Problem p02782 (C++)

Buggy submission (status: Runtime Error):
#ifdef LOCAL
#define _GLIBCXX_DEBUG
#define __clock__
#else
#pragma GCC optimize("Ofast")
#endif
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using VI = vector<ll>;
using VV = vector<VI>;
using VS = vector<string>;
using PII = pair<ll, ll>;

// tourist set
template <typename A, typename B> string to_string(pair<A, B> p);

template <typename A, typename B, typename C>
string to_string(tuple<A, B, C> p);

template <typename A, typename B, typename C, typename D>
string to_string(tuple<A, B, C, D> p);

string to_string(const string &s) { return '"' + s + '"'; }

string to_string(const char *s) { return to_string((string)s); }

string to_string(bool b) { return (b ? "true" : "false"); }

string to_string(vector<bool> v) {
  bool first = true;
  string res = "{";
  for (int i = 0; i < static_cast<int>(v.size()); i++) {
    if (!first) {
      res += ", ";
    }
    first = false;
    res += to_string(v[i]);
  }
  res += "}";
  return res;
}

template <size_t N> string to_string(bitset<N> v) {
  string res = "";
  for (size_t i = 0; i < N; i++) {
    res += static_cast<char>('0' + v[i]);
  }
  return res;
}

template <typename A> string to_string(A v) {
  bool first = true;
  string res = "{";
  for (const auto &x : v) {
    if (!first) {
      res += ", ";
    }
    first = false;
    res += to_string(x);
  }
  res += "}";
  return res;
}

template <typename A, typename B> string to_string(pair<A, B> p) {
  return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
}

template <typename A, typename B, typename C>
string to_string(tuple<A, B, C> p) {
  return "(" + to_string(get<0>(p)) + ", " + to_string(get<1>(p)) + ", " +
         to_string(get<2>(p)) + ")";
}

template <typename A, typename B, typename C, typename D>
string to_string(tuple<A, B, C, D> p) {
  return "(" + to_string(get<0>(p)) + ", " + to_string(get<1>(p)) + ", " +
         to_string(get<2>(p)) + ", " + to_string(get<3>(p)) + ")";
}

void debug_out() { cerr << '\n'; }

template <typename Head, typename... Tail> void debug_out(Head H, Tail... T) {
  cerr << " " << to_string(H);
  debug_out(T...);
}

#ifdef LOCAL
#define debug(...) cerr << "[" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__)
#else
#define debug(...) 42
#endif
// tourist set end

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 (b < a) {
    a = b;
    return 1;
  }
  return 0;
}

#define FOR(i, a, b) for (ll i = (a); i < (b); ++i)
#define rep(i, b) FOR(i, 0, b)
#define ALL(v) (v).begin(), (v).end()
#define p(s) cout << (s) << '\n'
#define p2(s, t) cout << (s) << " " << (t) << '\n'
#define br() p("")
#define pn(s) cout << (#s) << " " << (s) << '\n'
#define p_yes() p("YES")
#define p_no() p("NO")
#define SZ(x) ((int)(x).size())
#define SORT(A) sort(ALL(A))
#define RSORT(A) sort(ALL(A), greater<ll>())
#define MP make_pair

void no() {
  p_no();
  exit(0);
}
void yes() {
  p_yes();
  exit(0);
}

const ll mod = 1e9 + 7;
const ll inf = 1e18;
const double PI = acos(-1);

const int N_MAX = 400010;
ll Per[N_MAX] = {};     // n!
ll Per_inv[N_MAX] = {}; //(n!)^-1

ll nCr(ll n, ll r) {
  if (n < r)
    return 0;

  if (n == r || r == 0)
    return 1;
  else
    return Per[n] * Per_inv[n - r] % mod * Per_inv[r] % mod;
}

// a^b mod p
ll mod_pow(ll a, ll b) {
  if (b == 0)
    return 1;

  // 肩が奇数
  if (b % 2 == 1) {
    return a * mod_pow(a, b - 1) % mod;
  } else {
    return mod_pow(a * a % mod, b / 2) % mod;
  }
}

void prepare_nCr() {
  Per[0] = 1;
  Per_inv[0] = 1;

  // nCr高速化準備
  Per[1] = 1;
  FOR(i, 2, N_MAX) { Per[i] = i * Per[i - 1] % mod; }
  Per_inv[1] = 1;
  FOR(i, 2, N_MAX) { Per_inv[i] = mod_pow(Per[i], mod - 2); }
}

ll nHr(ll n, ll r) { return nCr(n - 1 + r, n - 1); }

ll f_naive(ll r, ll c) {
  ll sum = 0;
  debug(r, c);
  rep(i, r + 1) {
    rep(j, c + 1) { sum += nCr(i + j, j); }
  }
  debug(sum);
  return sum;
}

ll f(ll r, ll c) {
  // return f_naive(r, c);
  ll ans = r + 1;
  FOR(i, 1, c + 1) {
    ans += nCr(r + i + 1, r);
    ans %= mod;
  }
  return ans;
}

int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);

  prepare_nCr();

  // input
  ll r1, c1, r2, c2;
  cin >> r1 >> c1 >> r2 >> c2;

  ll a = f(r2, c2);
  debug(a);
  ll b = f(r2, c1 - 1);
  ll c = f(r1 - 1, c2);
  ll d = f(r1 - 1, c1 - 1);

  ll ans = a - b - c + d;
  ans %= mod;
  if (ans < 0)
    ans += mod;
  p(ans);

  return 0;
}

Fixed submission:
#ifdef LOCAL
#define _GLIBCXX_DEBUG
#define __clock__
#else
#pragma GCC optimize("Ofast")
#endif
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using VI = vector<ll>;
using VV = vector<VI>;
using VS = vector<string>;
using PII = pair<ll, ll>;

