#include <bits/stdc++.h>

using namespace std;

#define DUMP(x) std::cerr << (#x) << " = " << (x) << "\n"
#define rep(i, n) for (int i = 0; i < (int)(n); ++i)
#define REP(i, k, n) for (int i = (k); i < (int)(n); ++i)
#define ALL(r) r.begin(), r.end()
#define YES puts("YES")
#define Yes puts("Yes")
#define NO puts("NO")
#define No puts("No")
#define IMP puts("IMPOSSIBLE")
#define Imp puts("Impossible")
#define imp puts("impossible")
#define M1 puts("-1")
#define pb push_back

template <typename T>
ostream &operator<<(ostream &os, vector<T> &v)
{
    os << "{";
    rep(i, v.size()) os << v[i] << (i == (int)v.size() - 1 ? "" : ", ");
    os << "}";
    return os;
}
template <typename T>
T dup(T x, T y)
{
    return (x + y - 1) / y;
};
template <typename A, size_t N, typename T>
inline void arrayFill(A (&array)[N], const T &val) { std::fill((T *)array, (T *)(array + N), val); }
struct in
{
    const size_t n = 0;
    in() = default;
    in(size_t n) : n(n){};
    template <typename T>
    operator T()
    {
        T ret;
        cin >> ret;
        return ret;
    }
    template <typename T>
    operator vector<T>()
    {
        assert(n != 0);
        vector<T> ret(n);
        for (auto &x : ret)
            cin >> x;
        return ret;
    }
};

using ll = int64_t;
using vint = vector<int32_t>;
using vvint = vector<vint>;
using vll = vector<ll>;
using vvll = vector<vll>;
using vstr = vector<string>;
using pint = pair<int32_t, int32_t>;
using pll = pair<ll, ll>;
using setint = set<int32_t>;
using setstr = set<string>;
using qint = queue<int32_t>;
using qpint = queue<pint>;

constexpr std::int32_t INF = 1001001001;
constexpr std::int64_t LINF = 1001001001001001001;

//                  9876543210
constexpr int mod = 1000000007;
class mint
{
private:
    std::int64_t m_x;

public:
    mint(std::int64_t m_x = 0) : m_x(m_x % mod) {}
    std::int64_t get() const { return m_x; }
    mint &operator+=(const mint a)
    {
        if ((m_x += a.m_x) >= mod)
            m_x -= mod;
        return *this;
    }
    mint &operator-=(const mint a)
    {
        if ((m_x += mod - a.m_x) >= mod)
            m_x -= mod;
        return *this;
    }
    mint &operator*=(const mint a)
    {
        (m_x *= a.m_x) %= mod;
        return *this;
    }
    mint operator+(const mint a) const
    {
        mint res(*this);
        return res += a;
    }
    mint operator-(const mint a) const
    {
        mint res(*this);
        return res -= a;
    }
    mint operator*(const mint a) const
    {
        mint res(*this);
        return res *= a;
    }

    mint pow(const std::int64_t t) const
    {
        if (!t)
            return 1;
        mint a = pow(t >> 1);
        a *= a;
        if (t & 1)
            a *= *this;
        return a;
    }
    // for prime mod
    mint inv() const
    {
        return pow(mod - 2);
    }
    mint &operator/=(const mint a)
    {
        return (*this) *= a.inv();
    }
    mint operator/(const mint a) const
    {
        mint res(*this);
        return res /= a;
    }
};
ostream &operator<<(ostream &os, const mint a)
{
    os << a.get();
    return os;
}

// require modint
struct combination
{
    vector<mint> fact, ifact;
    combination(int n) : fact(n + 1), ifact(n + 1)
    {
        fact[0] = 1;
        for (int i = 1; i <= n; ++i)
            fact[i] = fact[i - 1] * i;
        ifact[n] = fact[n].inv();
        for (int i = n; i >= 1; --i)
            ifact[i - 1] = ifact[i] * i;
    }
    mint operator()(int n, int k)
    {
        if (k < 0 || k > n)
            return 0;
        return fact[n] * ifact[k] * ifact[n - k];
    }
} comb(200005);

void Main()
{
    int n = in(), m = in(), k = in();

    mint ans = 0;
    REP(i, 1, m)
    {
        ans += comb(n * m - 2, k - 2) * n * n * (m - i) * i;
    }

    REP(i, 1, n)
    {
        ans += comb(n * m - 2, k - 2) * m * m * (n - i) * i;
    }
    cout << ans << endl;
}

int main()
{
    std::cin.tie(nullptr);
    std::ios_base::sync_with_stdio(false);
    std::cout << std::fixed << std::setprecision(15);
    Main();
    return 0;
}


Measured memory_bytes: 3328