Problem p03039 (C++)

Buggy submission (status: Time Limit Exceeded):
#include <bits/stdc++.h>
const int INF = 1e9;
const int MOD = 1e9 + 7;
const long long LINF = 1e18;
#define dump(x) cout << 'x' << ' = ' << (x) << ` `;
#define FOR(i, a, b) for (ll i = (a); i < (b); ++i)
#define rep(i, n) for (ll i = 0; i < (n); ++i)
#define REPR(i, n) for (ll i = n; i >= 0; i--)
#define FOREACH(x, a) for (auto &(x) : (a))
typedef long long ll;
using namespace std;
typedef pair<ll, ll> P;

template <typename T> void print(const vector<T> &x) {
  int n = x.size();
  rep(i, n) {
    cout << x[i];
    if (i != n - 1)
      cout << " ";
    else
      cout << endl;
  }
}

template <typename T> void print(const vector<vector<T>> &x) {
  int n = x.size();
  rep(i, n) {
    rep(j, x[i].size()) { cout << x[i][j] << " "; }
    cout << endl;
  }
}

template <typename T> void print(const vector<T> &x, int n) {
  rep(i, n) {
    cout << x[i];
    if (i != n - 1)
      cout << " ";
    else
      cout << endl;
  }
}

template <typename T> void print(const vector<vector<T>> &x, int n, int m) {
  rep(i, n) {
    rep(j, m) { cout << x[i][j] << " "; }
    cout << endl;
  }
}

template <class T> inline bool chmax(T &a, T b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
}
template <class T> inline bool chmin(T &a, T b) {
  if (a > b) {
    a = b;
    return 1;
  }
  return 0;
}

void input_init() {
  cin.tie(0);
  ios::sync_with_stdio(false);
}

template <int mod> struct ModInt {
  int x;

  ModInt() : x(0) {}

  ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}

  ModInt &operator+=(const ModInt &p) {
    if ((x += p.x) >= mod)
      x -= mod;
    return *this;
  }

  ModInt &operator-=(const ModInt &p) {
    if ((x += mod - p.x) >= mod)
      x -= mod;
    return *this;
  }

  ModInt &operator*=(const ModInt &p) {
    x = (int)(1LL * x * p.x % mod);
    return *this;
  }

  ModInt &operator/=(const ModInt &p) {
    *this *= p.inverse();
    return *this;
  }

  ModInt operator-() const { return ModInt(-x); }

  ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; }

  ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; }

  ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; }

  ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; }

  bool operator==(const ModInt &p) const { return x == p.x; }

  bool operator!=(const ModInt &p) const { return x != p.x; }

  ModInt inverse() const {
    int a = x, b = mod, u = 1, v = 0, t;
    while (b > 0) {
      t = a / b;
      swap(a -= t * b, b);
      swap(u -= t * v, v);
    }
    return ModInt(u);
  }

  ModInt pow(int64_t n) const {
    ModInt ret(1), mul(x);
    while (n > 0) {
      if (n & 1)
        ret *= mul;
      mul *= mul;
      n >>= 1;
    }
    return ret;
  }

  friend ostream &operator<<(ostream &os, const ModInt &p) { return os << p.x; }

  friend istream &operator>>(istream &is, ModInt &a) {
    int64_t t;
    is >> t;
    a = ModInt<mod>(t);
    return (is);
  }

  static int get_mod() { return mod; }
};

using modint = ModInt<MOD>;

class combM {
private:
  vector<ll> fac;  // n!(mod M)
  vector<ll> ifac; // k!^{M-2} (mod M)
public:
  ll mpow(ll x, ll n);
  combM();
  ll com(ll a, ll b);
};

// x^n(mod M)
ll combM::mpow(ll x, ll n) {
  ll ans = 1ll;
  while (n != 0) {
    if (n & 1)
      ans = ans * x % MOD;
    x = x * x % MOD;
    n = n >> 1;
  }
  return ans;
}

// aCb をmod計算
ll combM::com(ll a, ll b) {
  if (a == 0 && b == 0)
    return 1;
  if (a < b || a < 0)
    return 0;
  ll tmp = ifac[a - b] * ifac[b] % MOD;
  return tmp * fac[a] % MOD;
}

combM::combM() {
  fac.resize(500001);
  ifac.resize(500001);
  fac[0] = 1;
  ifac[0] = 1;
  for (ll i = 0; i < 500000; ++i) {
    fac[i + 1] = fac[i] * (i + 1) % MOD;
    ifac[i + 1] = ifac[i] * mpow(i + 1, MOD - 2) % MOD;
  }
}

ll mpow(ll x, ll n) {
  ll ans = 1ll;
  while (n != 0) {
    if (n & 1)
      ans = ans * x % MOD;
    x = x * x % MOD;
    n = n >> 1;
  }
  return ans;
}

int main(int argc, char const *argv[]) {
  ll n, m, k;
  cin >> n >> m >> k;
  modint N = n, M = m;
  combM C;
  modint x = 0, y = 0;
  for (int i = 0; i < m; ++i) {
    for (int j = i; j < m; ++j) {
      modint A = j - i;
      x += A * N * N * (C.com(n * m - 2, k - 2));
    }
  }
  for (int i = 0; i < n; ++i) {
    for (int j = i; j < n; ++j) {
      modint A = j - i;
      y += A * M * M * (C.com(n * m - 2, k - 2));
    }
  }

