#include <bits/stdc++.h>

#define rep(i, n) for(int i = 0; i<(n); i++)
#define chmax(x, y) x = max(x, y)
#define chmin(x, y) x = min(x, y)
using namespace std;
typedef long long ll;

// modint: mod 計算を int を扱うように扱える構造体
template<int MOD>
struct Fp {
    long long val;

    constexpr Fp(long long v = 0) noexcept : val(v % MOD) {
        if (val < 0) v += 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> &x) noexcept {
        return is >> x.val;
    }

    friend constexpr Fp<MOD> modpow(const Fp<MOD> &a, long long n) noexcept {
        if (n == 0) return 1;
        auto t = modpow(a, n / 2);
        t = t * t;
        if (n & 1) t = t * a;
        return t;
    }
};

// 二項係数ライブラリ
template<class T>
struct BiCoef {
    vector<T> fact_, inv_, finv_;

    constexpr BiCoef() {}

    constexpr BiCoef(int n) noexcept : fact_(n, 1), inv_(n, 1), finv_(n, 1) {
        init(n);
    }

    constexpr void init(int n) noexcept {
        fact_.assign(n, 1), inv_.assign(n, 1), finv_.assign(n, 1);
        int MOD = fact_[0].getmod();
        for (int i = 2; i < n; i++) {
            fact_[i] = fact_[i - 1] * i;
            inv_[i] = -inv_[MOD % i] * (MOD / i);
            finv_[i] = finv_[i - 1] * inv_[i];
        }
    }

    constexpr T com(int n, int k) const noexcept {
        if (n < k || n < 0 || k < 0) return 0;
        return fact_[n] * finv_[k] * finv_[n - k];
    }

    constexpr T fact(int n) const noexcept {
        if (n < 0) return 0;
        return fact_[n];
    }

    constexpr T inv(int n) const noexcept {
        if (n < 0) return 0;
        return inv_[n];
    }

    constexpr T finv(int n) const noexcept {
        if (n < 0) return 0;
        return finv_[n];
    }
};

const int MOD = 1000000007;
using mint = Fp<MOD>;
BiCoef<mint> bc;


int main() {
    long long N, M, K;
    cin >> N >> M >> K;
    bc.init(510000);

    mint sum = 0;
    rep(d, N) sum += mint(d) * mint(N - d) * mint(M) * mint(M); // |xi - xj| = d となる２駒の距離の合計 横方向にN-d個,縦方向にM*2パターンの置き方がある
    rep(d, M) sum += mint(d) * mint(M - d) * mint(N) * mint(N); // |yi - yj| = d となる２駒の距離の合計 縦方向にM-d個,横方向にN*2パターンの置き方がある
    cout << sum * bc.com(N * M - 2, K - 2) << endl; // ある2マスを固定したときの残りのN*M-2マスにK-2個の駒を置く通り数を掛ける
}

Measured memory_bytes: 12160