#include <algorithm>
#include <iostream>
#include <limits>
#include <numeric>
#include <vector>

#define rep(i, x, n) for(int i = x; i < n; i++)
using namespace std;
const long long INF = 1LL << 60;
bool compare_by_b(pair<int, long long> a, pair<int, long long> b) {
    if(a.second != b.second) {
        return a.second > b.second;
    } else {
        return a.first > b.first;
    }
}
// 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(i, 0, N) {
        rep(j, 0, M) {
            mint tmp = mint(N - i) * mint(M - j) * mint(i + j);
            if(i != 0 && j != 0) {
                tmp *= 2;
            }
            sum += tmp;
        }
    }
    sum *= bc.com(N * M - 2, K - 2);
    cout << sum << endl;
}

Measured memory_bytes: 12160