結果

問題 No.1999 Lattice Teleportation
ユーザー NyaanNyaanNyaanNyaan
提出日時 2022-07-01 21:54:40
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 67 ms / 2,000 ms
コード長 21,377 bytes
コンパイル時間 3,283 ms
コンパイル使用メモリ 273,272 KB
実行使用メモリ 17,836 KB
最終ジャッジ日時 2024-05-04 16:18:51
合計ジャッジ時間 5,213 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge5
このコードへのチャレンジ
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 1 ms
6,816 KB
testcase_01 AC 2 ms
6,944 KB
testcase_02 AC 2 ms
6,944 KB
testcase_03 AC 2 ms
6,940 KB
testcase_04 AC 1 ms
6,940 KB
testcase_05 AC 2 ms
6,944 KB
testcase_06 AC 2 ms
6,944 KB
testcase_07 AC 2 ms
6,944 KB
testcase_08 AC 1 ms
6,944 KB
testcase_09 AC 2 ms
6,940 KB
testcase_10 AC 1 ms
6,940 KB
testcase_11 AC 2 ms
6,940 KB
testcase_12 AC 53 ms
17,836 KB
testcase_13 AC 62 ms
17,188 KB
testcase_14 AC 1 ms
6,940 KB
testcase_15 AC 65 ms
17,280 KB
testcase_16 AC 32 ms
11,504 KB
testcase_17 AC 61 ms
16,364 KB
testcase_18 AC 49 ms
17,396 KB
testcase_19 AC 50 ms
15,672 KB
testcase_20 AC 67 ms
16,768 KB
testcase_21 AC 66 ms
16,564 KB
testcase_22 AC 66 ms
17,360 KB
testcase_23 AC 6 ms
6,944 KB
testcase_24 AC 22 ms
8,948 KB
testcase_25 AC 52 ms
15,352 KB
testcase_26 AC 40 ms
11,500 KB
testcase_27 AC 35 ms
10,220 KB
testcase_28 AC 56 ms
17,356 KB
testcase_29 AC 28 ms
9,864 KB
testcase_30 AC 13 ms
6,940 KB
testcase_31 AC 10 ms
6,944 KB
testcase_32 AC 35 ms
10,740 KB
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ソースコード

diff # 

/**
 *  date : 2022-07-01 21:54:35
 */

#define NDEBUG
// https://onlinejudge.u-aizu.ac.jp/beta/room.html#OUPC2020/problems/I

using namespace std;

// intrinstic
#include <immintrin.h>

#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cctype>
#include <cfenv>
#include <cfloat>
#include <chrono>
#include <cinttypes>
#include <climits>
#include <cmath>
#include <complex>
#include <cstdarg>
#include <cstddef>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <deque>
#include <fstream>
#include <functional>
#include <initializer_list>
#include <iomanip>
#include <ios>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <ostream>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <streambuf>
#include <string>
#include <tuple>
#include <type_traits>
#include <typeinfo>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

// utility
namespace Nyaan {
using ll = long long;
using i64 = long long;
using u64 = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;

template <typename T>
using V = vector<T>;
template <typename T>
using VV = vector<vector<T>>;
using vi = vector<int>;
using vl = vector<long long>;
using vd = V<double>;
using vs = V<string>;
using vvi = vector<vector<int>>;
using vvl = vector<vector<long long>>;

template <typename T, typename U>
struct P : pair<T, U> {
  template <typename... Args>
  P(Args... args) : pair<T, U>(args...) {}

  using pair<T, U>::first;
  using pair<T, U>::second;

