Problem p04051 (C++)

Buggy submission (status: Runtime Error):
#include <bits/stdc++.h>
#define BIT(n) (1LL << (n))
#define BITF(n, i) (((n) >> i) & 1)
#define REP(i, n) for (int i = 0; i < n; i++)
#define REPB(i, n) for (int i = 0; i < BIT(n); i++)
#define REPS(i, x) for (int i = 1; i <= x; i++)
#define REPR(i, n) for (int i = n; i >= 0; i--)
#define REPZ(i, x) for (int i = 0; i <= x; i++)
#define FOR(i, m, n) for (int i = m; i < n; i++)
#define FORA(i, n) for (auto &&i : n)
#define FORS(i, m, n) for (int i = m; i <= n; i++)
using namespace std;
#define PRINTARR(x, y)                                                         \
  cerr << #x << "=\n";                                                         \
  for (auto itr = x; itr != y; itr++)                                          \
    cerr << *itr << " ";                                                       \
  cerr << endl;
#define PRINTARR2(x, i0, i1)                                                   \
  cerr << #x << "=\n";                                                         \
  for (int ii0 = 0; ii0 < i0; ii0++) {                                         \
    for (int ii1 = 0; ii1 < i1; ii1++)                                         \
      cerr << x[ii0][ii1] << " ";                                              \
    cerr << endl;                                                              \
  }
#define DUMPOUT cerr
// vector
template <typename T> istream &operator>>(istream &is, vector<T> &vec) {
  for (T &x : vec)
    is >> x;
  return is;
}
// pair
template <typename T, typename U>
ostream &operator<<(ostream &os, pair<T, U> &pair_var) {
  os << "(" << pair_var.first << ", " << pair_var.second << ")";
  return os;
}
// vector
template <typename T> ostream &operator<<(ostream &os, const vector<T> &vec) {
  os << "{";
  REP(i, (int)vec.size())
  os << vec[i] << (i + 1 == (int)vec.size() ? "" : ", ");
  os << "}";
  return os;
}
// map
template <typename T, typename U>
ostream &operator<<(ostream &os, map<T, U> &map_var) {
  os << "{";
  FORA(itr, map_var) {
    os << *itr;
    itr++;
    if (itr != map_var.end())
      os << ", ";
    itr--;
  }
  os << "}";
  return os;
}
// set
template <typename T> ostream &operator<<(ostream &os, set<T> &set_var) {
  os << "{";
  FORA(itr, set_var) {
    os << *itr;
    itr++;
    if (itr != set_var.end())
      os << ", ";
    itr--;
  }
  os << "}";
  return os;
}
void dump_func() { DUMPOUT << endl; }
template <class Head, class... Tail>
void dump_func(Head &&head, Tail &&...tail) {
  DUMPOUT << head;
  if (sizeof...(Tail) > 0)
    DUMPOUT << ", ";
  dump_func(std::move(tail)...);
}
#ifdef DEBUG_
#define DEB
#define DUMP(...)                                                              \
  DUMPOUT << "  " << string(#__VA_ARGS__) << ": "                              \
          << "[" << to_string(__LINE__) << ":" << __FUNCTION__ << "]" << endl  \
          << "    ",                                                           \
      dump_func(__VA_ARGS__)
#else
#define DEB if (false)
#define DUMP(...)
#endif

#define ALL(v) v.begin(), v.end()
#define fst first
#define snd second
#define mp make_pair
#define pb push_back
#define epb emplace_back
#define int long long
#define pint pair<int, int>
#define ld long double
using namespace std;
template <class T> bool chmax(T &a, const T &b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
}
template <class T> bool chmin(T &a, const T &b) {
  if (a > b) {
    a = b;
    return 1;
  }
  return 0;
}
template <class T> using vec = std::vector<T>;
template <class T> void print(const T &x) { cout << x << "\n"; }
const int MOD = 1000000007, INF0 = 1061109567, INF = INF0 * INF0;
const double EPS = 1e-10, PI = acos(-1.0);
const int dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1};
const int FACTSIZE = 4040;
int fact[FACTSIZE];
int revfact[FACTSIZE];

