#include<iostream>
#include<algorithm>
#include<string>
#include<vector>
#include<cstdlib>
#include<queue>
#include<set>
#include<cstdio>

using namespace std;

#define ll long long
#define rep(i, n) for(int i = 0; i < n; i++)
#define P pair<int, int>

typedef vector<int> vec;
typedef vector<vec> mat;




// a^n mod を計算する
long int modpow(long int a, long int n, long int mod) {
    long int res = 1;
    while (n > 0) {
        if (n & 1) res = res * a % mod;
        a = (a * a) % mod;
        n >>= 1;
    }
    return res;
}

long int modcomb(long int a, long int b, long int mod){
    long int res = 1;
    for(long int i = a; i > a - b; i--){
        res *= i % mod;
        res %= mod;
    }
    res %= mod;
    for(long int i = 1; i <= b; i++){
        long int i_inv = modpow(i, mod - 2, mod);
        res *= i_inv % mod;
        res %= mod;
    }
    res %= mod;
    // cout << res << endl;
    return res;
}



int main(){
    ll n, m, k;
    cin >> n >> m >> k;
    ll mod = 1000000007;
    ll combx = modcomb(n * m - 2, k - 2, mod);
    ll comby = modcomb(n * m - 2, k - 2, mod);
    ll ans = 0;
    rep(i, n){
        ans += (((((i * (n - i)) % mod) * m) % mod * m) % mod) * combx;
        ans %= mod;
    }
    rep(i, m){
        ans += (((((i * (m - i)) % mod) * n) % mod * n) % mod) * comby;
        ans %= mod;
    }
    cout << ans << endl;
}
#include <bits/stdc++.h>
#define all(v) v.begin(), v.end()
#define rall(v) v.rbegin(), v.rend()
#define rep(i,n) for (int i=0;i<(int)(n);i++)
#define codefor int test;scanf("%d",&test);while(test--)
#define INT(...) int __VA_ARGS__;in(__VA_ARGS__)
#define LL(...) ll __VA_ARGS__;in(__VA_ARGS__)
#define yn(ans) if(ans)printf("Yes\n");else printf("No\n")
#define YN(ans) if(ans)printf("YES\n");else printf("NO\n")
#define vector1d(type,name,...) vector<type>name(__VA_ARGS__)
#define vector2d(type,name,h,...) vector<vector<type>>name(h,vector<type>(__VA_ARGS__))
#define umap unordered_map
#define uset unordered_set
using namespace std;
using ll = long long;
const int MOD=1000000007;
//入力系
void scan(int& a){scanf("%d",&a);}
void scan(long long& a){scanf("%lld",&a);}
template<class T> void scan(T& a){cin>>a;}
template<class T> void scan(vector<T>& vec){for(auto&& it:vec)scan(it);}
void in(){}
template <class Head, class... Tail> void in(Head& head, Tail&... tail){scan(head);in(tail...);}
//出力系
void print(const int& a){printf("%d",a);}
void print(const long long& a){printf("%lld",a);}
void print(const double& a){printf("%.15lf",a);}
template<class T> void print(const T& a){cout<<a;}
template<class T> void print(const vector<T>& vec){if(vec.empty())return;print(vec[0]);for(auto it=vec.begin();++it!= vec.end();){putchar(' ');print(*it);}}
void out(){putchar('\n');}
template<class T> void out(const T& t){print(t);putchar('\n');}
template <class Head, class... Tail> void out(const Head& head,const Tail&... tail){print(head);putchar(' ');out(tail...);}
//デバッグ系
template<class T> void dprint(const T& a){cerr<<a;}
template<class T> void dprint(const vector<T>& vec){if(vec.empty())return;cerr<<vec[0];for(auto it=vec.begin();++it!= vec.end();){cerr<<" "<<*it;}}
void debug(){cerr<<endl;}
template<class T> void debug(const T& t){dprint(t);cerr<<endl;}
template <class Head, class... Tail> void debug(const Head& head, const Tail&... tail){dprint(head);cerr<<" ";debug(tail...);}
ll intpow(ll a, ll b){ ll ans = 1; while(b){ if(b & 1) ans *= a; a *= a; b /= 2; } return ans; }
ll modpow(ll a, ll b, ll p){ ll ans = 1; while(b){ if(b & 1) (ans *= a) %= p; (a *= a) %= p; b /= 2; } return ans; }
ll updivide(ll a,ll b){if(a%b==0) return a/b;else return (a/b)+1;}

int main(){
    LL(n,m);
    ll ans=1,Msqrt=sqrt(m);
    for(ll i=1;i<=Msqrt;i++){
        if(m%i==0){
            if(i*n<=m)ans=max(ans,i);
            if((m/i)*n<=m)ans=max(ans,m/i);
        }
    }
    out(ans);
}