#include "bits/stdc++.h"
#define rep(i,b) for(ll i=0;i<b;i++)
#define ll long long
using namespace std;
/*--Input//////////////////////////////////////////////////*/
inline void IN(void){return;}
template <typename First, typename... Rest>
void IN(First& first, Rest&... rest){
    cin >> first;
    IN(rest...);
    return;
}
#define SS(T, ...)      T __VA_ARGS__; IN(__VA_ARGS__);
#define SV(type,c,n) vector<type> c(n);for(auto& i:c)cin >> i;
/*--Output/////////////////////////////////////////////////*/
#define Yes(n) cout << ((n) ? "Yes" : "No"  ) << endl
inline int p(void){cout << endl; return 0;}
template<class Head> int p(Head&& head){cout << head;p();return 0;} template<class Head,class... Tail> int p(Head&& head,Tail&&... tail){cout<<head<<" ";p(forward<Tail>(tail)...);return 0;}
struct ProconInit {
    static constexpr int IOS_PREC = 15;
    static constexpr bool AUTOFLUSH = false;

    ProconInit() {
        cin.tie(nullptr);
        ios::sync_with_stdio(false);
        cout << fixed << setprecision(IOS_PREC);
        if(AUTOFLUSH)
            cout << unitbuf;
    }
} PROCON_INIT;


#define vl vector<ll>
#define vvl vector<vector<ll>>
#define vvvl vector<vector<vector<ll>>>
#define debug(x) cerr<<#x<<" "<<x<<'\n';
#define all(x) (x).begin(),(x).end()
#define bit(n) (1LL<<(n))

template<class T>bool chmax(T &a, const T &b) { if (a<b) { a=b; return 1; } return 0; }
template<class T>bool chmin(T &a, const T &b) { if (b<a) { a=b; return 1; } return 0; }
bool cmp(pair<ll,ll> a, pair<ll,ll> b) { return a.second < b.second; }

const int MOD = 1000000007;

const int dx[4] = {1, 0, -1, 0};
const int dy[4] = {0, 1, 0, -1};


// 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];
    }
};

using mint = Fp<MOD>;
BiCoef<mint> bc;
int main() {
    SS(ll,N,M,K);
    bc.init(510000);
    mint sum = 0;
    rep(i,N)rep(j,M){
            mint tmp = (N - i) * (M - j) * (i + j);
            if (i != 0 && j != 0) tmp *= 2;
            sum += tmp;
    }
    p(sum * bc.com(N*M-2, K-2));
}

Measured memory_bytes: 12288