#include<bits/stdc++.h>
using namespace std;
#define MD 1000000007
void *wmem;
template<class T> void walloc1d(T **arr, int x, void **mem = &wmem){
  (*arr)=(T*)(*mem);
  (*mem)=((*arr)+x);
}
struct mint{
  static unsigned R, RR, Rinv, W, md, mdninv;
  unsigned val;
  mint(){
  }
  mint(int a){
    val = mulR(a);
  }
  mint(unsigned a){
    val = mulR(a);
  }
  mint(long long a){
    val = mulR(a);
  }
  mint(unsigned long long a){
    val = mulR(a);
  }
  int get_inv(long long a, int md){
    long long e, s=md, t=a, u=1, v=0;
    while(s){
      e=t/s;
      t-=e*s;
      u-=e*v;
      swap(t,s);
      swap(u,v);
    }
    if(u<0){
      u+=md;
    }
    return u;
  }
  void setmod(unsigned m){
    int i;
    unsigned t;
    W = 32;
    md = m;
    R = (1ULL << W) % md;
    RR = (unsigned long long)R*R % md;
    switch(m){
      case 104857601:
      Rinv = 2560000;
      mdninv = 104857599;
      break;
      case 998244353:
      Rinv = 232013824;
      mdninv = 998244351;
      break;
      case 1000000007:
      Rinv = 518424770;
      mdninv = 2226617417U;
      break;
      case 1000000009:
      Rinv = 171601999;
      mdninv = 737024967;
      break;
      case 1004535809:
      Rinv = 234947584;
      mdninv = 1004535807;
      break;
      case 1007681537:
      Rinv = 236421376;
      mdninv = 1007681535;
      break;
      case 1012924417:
      Rinv = 238887936;
      mdninv = 1012924415;
      break;
      case 1045430273:
      Rinv = 254466304;
      mdninv = 1045430271;
      break;
      case 1051721729:
      Rinv = 257538304;
      mdninv = 1051721727;
      break;
      default:
      Rinv = get_inv(R, md);
      mdninv = 0;
      t = 0;
      for(i=0;i<(int)W;i++){
        if(t%2==0){
          t+=md;
          mdninv |= (1U<<i);
        }
        t /= 2;
      }
    }
  }
  unsigned mulR(unsigned a){
    return (unsigned long long)a*R%md;
  }
  unsigned mulR(int a){
    if(a < 0){
      a = a%md+md;
    }
    return mulR((unsigned)a);
  }
  unsigned mulR(unsigned long long a){
    return mulR((unsigned)(a%md));
  }
  unsigned mulR(long long a){
    a %= md;
    if(a < 0){
      a += md;
    }
    return mulR((unsigned)a);
  }
  unsigned reduce(unsigned T){
    unsigned m=T * mdninv, t=(unsigned)((T + (unsigned long long)m*md) >> W);
    if(t >= md){
      t -= md;
    }
    return t;
  }
  unsigned reduce(unsigned long long T){
    unsigned m=(unsigned)T * mdninv, t=(unsigned)((T + (unsigned long long)m*md) >> W);
    if(t >= md){
      t -= md;
    }
    return t;
  }
  unsigned get(){
    return reduce(val);
  }
  mint &operator+=(mint a){
    val += a.val;
    if(val >= md){
      val -= md;
    }
    return *this;
  }
  mint &operator-=(mint a){
    if(val < a.val){
      val = val + md - a.val;
    }
    else{
      val -= a.val;
    }
    return *this;
  }
  mint &operator*=(mint a){
    val = reduce((unsigned long long)val*a.val);
    return *this;
  }
  mint &operator/=(mint a){
    return *this *= a.inverse();
  }
  mint operator+(mint a){
    return mint(*this)+=a;
  }
  mint operator-(mint a){
    return mint(*this)-=a;
  }
  mint operator*(mint a){
    return mint(*this)*=a;
  }
  mint operator/(mint a){
    return mint(*this)/=a;
  }
  mint operator+(int a){
    return mint(*this)+=mint(a);
  }
  mint operator-(int a){
    return mint(*this)-=mint(a);
  }
  mint operator*(int a){
    return mint(*this)*=mint(a);
  }
  mint operator/(int a){
    return mint(*this)/=mint(a);
  }
  mint operator+(long long a){
    return mint(*this)+=mint(a);
  }
  mint operator-(long long a){
    return mint(*this)-=mint(a);
  }
  mint operator*(long long a){
    return mint(*this)*=mint(a);
  }
  mint operator/(long long a){
    return mint(*this)/=mint(a);
  }
  mint operator-(void){
    mint res;
    if(val){
      res.val=md-val;
    }
    else{
      res.val=0;
    }
    return res;
  }
  operator bool(void){
    return val!=0;
  }
  operator int(void){
    return get();
  }
  operator long long(void){
    return get();
  }

