Language: C++

//インクルード(アルファベット順)
#include<algorithm>//sort,二分探索,など
#include<bitset>//固定長bit集合
#include<cmath>//pow,logなど
#include<complex>//複素数
#include<deque>//両端アクセスのキュー
#include<functional>//sortのgreater
#include<iomanip>//setprecision(浮動小数点の出力の誤差)
#include<iostream>//入出力
#include<iterator>//集合演算(積集合,和集合,差集合など)
#include<map>//map(辞書)
#include<numeric>//iota(整数列の生成),gcdとlcm(c++17)
#include<queue>//キュー
#include<set>//集合
#include<stack>//スタック
#include<string>//文字列
#include<unordered_map>//イテレータあるけど順序保持しないmap
#include<unordered_set>//イテレータあるけど順序保持しないset
#include<utility>//pair
#include<vector>//可変長配列

using namespace std;
typedef long long ll;

//マクロ
//forループ関係
//引数は、(ループ内変数,動く範囲)か(ループ内変数,始めの数,終わりの数)、のどちらか
//Dがついてないものはループ変数は1ずつインクリメントされ、Dがついてるものはループ変数は1ずつデクリメントされる
#define REP(i,n) for(ll i=0;i<(ll)(n);i++)
#define REPD(i,n) for(ll i=n-1;i>=0;i--)
#define FOR(i,a,b) for(ll i=a;i<=(ll)(b);i++)
#define FORD(i,a,b) for(ll i=a;i>=(ll)(b);i--)
//xにはvectorなどのコンテナ
#define ALL(x) (x).begin(),(x).end() //sortなどの引数を省略したい
#define SIZE(x) ((ll)(x).size()) //sizeをsize_tからllに直しておく
#define MAX(x) *max_element(ALL(x)) //最大値を求める
#define MIN(x) *min_element(ALL(x)) //最小値を求める
//定数
#define INF 1000000000000 //10^12:極めて大きい値,∞
#define MOD 1000000007 //10^9+7:合同式の法
#define MAXR 300000 //10^5:配列の最大のrange(素数列挙などで使用)
//略記
#define PB push_back //vectorヘの挿入
#define MP make_pair //pairのコンストラクタ
#define F first //pairの一つ目の要素
#define S second //pairの二つ目の要素

template<ll mod> class modint{
public:
    ll val=0;
    //コンストラクタ
    modint(ll x=0):val(x%mod){while(x<0)x+=mod;}
    //コピーコンストラクタ
    modint(const modint &r):val(r.val){}
    //算術演算子
    modint operator -(){return modint(-val);}//単項
    modint operator +(const modint &r){return modint(*this)+=r;}
    modint operator -(const modint &r){return modint(*this)-=r;}
    modint operator *(const modint &r){return modint(*this)*=r;}
    modint operator /(const modint &r){return modint(*this)/=r;}
    //代入演算子
    modint &operator +=(const modint &r){
        val+=r.val;
        if(val>=mod)val-=mod;
        return *this;
    }
    modint &operator -=(const modint &r){
        if(val<r.val)val+=mod;
        val-=r.val;
        return *this;
    }
    modint &operator *=(const modint &r){
        val=val*r.val%mod;
        return *this;
    }
    modint &operator /=(const modint &r){
        ll a=r.val,b=mod,u=1,v=0;
        while(b){
            ll t=a/b;
            a-=t*b;swap(a,b);
            u-=t*v;swap(u,v);
        }
        val=val*u%mod;
        if(val<0)val+=mod;
        return *this;
    }
    //等価比較演算子
    bool operator ==(const modint& r){return this->val==r.val;}
    bool operator <(const modint& r){return this->val<r.val;}
    bool operator !=(const modint& r){return this->val!=r.val;}
};

using mint = modint<MOD>;

//入出力ストリーム
istream &operator >>(istream &is,mint& x){//xにconst付けない
    ll t;is >> t;
    x=t;
    return (is);
}
ostream &operator <<(ostream &os,const mint& x){
    return os<<x.val;
}

//累乗
mint modpow(const mint &a,ll n){
    if(n==0)return 1;
    mint t=modpow(a,n/2);
    t=t*t;
    if(n&1)t=t*a;
    return t;
}

mint fac[MAXR+1],finv[MAXR+1],inv[MAXR+1];

//テーブルの作成
void COMinit() {
    fac[0]=fac[1]=1;
    finv[0]=finv[1]=1;
    inv[1]=1;
    FOR(i,2,MAXR){
        fac[i]=fac[i-1]*mint(i);
        inv[i]=0-inv[MOD%i]*mint(MOD/i);
        finv[i]=finv[i-1]*inv[i];
    }
}