// tourist set
template <typename A, typename B> string to_string(pair<A, B> p);

template <typename A, typename B, typename C>
string to_string(tuple<A, B, C> p);

template <typename A, typename B, typename C, typename D>
string to_string(tuple<A, B, C, D> p);

string to_string(const string &s) { return '"' + s + '"'; }

string to_string(const char *s) { return to_string((string)s); }

string to_string(bool b) { return (b ? "true" : "false"); }

string to_string(vector<bool> v) {
  bool first = true;
  string res = "{";
  for (int i = 0; i < static_cast<int>(v.size()); i++) {
    if (!first) {
      res += ", ";
    }
    first = false;
    res += to_string(v[i]);
  }
  res += "}";
  return res;
}

template <size_t N> string to_string(bitset<N> v) {
  string res = "";
  for (size_t i = 0; i < N; i++) {
    res += static_cast<char>('0' + v[i]);
  }
  return res;
}

template <typename A> string to_string(A v) {
  bool first = true;
  string res = "{";
  for (const auto &x : v) {
    if (!first) {
      res += ", ";
    }
    first = false;
    res += to_string(x);
  }
  res += "}";
  return res;
}

template <typename A, typename B> string to_string(pair<A, B> p) {
  return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
}

template <typename A, typename B, typename C>
string to_string(tuple<A, B, C> p) {
  return "(" + to_string(get<0>(p)) + ", " + to_string(get<1>(p)) + ", " +
         to_string(get<2>(p)) + ")";
}

template <typename A, typename B, typename C, typename D>
string to_string(tuple<A, B, C, D> p) {
  return "(" + to_string(get<0>(p)) + ", " + to_string(get<1>(p)) + ", " +
         to_string(get<2>(p)) + ", " + to_string(get<3>(p)) + ")";
}

void debug_out() { cerr << '\n'; }

template <typename Head, typename... Tail> void debug_out(Head H, Tail... T) {
  cerr << " " << to_string(H);
  debug_out(T...);
}

#ifdef LOCAL
#define debug(...) cerr << "[" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__)
#else
#define debug(...) 42
#endif
// tourist set end

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 (b < a) {
    a = b;
    return 1;
  }
  return 0;
}

#define FOR(i, a, b) for (ll i = (a); i < (b); ++i)
#define rep(i, b) FOR(i, 0, b)
#define ALL(v) (v).begin(), (v).end()
#define p(s) cout << (s) << '\n'
#define p2(s, t) cout << (s) << " " << (t) << '\n'
#define br() p("")
#define pn(s) cout << (#s) << " " << (s) << '\n'
#define p_yes() p("YES")
#define p_no() p("NO")
#define SZ(x) ((int)(x).size())
#define SORT(A) sort(ALL(A))
#define RSORT(A) sort(ALL(A), greater<ll>())
#define MP make_pair

void no() {
  p_no();
  exit(0);
}
void yes() {
  p_yes();
  exit(0);
}

const ll mod = 1e9 + 7;
const ll inf = 1e18;
const double PI = acos(-1);

const int N_MAX = 2000010;
ll Per[N_MAX] = {};     // n!
ll Per_inv[N_MAX] = {}; //(n!)^-1

ll nCr(ll n, ll r) {
  if (n < r)
    return 0;

  if (n == r || r == 0)
    return 1;
  else
    return Per[n] * Per_inv[n - r] % mod * Per_inv[r] % mod;
}

// a^b mod p
ll mod_pow(ll a, ll b) {
  if (b == 0)
    return 1;

  // 肩が奇数
  if (b % 2 == 1) {
    return a * mod_pow(a, b - 1) % mod;
  } else {
    return mod_pow(a * a % mod, b / 2) % mod;
  }
}

void prepare_nCr() {
  Per[0] = 1;
  Per_inv[0] = 1;

  // nCr高速化準備
  Per[1] = 1;
  FOR(i, 2, N_MAX) { Per[i] = i * Per[i - 1] % mod; }
  Per_inv[1] = 1;
  FOR(i, 2, N_MAX) { Per_inv[i] = mod_pow(Per[i], mod - 2); }
}

ll nHr(ll n, ll r) { return nCr(n - 1 + r, n - 1); }

ll f_naive(ll r, ll c) {
  ll sum = 0;
  debug(r, c);
  rep(i, r + 1) {
    rep(j, c + 1) { sum += nCr(i + j, j); }
  }
  debug(sum);
  return sum;
}

ll f(ll r, ll c) {
  // return f_naive(r, c);
  ll ans = r + 1;
  FOR(i, 1, c + 1) {
    ans += nCr(r + i + 1, r);
    ans %= mod;
  }
  return ans;
}

int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);

  prepare_nCr();

  // input
  ll r1, c1, r2, c2;
  cin >> r1 >> c1 >> r2 >> c2;

  ll a = f(r2, c2);
  debug(a);
  ll b = f(r2, c1 - 1);
  ll c = f(r1 - 1, c2);
  ll d = f(r1 - 1, c1 - 1);

  ll ans = a - b - c + d;
  ans %= mod;
  if (ans < 0)
    ans += mod;
  p(ans);

  return 0;
}