int binpow(int a, int b, int mo) {
  int ans = 1;
  do {
    if (b & 1)
      ans = 1ll * ans * a % mo;
    a = 1ll * a * a % mo;
  } while (b >>= 1);
  return ans;
}

int ncr(int n, int r) {
  if (n < r)
    return 0;
  int rs = fact[n] * revfact[r];
  if (rs >= MOD)
    rs %= MOD;
  rs *= revfact[n - r];
  if (rs >= MOD)
    rs %= MOD;
  return rs;
}
void init() {
  fact[0] = 1, revfact[0] = 1;
  for (int i = 1; i < FACTSIZE; ++i) {
    fact[i] = fact[i - 1] * i % MOD;
    revfact[i] = binpow(fact[i], MOD - 2, MOD);
  }
}

#define MAXN 200200
//----//
int N;
int a[MAXN];
int b[MAXN];
int dp[4001][4001];
signed main() {
  init();
  cin.tie(0), ios::sync_with_stdio(false);
  cout << fixed << setprecision(10);
  cin >> N;
  REP(i, N) cin >> a[i] >> b[i];
  REP(i, N) { dp[2000 - a[i]][2000 - b[i]]++; }
  //  REP(i, N) { dp[2000 + a[i]][2000 + b[i]]++; }
  REP(i, 4001) {
    REP(j, 4001) {
      //      if (i > 0 && j > 0) dp[i][j] += dp[i - 1][j - 1];
      if (i > 0)
        dp[i][j] += dp[i - 1][j];
      if (j > 0)
        dp[i][j] += dp[i][j - 1];
      dp[i][j] %= MOD;
    }
  }
  int ans = 0;
  REP(i, N) { ans += dp[2000 + a[i]][2000 + b[i]], ans %= MOD; }
  // DUMP(dp[1999][1999], dp[2000][2000], ans);
  int cnt = 0;
  REP(i, N) cnt += ncr(2 * (a[i] + b[i]), 2 * a[i]), cnt %= MOD;
  cnt = MOD - cnt;
  ans += cnt;
  ans %= MOD;
  ans = ans * revfact[2];
  ans %= MOD;
  print(ans);
}

Fixed submission:
#include <bits/stdc++.h>
#define BIT(n) (1LL << (n))
#define BITF(n, i) (((n) >> i) & 1)
#define REP(i, n) for (int i = 0; i < n; i++)
#define REPB(i, n) for (int i = 0; i < BIT(n); i++)
#define REPS(i, x) for (int i = 1; i <= x; i++)
#define REPR(i, n) for (int i = n; i >= 0; i--)
#define REPZ(i, x) for (int i = 0; i <= x; i++)
#define FOR(i, m, n) for (int i = m; i < n; i++)
#define FORA(i, n) for (auto &&i : n)
#define FORS(i, m, n) for (int i = m; i <= n; i++)
using namespace std;
#define PRINTARR(x, y)                                                         \
  cerr << #x << "=\n";                                                         \
  for (auto itr = x; itr != y; itr++)                                          \
    cerr << *itr << " ";                                                       \
  cerr << endl;
#define PRINTARR2(x, i0, i1)                                                   \
  cerr << #x << "=\n";                                                         \
  for (int ii0 = 0; ii0 < i0; ii0++) {                                         \
    for (int ii1 = 0; ii1 < i1; ii1++)                                         \
      cerr << x[ii0][ii1] << " ";                                              \
    cerr << endl;                                                              \
  }
#define DUMPOUT cerr
// vector
template <typename T> istream &operator>>(istream &is, vector<T> &vec) {
  for (T &x : vec)
    is >> x;
  return is;
}
// pair
template <typename T, typename U>
ostream &operator<<(ostream &os, pair<T, U> &pair_var) {
  os << "(" << pair_var.first << ", " << pair_var.second << ")";
  return os;
}
// vector
template <typename T> ostream &operator<<(ostream &os, const vector<T> &vec) {
  os << "{";
  REP(i, (int)vec.size())
  os << vec[i] << (i + 1 == (int)vec.size() ? "" : ", ");
  os << "}";
  return os;
}
// map
template <typename T, typename U>
ostream &operator<<(ostream &os, map<T, U> &map_var) {
  os << "{";
  FORA(itr, map_var) {
    os << *itr;
    itr++;
    if (itr != map_var.end())
      os << ", ";
    itr--;
  }
  os << "}";
  return os;
}
// set
template <typename T> ostream &operator<<(ostream &os, set<T> &set_var) {
  os << "{";
  FORA(itr, set_var) {
    os << *itr;
    itr++;
    if (itr != set_var.end())
      os << ", ";
    itr--;
  }
  os << "}";
  return os;
}
void dump_func() { DUMPOUT << endl; }
template <class Head, class... Tail>
void dump_func(Head &&head, Tail &&...tail) {
  DUMPOUT << head;
  if (sizeof...(Tail) > 0)
    DUMPOUT << ", ";
  dump_func(std::move(tail)...);
}
#ifdef DEBUG_
#define DEB
#define DUMP(...)                                                              \
  DUMPOUT << "  " << string(#__VA_ARGS__) << ": "                              \
          << "[" << to_string(__LINE__) << ":" << __FUNCTION__ << "]" << endl  \
          << "    ",                                                           \
      dump_func(__VA_ARGS__)
#else
#define DEB if (false)
#define DUMP(...)
#endif