  cout << x + y << '\n';
  return 0;
}

Fixed submission:
#include <bits/stdc++.h>
const int INF = 1e9;
const int MOD = 1e9 + 7;
const long long LINF = 1e18;
#define dump(x) cout << 'x' << ' = ' << (x) << ` `;
#define FOR(i, a, b) for (ll i = (a); i < (b); ++i)
#define rep(i, n) for (ll i = 0; i < (n); ++i)
#define REPR(i, n) for (ll i = n; i >= 0; i--)
#define FOREACH(x, a) for (auto &(x) : (a))
typedef long long ll;
using namespace std;
typedef pair<ll, ll> P;

template <typename T> void print(const vector<T> &x) {
  int n = x.size();
  rep(i, n) {
    cout << x[i];
    if (i != n - 1)
      cout << " ";
    else
      cout << endl;
  }
}

template <typename T> void print(const vector<vector<T>> &x) {
  int n = x.size();
  rep(i, n) {
    rep(j, x[i].size()) { cout << x[i][j] << " "; }
    cout << endl;
  }
}

template <typename T> void print(const vector<T> &x, int n) {
  rep(i, n) {
    cout << x[i];
    if (i != n - 1)
      cout << " ";
    else
      cout << endl;
  }
}

template <typename T> void print(const vector<vector<T>> &x, int n, int m) {
  rep(i, n) {
    rep(j, m) { cout << x[i][j] << " "; }
    cout << endl;
  }
}

template <class T> inline bool chmax(T &a, T b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
}
template <class T> inline bool chmin(T &a, T b) {
  if (a > b) {
    a = b;
    return 1;
  }
  return 0;
}

void input_init() {
  cin.tie(0);
  ios::sync_with_stdio(false);
}

template <int mod> struct ModInt {
  int x;

  ModInt() : x(0) {}

  ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}

  ModInt &operator+=(const ModInt &p) {
    if ((x += p.x) >= mod)
      x -= mod;
    return *this;
  }

  ModInt &operator-=(const ModInt &p) {
    if ((x += mod - p.x) >= mod)
      x -= mod;
    return *this;
  }

  ModInt &operator*=(const ModInt &p) {
    x = (int)(1LL * x * p.x % mod);
    return *this;
  }

  ModInt &operator/=(const ModInt &p) {
    *this *= p.inverse();
    return *this;
  }

  ModInt operator-() const { return ModInt(-x); }

  ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; }

  ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; }

  ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; }

  ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; }

  bool operator==(const ModInt &p) const { return x == p.x; }

  bool operator!=(const ModInt &p) const { return x != p.x; }

  ModInt inverse() const {
    int a = x, b = mod, u = 1, v = 0, t;
    while (b > 0) {
      t = a / b;
      swap(a -= t * b, b);
      swap(u -= t * v, v);
    }
    return ModInt(u);
  }

  ModInt pow(int64_t n) const {
    ModInt ret(1), mul(x);
    while (n > 0) {
      if (n & 1)
        ret *= mul;
      mul *= mul;
      n >>= 1;
    }
    return ret;
  }

  friend ostream &operator<<(ostream &os, const ModInt &p) { return os << p.x; }

  friend istream &operator>>(istream &is, ModInt &a) {
    int64_t t;
    is >> t;
    a = ModInt<mod>(t);
    return (is);
  }

  static int get_mod() { return mod; }
};

using modint = ModInt<MOD>;

class combM {
private:
  vector<ll> fac;  // n!(mod M)
  vector<ll> ifac; // k!^{M-2} (mod M)
public:
  ll mpow(ll x, ll n);
  combM();
  ll com(ll a, ll b);
};

// x^n(mod M)
ll combM::mpow(ll x, ll n) {
  ll ans = 1ll;
  while (n != 0) {
    if (n & 1)
      ans = ans * x % MOD;
    x = x * x % MOD;
    n = n >> 1;
  }
  return ans;
}

// aCb をmod計算
ll combM::com(ll a, ll b) {
  if (a == 0 && b == 0)
    return 1;
  if (a < b || a < 0)
    return 0;
  ll tmp = ifac[a - b] * ifac[b] % MOD;
  return tmp * fac[a] % MOD;
}

combM::combM() {
  fac.resize(500001);
  ifac.resize(500001);
  fac[0] = 1;
  ifac[0] = 1;
  for (ll i = 0; i < 500000; ++i) {
    fac[i + 1] = fac[i] * (i + 1) % MOD;
    ifac[i + 1] = ifac[i] * mpow(i + 1, MOD - 2) % MOD;
  }
}

ll mpow(ll x, ll n) {
  ll ans = 1ll;
  while (n != 0) {
    if (n & 1)
      ans = ans * x % MOD;
    x = x * x % MOD;
    n = n >> 1;
  }
  return ans;
}

int main(int argc, char const *argv[]) {
  ll n, m, k;
  cin >> n >> m >> k;
  modint N = n, M = m;
  combM C;
  modint x = 0, y = 0;
  map<int, int> mpn, mpm;

  for (int i = 1; i < n; ++i) {
    mpn[i] = n - i;
  }
  for (int i = 1; i < m; ++i) {
    mpm[i] = m - i;
  }

  for (auto &&e : mpm) {
    modint A = e.first;
    modint B = e.second;
    x += A * N * N * (C.com(n * m - 2, k - 2)) * B;
  }

  for (auto &&e : mpn) {
    modint A = e.first;
    modint B = e.second;
    y += A * M * M * (C.com(n * m - 2, k - 2)) * B;
  }

  cout << x + y << '\n';
  return 0;
}