#include <bits/stdc++.h>

 using namespace std;

 #define INIT() ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);

 #define Rep(i,n) for (int i = 0; i < (n); ++i)

 #define For(i,s,t) for (int i = (s); i <= (t); ++i)

 #define rFor(i,t,s) for (int i = (t); i >= (s); --i)

 #define ForLL(i, s, t) for (LL i = LL(s); i <= LL(t); ++i)

 #define rForLL(i, t, s) for (LL i = LL(t); i >= LL(s); --i)

 #define foreach(i,c) for (__typeof(c.begin()) i = c.begin(); i != c.end(); ++i)

 #define rforeach(i,c) for (__typeof(c.rbegin()) i = c.rbegin(); i != c.rend(); ++i)

 #define pr(x) cout << #x << " = " << x << "  "

 #define prln(x) cout << #x << " = " << x << endl

 #define LOWBIT(x) ((x)&(-x))

 #define ALL(x) x.begin(),x.end()

 #define INS(x) inserter(x,x.begin())

 #define ms0(a) memset(a,0,sizeof(a))

 #define msI(a) memset(a,inf,sizeof(a))

 #define msM(a) memset(a,-1,sizeof(a))

 #define MP make_pair

 #define PB push_back

 #define ft first

 #define sd second

 template<typename T1, typename T2>

 istream &operator>>(istream &in, pair<T1, T2> &p) {

     in >> p.first >> p.second;

     return in;

 }

 template<typename T>

 istream &operator>>(istream &in, vector<T> &v) {

     for (auto &x: v)

         in >> x;

     return in;

 }

 template<typename T1, typename T2>

 ostream &operator<<(ostream &out, const std::pair<T1, T2> &p) {

     out << "[" << p.first << ", " << p.second << "]" << "\n";

     return out;

 }

 inline int gc(){

     static const int BUF = 1e7;

     static char buf[BUF], *bg = buf + BUF, *ed = bg;

     if(bg == ed) fread(bg = buf, , BUF, stdin);

     return *bg++;

 } 

 inline int ri(){

     int x = , f = , c = gc();

     for(; c<||c>; f = c=='-'?-:f, c=gc());

     for(; c>&&c<; x = x* + c - , c=gc());

     return x*f;

 }

 typedef long long LL;

 typedef unsigned long long uLL;

 typedef pair< double, double > PDD;

 typedef pair< int, int > PII;

 typedef pair< string, int > PSI;

 typedef set< int > SI;

 typedef vector< int > VI;

 typedef vector< PII > VPII;

 typedef map< int, int > MII;

 typedef pair< LL, LL > PLL;

 typedef vector< LL > VL;

 typedef vector< VL > VVL;

 const double EPS = 1e-;

 const LL inf = 0x7fffffff;

 const LL infLL = 0x7fffffffffffffffLL;

 const LL mod = 1e9 + ;

 const int maxN = 2e5 + ;

 const LL ONE = ;

 const LL evenBits = 0xaaaaaaaaaaaaaaaa;

 const LL oddBits = 0x5555555555555555;

 LL fac[maxN];

 void init_fact() {

     fac[] = ;

     For(i, , maxN - ) {

         fac[i] = (i * fac[i - ]) % mod;

     }

 }

 //ax + by = gcd(a, b) = d

 // 扩展欧几里德算法

 /**

  *    a*x + b*y = 1

  *    如果ab互质，有解

  *    x就是a关于b的逆元

  *    y就是b关于a的逆元

  *

  *    证明：

  *        a*x % b + b*y % b = 1 % b

  *        a*x % b = 1 % b

  *        a*x = 1 (mod b)

  */

 inline void ex_gcd(LL a, LL b, LL &x, LL &y, LL &d){

     if (!b) {d = a, x = , y = ;}

     else{

         ex_gcd(b, a % b, y, x, d);

         y -= x * (a / b);

     }

 }

 // 求a关于p的逆元，如果不存在，返回-1

 // a与p互质，逆元才存在

 inline LL inv_mod(LL a, LL p = mod){

     LL d, x, y;

     ex_gcd(a, p, x, y, d);

     return d ==  ? (x % p + p) % p : -;

 }

 inline LL comb_mod(LL m, LL n) {

     LL ret;

     if(m > n) swap(m, n);

     ret = (fac[n] * inv_mod(fac[m], mod)) % mod;

     ret = (ret * inv_mod(fac[n - m], mod)) % mod;

     return ret;

 }

 void add_mod(LL &a, LL b) {

     a = (a + b) % mod;

     if(a < ) a += mod;

 }

 int N, M, K;

 LL ans;

 int main(){

     INIT();

     init_fact();

     cin >> N >> M >> K;

     LL cnt = comb_mod(K - , N * M - );

     ForLL(d, , N - ) add_mod(ans, cnt * ((d * M * M * (N - d)) % mod));

     ForLL(d, , M - ) add_mod(ans, cnt * ((d * N * N * (M - d)) % mod));

     cout << ans << endl;

     return ;

 }