//#include <bits/stdc++.h>

#include <iostream>
#include <algorithm>

#include <bitset>
#include <vector>
#include <set>
#include <map>
#include <unordered_set>
#include <unordered_map>
#include <stack>
#include <queue>
#include <deque>
#include <cstring>
#include <string>
#include <utility>
#include <array>
#include <complex>
#include <valarray>

#include <cassert>
#include <cmath>
#include <functional>
#include <iomanip>
#include <chrono>
#include <random>
#include <numeric>

#include<memory>


using namespace std;
#define int long long

typedef long long ll;
typedef unsigned long long ull;
//typedef unsigned __int128 HASH;
typedef pair<int,int> pii;
typedef pair<ll, ll> pll;
typedef pair<ull, ull> pullull;
typedef pair<ll,int> plli;
typedef pair<double,int> pdi;
typedef pair<long double, int> pdbi;
typedef pair<int,pii> pipii;
typedef pair<ll,pll> plpll;
typedef vector<int> vi;
typedef vector<ll> vll;
typedef vector<vi> vvi;
typedef vector<vvi> vvvi;
typedef vector<pii> vpii;
typedef vector<vector<int>> mat;

#define rep(i,n) for (int i=0;i<(n);i++)
#define rep2(i,a,b) for (int i=(a);i<(b);i++)
#define rrep(i,n) for (int i=(n);i>0;i--)
#define rrep2(i,a,b) for (int i=(a);i>b;i--)
#define pb push_back
#define fi first
#define se second
#define all(a) (a).begin(),(a).end()
#define rall(a) (a).rbegin(),(a).rend()

const ll hmod1 = 999999937;
const ll hmod2 = 1000000000 + 9;
const int INF = 1<<30;
const ll INFLL = 1LL<<62;
const long double EPS = 1e-12;
const ll mod = 1000000000 + 7;
//const ll mod = 998244353;
const int dx4[4] = {1, 0, -1, 0};
const int dy4[4] = {0, 1, 0, -1};
const int dx8[8] = {1, 1, 1, 0, 0, -1, -1, -1};
const int dy8[8] = {0, 1, -1, 1, -1, 0, 1, -1};
const long double pi = 3.141592653589793;

#define addm(X, Y) (X) = ((X) + ((Y) % mod) + mod) % mod
#define inside(y, x, h, w) (0 <= (y) && (y) < (h) && 0 <= (x) && (x) < (w)) ? true : false

//debug
#define DEBUG

#define DUMPOUT cout

#ifdef DEBUG
#define dump(...) DUMPOUT<<#__VA_ARGS__<<" :["<<__FUNCTION__<<":"<<__LINE__<<"]"<<endl; DUMPOUT<<"    "; dump_func(__VA_ARGS__)
#else
#define dump(...)
#endif

void dump_func() {DUMPOUT << endl;};

template <class Head, class... Tail> void dump_func(Head&& head, Tail&&... tail) {
    DUMPOUT << head;
    if (sizeof...(Tail) == 0) DUMPOUT << " ";
    else DUMPOUT << ", ";
    dump_func(std::move(tail)...);
}

//ostream
template<typename T> ostream& operator << (ostream& os, vector<T>& vec) {
    os << "["; for (int i = 0; i<vec.size(); i++) os << vec[i] << (i + 1 == vec.size() ? "" : ", "); os << "]";
    return os;
}

template<typename T, typename U> ostream& operator << (ostream& os, pair<T, U>& pair_var) {
    os << "(" << pair_var.first << ", " << pair_var.second << ")";
    return os;
}

template<typename T, typename U> ostream& operator << (ostream& os, map<T, U>& map_var) {
    os << "[";
    for (auto itr = map_var.begin(); itr != map_var.end(); itr++) {
        os << "(" << itr->first << ", " << itr->second << ")"; itr++;  if(itr != map_var.end()) os << ", "; itr--;
    }
    os << "]";
    return os;
}

template<typename T> ostream& operator << (ostream& os, set<T>& set_var) {
    os << "[";
    for (auto itr = set_var.begin(); itr != set_var.end(); itr++) {
        os << *itr; ++itr; if(itr != set_var.end()) os << ", "; itr--;
    }
    os << "]";
    return os;
}

int n, m, k;
pii dp[200000 + 5];

vector<long long> fact(200000 + 5, 1);

long long powmod(long long n, long long k){
    if (k == 0) return 1;
    else if (k % 2 == 0){
        long long tmp = powmod(n, k / 2);
        return tmp * tmp % mod;
    }
    else return powmod(n, k - 1) * n % mod;
}

long long inverse(long long n) {
    return powmod(n, mod - 2);
}

vector<long long> init_fact(long long n) {
    for (int i = 1; i <= n; i++) {
        fact[i] = fact[i - 1] * i % mod;
    }
    return fact;
}

long long nCk(long long n, long long k) {
    if (n - k < k) k = n - k;
    return fact[n] * (inverse(fact[n - k]) * inverse(fact[k]) % mod) % mod;
}

signed main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  cin >> n >> m >> k;
  dp[0].fi = 0;
  dp[0].se = 0;
  rep2(i, 1, n*m) dp[i].se = i;
  rep2(i, 0, n)rep2(j, 0, m) {
    if (i == 0 && j == 0) continue;
    if (i >= 1) {
      int plus = dp[m*(i-1)+j].se % mod;
      addm(dp[m*i+j].fi, dp[m*(i-1)+j].fi+plus);
      plus = (j * (j+1)) / 2 + 1 * (m-1-j) + (1+m-1-j) * (m-j-1)/2 + 1;
      addm(dp[m*i+j].fi, plus);
    }
    else {
      addm(dp[m*i+j].fi, dp[m*i+j-1].fi+j);
    }
  }
  int ans = 0;
  init_fact(n*m);
  rep2(i,0, n)rep2(j, 0, m) {
    if (i == 0 && j == 0) continue;
    addm(ans, dp[m*i+j].fi * nCk(n*m-2, k-2) % mod);
    //cerr << dp[m*i+j].fi << endl;
  }
  cout << ans << endl;
}


Measured memory_bytes: 6528