#include <bits/stdc++.h>
#pragma GCC target("avx2")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
using namespace std;
/*----------------------------------ここからマクロ----------------------------------*/
#define all(a) (a).begin(),(a).end()
#define rall(a) (a).rbegin(),(a).rend()
#define vecin(a) rep(i,a.size())cin >> a[i]
#define overload4(_1,_2,_3,_4,name,...) name
#define rep1(n) for(int i=0;i<(int)n;++i)
#define rep2(i,n) for(int i=0;i<(int)n;++i)
#define rep3(i,a,b) for(int i=(int)a;i<(int)b;++i)
#define rep4(i,a,b,c) for(int i=(int)a;i<(int)b;i+=(int)c)
#define rep(...) overload4(__VA_ARGS__,rep4,rep3,rep2,rep1)(__VA_ARGS__)
#ifdef _DEBUG
#define debug1(a) cerr << #a << ": " << a << "\n"
#define debug2(a,b) cerr << #a << ": " << a << ", " << #b << ": " << b << "\n"
#define debug3(a,b,c) cerr << #a << ": " << a << ", " << #b << ": " << b << ", " << #c << ": " << c << "\n"
#define debug4(a,b,c,d) cerr << #a << ": " << a << ", " << #b << ": " << b << ", " << #c << ": " << c << ", " << #d << ": " << d << "\n"
#define debug(...) overload4(__VA_ARGS__,debug4,debug3,debug2,debug1)(__VA_ARGS__)
#define vecout(a) cerr << #a << ": [";rep(i,a.size()){cout << a[i];cout << (i == a.size() - 1 ? "":",");}cerr << "]\n"
#else
#define debug(...)
#define vecout(a)
#endif
#define mp make_pair
//struct doset{doset(int n){cout << fixed << setprecision(n);cerr << fixed << setprecision(n);}};
//struct myset{myset(){ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);}};
void myset(){ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);}
void doset(int n){cout << fixed << setprecision(n);}
using ll = long long;
using ld = long double;
using dou = double;
const int inf = 1 << 30;
const ll INF = 1LL << 60;
const ld pi = 3.14159265358;
const ll mod1 = 1000000007LL;
const ll mod2 = 998244353LL;
typedef pair<ll,ll> P;
template<class T, class U> inline bool chmin(T& a, const U& b){ if(a > b){ a = b; return 1; } return 0; }
template<class T, class U> inline bool chmax(T& a, const U& b){ if(a < b){ a = b; return 1; } return 0; }
template<class T, class U> inline bool change(T& a,U& b){if(a > b){swap(a,b);return 1;}return 0;}
//nのm乗をMODで割ったあまりO(logm)
ll modpow(ll n,ll m,ll MOD){
    if(m == 0)return 1;
    if(m < 0)return -1;
    ll res = 1;
    while(m){
        if(m & 1)res = (res * n) % MOD;
        m >>= 1;
        n *= n;
        n %= MOD;
    }
    return res;
}

ll mypow(ll n,ll m){
    if(m == 0)return 1;
    if(m < 0)return -1;
    ll res = 1;
    while(m){
        if(m & 1)res = (res * n);
        m >>= 1;
        n *= n;
    }
    return res;
}

//素数判定O(sqrt(N))
template<class T>
inline bool isp(T n){
    bool res = true;
    if(n == 1 || n == 0)return false;
    else{
        for(ll i = 2;i * i <= n;i++){
            if(n % i == 0){
                res = false;
                break;
            }
        }
        return res;
    }
}

template<class T = int>
T in(){T x;cin >> x;return x;}

inline bool Yes(bool b){cout << (b ? "Yes\n":"No\n");return b;}
inline bool YES(bool b){cout << (b ? "YES\n":"NO\n");return b;}

/*----------------------------------マクロここまで----------------------------------*/

ll nCk(ll n,ll k){
    ll up = 1,si = 1;
    for(ll i = n;i >= n - k + 1;i--){
        up = up * (i % mod1) % mod1;
    }
    for(ll i = 1;i <= k;i++){
        si = si * i % mod1;
    }
    return up * modpow(si,mod1 - 2,mod1) % mod1;
}

int main(){
    myset();
    ll N,M,K;
    cin >> N >> M >> K;
    ll n_sa = 0,m_sa = 0;
    ll now = N * (N - 1) / 2;
    rep(i,N){
        n_sa = (n_sa + now) % mod1;
        now = now - N + i * 2 + 2;
    }
    now = M * (M - 1) / 2;
    rep(i,M){
        m_sa = (m_sa + now) % mod1;
        now = now - M + i * 2 + 2;
    }
    ll wa = (M * M % mod1 * n_sa % mod1 + N * N % mod1 * m_sa % mod1) % mod1;
    wa = wa * modpow(2,mod1 - 2,mod1) % mod1;
    debug(wa);
    ll ret = nCk(N * M - 2,K - 2);
    debug(ret);
    cout << ret * wa % mod1 << "\n";
}

Measured memory_bytes: 3572