  mint inverse(){
    int a = val, b = md, u = 1, v = 0, t;
    mint res;
    while(b){
      t = a / b;
      a -= t * b; swap(a, b);
      u -= t * v; swap(u, v);
    }
    if(u < 0) u += md;
    res.val = (unsigned long long)u*RR % md;
    return res;
  }

  mint pw(unsigned long long b){
    mint a(*this), res;
    res.val = R;
    while(b){
      if(b&1) res *= a;
      b >>= 1;
      a *= a;
    }
    return res;
  }

  bool operator==(int a){return mulR(a)==val;}
  bool operator!=(int a){return mulR(a)!=val;}
};
unsigned mint::md, mint::W, mint::R, mint::Rinv, mint::mdninv, mint::RR;
mint operator+(int a, mint b){return mint(a)+=b;
}
mint operator-(int a, mint b){
  return mint(a)-=b;
}
mint operator*(int a, mint b){
  return mint(a)*=b;
}
mint operator/(int a, mint b){
  return mint(a)/=b;
}
mint operator+(long long a, mint b){
  return mint(a)+=b;
}
mint operator-(long long a, mint b){
  return mint(a)-=b;
}
mint operator*(long long a, mint b){
  return mint(a)*=b;
}
mint operator/(long long a, mint b){
  return mint(a)/=b;
}
inline void rd(int &x){
  int k, m=0;
  x=0;
  for(;;){
    k = getchar_unlocked();
    if(k=='-'){
      m=1;
      break;
    }
    if('0'<=k&&k<='9'){
      x=k-'0';
      break;
    }
  }
  for(;;){
    k = getchar_unlocked();
    if(k<'0'||k>'9'){
      break;
    }
    x=x*10+k-'0';
  }
  if(m){
    x=-x;
  }
}
inline void wt_L(char a){
  putchar_unlocked(a);
}
inline void wt_L(int x){
  char f[10];
  int m=0, s=0;
  if(x<0){
    m=1;
    x=-x;
  }
  while(x){
    f[s++]=x%10;
    x/=10;
  }
  if(!s){
    f[s++]=0;
  }
  if(m){
    putchar_unlocked('-');
  }
  while(s--){
    putchar_unlocked(f[s]+'0');
  }
}
inline void wt_L(mint x){
  int i;
  i = (int)x;
  wt_L(i);
}
struct combination_mint{
  mint *fac, *ifac;
  void init(int n, void **mem = &wmem){
    int i;
    walloc1d(&fac, n, mem);
    walloc1d(&ifac, n, mem);
    fac[0] = 1;
    for(i=1;i<n;i++){
      fac[i] = fac[i-1] * i;
    }
    ifac[n-1] = 1 / fac[n-1];
    for(i=n-2;i>=0;i--){
      ifac[i] = ifac[i+1] * (i+1);
    }
  }
  mint C(int a, int b){
    if(b < 0 || b > a){
      return 0;
    }
    return fac[a]*ifac[b]*ifac[a-b];
  }
  mint P(int a, int b){
    if(b < 0 || b > a){
      return 0;
    }
    return fac[a]*ifac[a-b];
  }
  mint H(int a, int b){
    if(a==0 && b==0){
      return 1;
    }
    if(a<=0 || b<0){
      return 0;
    }
    return C(a+b-1, b);
  }
}
;
char memarr[96000000];
int N;
int M;
int K;
int main(){
  combination_mint comb;
  int i;
  mint a, b, res;
  wmem = memarr;
  {
    mint x;
    x.setmod(MD);
  }
  rd(N);
  rd(M);
  rd(K);
  comb.init(N*M+1);
  a = b = 0;
  for(i=1;i<N;i++){
    a += mint(i) * mint(N-i);
  }
  for(i=1;i<M;i++){
    b += mint(i) * mint(M-i);
  }
  res = (a * M * M + b * N * N) * comb.C(N*M-2, K-2);
  wt_L(res);
  wt_L('\n');
  return 0;
}
// cLay varsion 20190526-1

// --- original code ---
// int N, M, K;
// {
//   int i;
//   mint a, b, res;
//   combination_mint comb;
// 
//   rd(N,M,K);
// 
//   comb.init(N*M+1);
//   a = b = 0;
//   rep(i,1,N) a += mint(i) * mint(N-i);
//   rep(i,1,M) b += mint(i) * mint(M-i);
//   res = (a * M * M + b * N * N) * comb.C(N*M-2, K-2);
// 
//   wt(res);
// }


Measured memory_bytes: 1792