/*#include <iostream>
#include <cmath>
#include <vector>
#include <algorithm>
#include <array>
#include <vector>
#include <deque>
#include <set>
#include <map>
#include <string>
#include <stack>
#include <queue>
#include <unordered_map>
#include <unordered_set>
*/
 
#include <bits/stdc++.h>
using namespace std;
 
#define int long long
#define pb push_back
#define mp make_pair
#define F first
#define S second
#define FOR(i,a,b) for(int (i)=(a);(i)<(b);(i)++)
#define REP(i,n) FOR(i,0,n)
#define ALL(a) (a).begin(),(a).end()
#define RALL(a) (a).rbegin(),(a).rend()
#define SORT(c) sort((c).begin(),(c).end())
 
typedef long long ll;
const ll INF = LLONG_MAX / 8 - 100;
const ll mod = 1e9 + 7;
const int MAX_N = 2e5 + 5;
int dx[] = { -1LL,0,1LL,0 }, dy[] = { 0,1LL,0,-1LL };
vector<ll> prime;
 
ll inv[MAX_N], fac[MAX_N];
 
template <class T = ll> T in() { T x; cin >> x; return (x); }
inline ll GCD(ll a, ll b) { ll c; while (b != 0) { c = a % b; a = b; b = c; }return a; }
inline ll LCM(ll a, ll b) { return a * b / GCD(a, b); }
inline ll POW(ll a, ll b) { ll c = 1LL; while (b > 0) { if (b & 1LL) { c = a * c%mod; }a = a * a%mod; b >>= 1LL; }return c; }
inline void _nCr() { fac[0] = 1LL; for (int i = 1LL; i < MAX_N; i++) { fac[i] = fac[i - 1LL] * i%mod; }for (int i = 0; i < MAX_N; i++) { inv[i] = POW(fac[i], mod - 2); } }
inline ll nCr(ll n, ll r) { return (fac[n] * inv[r] % mod)*inv[n - r] % mod; }
inline void PRI(ll n) { bool a[n + 1LL]; for (int i = 0; i < n + 1LL; i++) { a[i] = 1LL; }for (int i = 2; i < n + 1LL; i++) { if (a[i]) { prime.pb(i); ll b = i; while (b <= n) { a[b] = 0; b += i; } } } }
 
typedef pair<int, pair<int, int>> edge;
 
class UnionFind {
public:
	vector<int> par;
	vector<int> color;
	UnionFind(int N) { par = vector<int>(N, -1LL); color = vector<int>(N,-1);}
	int find(int x);
	ll size(int x);
	bool unite(int x, int y);
	bool same(int x, int y);
};
 
 
 
class Kruskal {
private:
	UnionFind *uf;
	vector<edge> e;
public:
	vector<edge> mst;
	Kruskal(int N) { uf = new UnionFind(N); }
	void add(int x, int y, ll z);
	void run();
};
 
 
 
//----UnionFind-------------------------------
int UnionFind::find(int x) {
	if (par[x] < 0) return x;
	else return par[x] = find(par[x]);
}
 
ll UnionFind::size(int x) {
	return -par[find(x)];
}
 
bool UnionFind::unite(int x, int y) {
	x = find(x);
	y = find(y);
 	if (x == y) return true;
	//大きい方に小さい方をくっ付ける
	if (size(x) < size(y)) swap(x, y);
	par[x] += par[y];
	par[y] = x;
	if (color[x] != -1 && color[y] != -1 && color[x] != color[y]) return false;
	else color[x] = max(color[x],color[y]);
	return true;
}
 
bool UnionFind::same(int x, int y) {
	x = find(x);
	y = find(y);
	return x == y;
}
 
 
 
//----Kruskal-------------------------------
void Kruskal::add(int x, int y, ll z) {
	//x < y
	if (x > y) swap(x, y);
	e.push_back({ z,{x,y} });
}
 
void Kruskal::run() {
	sort(e.begin(), e.end());
	e.erase(unique(e.begin(), e.end()), e.end());
	for (auto x : e) {
		if (uf->same(x.second.first, x.second.second)) {
			continue;
		}
		else {
			mst.push_back(x);
			uf->unite(x.second.first, x.second.second);
		}
	}
}

class Warshall_Floyd {
public:
	vector<vector<int>> d;
	int nodecnt = -1;

	Warshall_Floyd(int n) {
		d = vector<vector<int>>(n,vector<int>(n,INF));
		nodecnt = n;
	}

	void add(int s,int e,int cost) {
		d[s][e] = cost;
	}

	bool wf() {
		for (int k = 0;k < nodecnt;k++) {
			for (int i = 0;i < nodecnt;i++) {
				for (int j = 0;j < nodecnt;j++) {
					//k経由でi->j
					d[i][j] = min(d[i][j],d[i][k] + d[k][j]);
				}
			}
		}
	}
};

signed main() {
	int n,m,k; cin >> n >> m >> k;
	int ans = 0;
	_nCr();
	REP (i,n) {
		int tmp = (n - i) * i; tmp %= mod;
		tmp *= m * m; tmp %= mod;
		tmp *= nCr(n*m-2,k-2) % mod; tmp %= mod;
		ans += tmp; ans %= mod;
	}
	REP (i,m) {
		int tmp = (m - i) * i; tmp %= mod;
		tmp *= n * n; tmp %= mod;
		tmp *= nCr(n*m-2,k-2) % mod; tmp %= mod;
		ans += tmp; ans %= mod;
	}
	cout << ans << endl;
}


Measured memory_bytes: 3328