " ";
    printf("\n");
#endif
}

inline ll inl() {
    ll x;
    cin >> x;
    return x;
}

inline string ins() {
    string x;
    cin >> x;
    return x;
}

/* ------------- ANSWER ------------- */
/* ---------------------------------- */
template<std::uint_fast64_t Modulus>
class modint {
    using u64 = std::uint_fast64_t;

public:
    u64 x;

    constexpr modint(const u64 x = 0) noexcept : x(x % Modulus) {}

    constexpr u64 &value() noexcept { return x; }

    constexpr const u64 &value() const noexcept { return x; }

    constexpr modint operator+(const modint rhs) const noexcept {
        return modint(*this) += rhs;
    }

    constexpr modint operator-(const modint rhs) const noexcept {
        return modint(*this) -= rhs;
    }

    constexpr modint operator*(const modint rhs) const noexcept {
        return modint(*this) *= rhs;
    }

    constexpr modint operator/(const modint rhs) const noexcept {
        return modint(*this) /= rhs;
    }

    constexpr modint &operator+=(const modint rhs) noexcept {
        x += rhs.x;
        if (x >= Modulus) {
            x -= Modulus;
        }
        return *this;
    }

    constexpr modint &operator-=(const modint rhs) noexcept {
        if (x < rhs.x) {
            x += Modulus;
        }
        x -= rhs.x;
        return *this;
    }

    constexpr modint &operator*=(const modint rhs) noexcept {
        x = x * rhs.x % Modulus;
        return *this;
    }

    constexpr modint &operator/=(modint rhs) noexcept {
        u64 exp = Modulus - 2;
        while (exp) {
            if (exp % 2) {
                *this *= rhs;
            }
            rhs *= rhs;
            exp /= 2;
        }
        return *this;
    }
};

const int MAX = 510000;
long long fac[MAX], finv[MAX], inv[MAX];

// テーブルを作る前処理
void COMinit() {
    fac[0] = fac[1] = 1;
    finv[0] = finv[1] = 1;
    inv[1] = 1;
    for (int i = 2; i < MAX; i++) {
        fac[i] = fac[i - 1] * i % mod;
        inv[i] = mod - inv[mod % i] * (mod / i) % mod;
        finv[i] = finv[i - 1] * inv[i] % mod;
    }
}

// 二項係数計算
ll COM(int n, int k) {
    if (n < k) return 0;
    if (n < 0 || k < 0) return 0;
    return fac[n] * (finv[k] * finv[n - k] % mod) % mod;
}

int main() {
#ifdef MY_DEBUG
    while (true) {
#endif

        ll n, m, k;
        cin >> n >> m >> k;
        COMinit();

        // sum for y
        modint<mod> sumy = 0;
        rep(i, m) sumy += i * (m - i) * n * n;
        sumy *= COM(n * m - 2, k - 2);

        // sum for x
        modint<mod> sumx = 0;
        rep(i, n) sumx += i * (n - i) * m * m;
        sumx *= COM(n * m - 2, k - 2);

        cout << (sumx + sumy).x << endl;

#ifdef MY_DEBUG
    }
#endif
    return 0;
}

Measured memory_bytes: 12160