#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef long double ld;
typedef pair<ll,ll> P;
typedef pair<int,int> Pi;
#define rep(i, n) for (ll i = 0; i < n; i++)
#define FOR(i, a, b) for (ll i = a; i < b; i++)
#define fi first
#define se second
#define PI (acos(-1))

template<class T>
inline bool chmax(T &a, T b) {
    if(a < b) {
        a = b;
        return true;
    }
    return false;
}
template<class T>
inline bool chmin(T &a, T b) {
    if(a > b) {
        a = b;
        return true;
    }
    return false;
}
template<typename T> ostream& operator<<(ostream& s,const complex<T>& d) {return s<<"("<<d.real()<<", "<<d.imag()<< ")";}
template<typename T1, typename T2> ostream& operator<<(ostream& s,const pair<T1,T2>& d) {return s<<"("<<d.first<<", "<<d.second<<")";}
template<typename T> ostream& operator<<(ostream& s, const vector<T>& d){
	int len=d.size();
	rep(i,len){
		s<<d[i];if(i<len-1) s<<" ";
	}
	return s;
}
template<typename T> ostream& operator<<(ostream& s,const vector<vector<T>>& d){
	int len=d.size();
	rep(i,len){
		s<<d[i]<<endl;
	}
	return s;
}
template<typename T> ostream& operator<<(ostream& s,const set<T>& v){
	s<<"{ ";
	for(auto itr=v.begin();itr!=v.end();++itr) {
		if (itr!=v.begin()) {s<< ", ";}
		s<<(*itr);
	}
	s<<" }";
	return s;
}
template<typename T1, typename T2> ostream& operator<<(ostream& s,const map<T1,T2>& m){
	s<<"{"<<endl;
	for(auto itr=m.begin();itr!=m.end();++itr){
		s<<" "<<(*itr).first<<" : "<<(*itr).second<<endl;
	}
	s<<"}"<<endl;
	return s;
}

const ll mod=1e9+7;
const ll inf=1e15;
const int INF=1e9;

struct mint {
    ll x;
    mint(ll x=0):x((x%mod+mod)%mod){}
    mint& operator+=(const mint a) {
        if ((x += a.x) >= mod) x -= mod;
        return *this;
    }
    mint& operator-=(const mint a) {
        if ((x += mod-a.x) >= mod) x -= mod;
        return *this;
    }
    mint& operator*=(const mint a) {
        (x *= a.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(ll 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;
    }
};

struct combination {
  vector<mint> fact, ifact;
  combination(int n):fact(n+1),ifact(n+1) {
    assert(n < mod);
    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];
  }
};

int main(){
	cin.tie(0);
	ios::sync_with_stdio(false);
	mint n,m,k;
	cin>>n.x>>m.x>>k.x;
	combination comb(200010);
	mint ans=0;
	rep(i,n.x){
		mint now=i;
		ans+=now*(n-now)*m*m*comb(n.x*m.x-2,k.x-2);
	}
	rep(i,m.x){
		mint now=i;
		ans+=now*(m-now)*n*n*comb(n.x*m.x-2,k.x-2);
	}
	cout<<ans.x<<endl;
}

Measured memory_bytes: 3328