#define ALL(v) v.begin(), v.end()
#define fst first
#define snd second
#define mp make_pair
#define pb push_back
#define epb emplace_back
#define int long long
#define pint pair<int, int>
#define ld long double
using namespace std;
template <class T> bool chmax(T &a, const T &b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
}
template <class T> bool chmin(T &a, const T &b) {
  if (a > b) {
    a = b;
    return 1;
  }
  return 0;
}
template <class T> using vec = std::vector<T>;
template <class T> void print(const T &x) { cout << x << "\n"; }
const int MOD = 1000000007, INF0 = 1061109567, INF = INF0 * INF0;
const double EPS = 1e-10, PI = acos(-1.0);
const int dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1};
const int FACTSIZE = 10100;
int fact[FACTSIZE];
int revfact[FACTSIZE];

int binpow(int a, int b, int mo) {
  int ans = 1;
  do {
    if (b & 1)
      ans = 1ll * ans * a % mo;
    a = 1ll * a * a % mo;
  } while (b >>= 1);
  return ans;
}

int ncr(int n, int r) {
  if (n < r)
    return 0;
  int rs = fact[n] * revfact[r];
  if (rs >= MOD)
    rs %= MOD;
  rs *= revfact[n - r];
  if (rs >= MOD)
    rs %= MOD;
  return rs;
}
void init() {
  fact[0] = 1, revfact[0] = 1;
  for (int i = 1; i < FACTSIZE; ++i) {
    fact[i] = fact[i - 1] * i % MOD;
    revfact[i] = binpow(fact[i], MOD - 2, MOD);
  }
}

#define MAXN 200200
//----//
int N;
int a[MAXN];
int b[MAXN];
int dp[4001][4001];
signed main() {
  init();
  cin.tie(0), ios::sync_with_stdio(false);
  cout << fixed << setprecision(10);
  cin >> N;
  REP(i, N) cin >> a[i] >> b[i];
  REP(i, N) { dp[2000 - a[i]][2000 - b[i]]++; }
  //  REP(i, N) { dp[2000 + a[i]][2000 + b[i]]++; }
  REP(i, 4001) {
    REP(j, 4001) {
      //      if (i > 0 && j > 0) dp[i][j] += dp[i - 1][j - 1];
      if (i > 0)
        dp[i][j] += dp[i - 1][j];
      if (j > 0)
        dp[i][j] += dp[i][j - 1];
      dp[i][j] %= MOD;
    }
  }
  int ans = 0;
  REP(i, N) { ans += dp[2000 + a[i]][2000 + b[i]], ans %= MOD; }
  // DUMP(dp[1999][1999], dp[2000][2000], ans);
  int cnt = 0;
  REP(i, N) cnt += ncr(2 * (a[i] + b[i]), 2 * a[i]), cnt %= MOD;
  cnt = MOD - cnt;
  ans += cnt;
  ans %= MOD;
  ans = ans * revfact[2];
  ans %= MOD;
  print(ans);
}