// 二項係数の計算
mint COM(ll n,ll k){
    if(n<k)return 0;
    if(n<0 || k<0)return 0;
    return fac[n]*finv[k]*finv[n-k];
}

signed main(){
    //入力の高速化用のコード
    //ios::sync_with_stdio(false);
    //cin.tie(nullptr);
    COMinit();
    ll n,m,k;cin >> n >> m >> k;
    mint ans1=COM(n*m-2,k-2);
    //cout << COM(k,2) << COM(n*m,k) << COM(n,2) << endl;
    mint ans1_=0;
    FOR(i,1,n-1)ans1_+=(i*m*m*(n-i));
    //cout << ans1_ << endl;
    ans1*=ans1_;
    mint ans2=COM(n*m-2,k-2);
    //cout << ans2 << endl;
    mint ans2_=0;
    FOR(i,1,m-1)ans2_+=(i*n*n*(m-i));
    //cout << ans2_ << endl;
    ans2*=ans2_;
    cout << ans1+ans2 << endl;
}

Compiler output:
a.cc: In function 'void COMinit()':
a.cc:123:17: error: no match for 'operator-' (operand types are 'int' and 'modint<1000000007>')
  123 |         inv[i]=0-inv[MOD%i]*mint(MOD/i);
      |                ~^~~~~~~~~~~~~~~~~~~~~~~
      |                |           |
      |                int         modint<1000000007>
In file included from /usr/include/c++/14/bits/stl_algobase.h:67,
                 from /usr/include/c++/14/algorithm:60,
                 from a.cc:2:
/usr/include/c++/14/bits/stl_iterator.h:618:5: note: candidate: 'template<class _IteratorL, class _IteratorR> constexpr decltype ((__y.base() - __x.base())) std::operator-(const reverse_iterator<_Iterator>&, const reverse_iterator<_IteratorR>&)'
  618 |     operator-(const reverse_iterator<_IteratorL>& __x,
      |     ^~~~~~~~
/usr/include/c++/14/bits/stl_iterator.h:618:5: note:   template argument deduction/substitution failed:
a.cc:123:39: note:   mismatched types 'const std::reverse_iterator<_Iterator>' and 'int'
  123 |         inv[i]=0-inv[MOD%i]*mint(MOD/i);
      |                                       ^
/usr/include/c++/14/bits/stl_iterator.h:1790:5: note: candidate: 'template<class _IteratorL, class _IteratorR> constexpr decltype ((__x.base() - __y.base())) std::operator-(const move_iterator<_IteratorL>&, const move_iterator<_IteratorR>&)'
 1790 |     operator-(const move_iterator<_IteratorL>& __x,
      |     ^~~~~~~~
/usr/include/c++/14/bits/stl_iterator.h:1790:5: note:   template argument deduction/substitution failed:
a.cc:123:39: note:   mismatched types 'const std::move_iterator<_IteratorL>' and 'int'
  123 |         inv[i]=0-inv[MOD%i]*mint(MOD/i);
      |                                       ^
In file included from a.cc:5:
/usr/include/c++/14/complex:370:5: note: candidate: 'template<class _Tp> std::complex<_Tp> std::operator-(const complex<_Tp>&, const complex<_Tp>&)'
  370 |     operator-(const complex<_Tp>& __x, const complex<_Tp>& __y)
      |     ^~~~~~~~
/usr/include/c++/14/complex:370:5: note:   template argument deduction/substitution failed:
a.cc:123:39: note:   mismatched types 'const std::complex<_Tp>' and 'int'
  123 |         inv[i]=0-inv[MOD%i]*mint(MOD/i);
      |                                       ^
/usr/include/c++/14/complex:379:5: note: candidate: 'template<class _Tp> std::complex<_Tp> std::operator-(const complex<_Tp>&, const _Tp&)'
  379 |     operator-(const complex<_Tp>& __x, const _Tp& __y)
      |     ^~~~~~~~
/usr/include/c++/14/complex:379:5: note:   template argument deduction/substitution failed:
a.cc:123:39: note:   mismatched types 'const std::complex<_Tp>' and 'int'
  123 |         inv[i]=0-inv[MOD%i]*mint(MOD/i);
      |                                       ^
/usr/include/c++/14/complex:388:5: note: candidate: 'template<class _Tp> std::complex<_Tp> std::operator-(const _Tp&, const complex<_Tp>&)'
  388 |     operator-(const _Tp& __x, const complex<_Tp>& __y)
      |     ^~~~~~~~
/usr/include/c++/14/complex:388:5: note:   template argument deduction/substitution failed:
a.cc:123:39: note:   'modint<1000000007>' is not derived from 'const std::complex<_Tp>'
  123 |         inv[i]=0-inv[MOD%i]*mint(MOD/i);
      |                                       ^
/usr/include/c++/14/complex:465:5: note: candidate: 'template<class _Tp> std::complex<_Tp> std::operator-(const complex<_Tp>&)'
  465 |     operator-(const complex<_Tp>& __x)
      |     ^~~~~~~~
/usr/include/c++/14/complex:465:5: note:   candidate expects 1 argument, 2 provided