  P &operator+=(const P &r) {
    first += r.first;
    second += r.second;
    return *this;
  }
  P &operator-=(const P &r) {
    first -= r.first;
    second -= r.second;
    return *this;
  }
  P &operator*=(const P &r) {
    first *= r.first;
    second *= r.second;
    return *this;
  }
  template <typename S>
  P &operator*=(const S &r) {
    first *= r, second *= r;
    return *this;
  }
  P operator+(const P &r) const { return P(*this) += r; }
  P operator-(const P &r) const { return P(*this) -= r; }
  P operator*(const P &r) const { return P(*this) *= r; }
  template <typename S>
  P operator*(const S &r) const {
    return P(*this) *= r;
  }
  P operator-() const { return P{-first, -second}; }
};

using pl = P<ll, ll>;
using pi = P<int, int>;
using vp = V<pl>;

constexpr int inf = 1001001001;
constexpr long long infLL = 4004004004004004004LL;

template <typename T>
int sz(const T &t) {
  return t.size();
}

template <typename T, typename U>
inline bool amin(T &x, U y) {
  return (y < x) ? (x = y, true) : false;
}
template <typename T, typename U>
inline bool amax(T &x, U y) {
  return (x < y) ? (x = y, true) : false;
}

template <typename T>
inline T Max(const vector<T> &v) {
  return *max_element(begin(v), end(v));
}
template <typename T>
inline T Min(const vector<T> &v) {
  return *min_element(begin(v), end(v));
}
template <typename T>
inline long long Sum(const vector<T> &v) {
  return accumulate(begin(v), end(v), 0LL);
}

template <typename T>
int lb(const vector<T> &v, const T &a) {
  return lower_bound(begin(v), end(v), a) - begin(v);
}
template <typename T>
int ub(const vector<T> &v, const T &a) {
  return upper_bound(begin(v), end(v), a) - begin(v);
}

constexpr long long TEN(int n) {
  long long ret = 1, x = 10;
  for (; n; x *= x, n >>= 1) ret *= (n & 1 ? x : 1);
  return ret;
}

template <typename T, typename U>
pair<T, U> mkp(const T &t, const U &u) {
  return make_pair(t, u);
}

template <typename T>
vector<T> mkrui(const vector<T> &v, bool rev = false) {
  vector<T> ret(v.size() + 1);
  if (rev) {
    for (int i = int(v.size()) - 1; i >= 0; i--) ret[i] = v[i] + ret[i + 1];
  } else {
    for (int i = 0; i < int(v.size()); i++) ret[i + 1] = ret[i] + v[i];
  }
  return ret;
};

template <typename T>
vector<T> mkuni(const vector<T> &v) {
  vector<T> ret(v);
  sort(ret.begin(), ret.end());
  ret.erase(unique(ret.begin(), ret.end()), ret.end());
  return ret;
}

template <typename F>
vector<int> mkord(int N,F f) {
  vector<int> ord(N);
  iota(begin(ord), end(ord), 0);
  sort(begin(ord), end(ord), f);
  return ord;
}

template <typename T>
vector<int> mkinv(vector<T> &v) {
  int max_val = *max_element(begin(v), end(v));
  vector<int> inv(max_val + 1, -1);
  for (int i = 0; i < (int)v.size(); i++) inv[v[i]] = i;
  return inv;
}

vector<int> mkiota(int n) {
  vector<int> ret(n);
  iota(begin(ret), end(ret), 0);
  return ret;
}

template <typename T>
T mkrev(const T &v) {
  T w{v};
  reverse(begin(w), end(w));
  return w;
}

template <typename T>
bool nxp(vector<T> &v) {
  return next_permutation(begin(v), end(v));
}



#define inV(T, v, n) \
  vector<T> v(n);    \
  in(v)

#define inVV(T, v, h, w)                \
  vector<vector<T>> v(h, vector<T>(w)); \
  in(v);

template <typename T>
using minpq = priority_queue<T, vector<T>, greater<T>>;

// 区間：半開区間 (ng, ok] または [ok, ng)
template <typename T, typename F>
T binary_search(T ng, T ok, const F& f) {
  if constexpr (is_integral<T>::value == true) {
    while (abs(ok - ng) > 1) {
      T x = (ok + ng) / 2;
      (f(x) ? ok : ng) = x;
    }
    return ok;
  } else {
    for (int iter = 0; iter < 60; iter++) {
      T x = (ok + ng) / 2;
      (f(x) ? ok : ng) = x;
    }
    return ok;
  }
}

// 解区間 (l, r)
template <typename T, typename F>
void ternary_search(T l, T r, const F& f, bool greater = false) {
  if constexpr (is_integral<T>::value == true) {
    while (abs(l - r) > 2) {
      T llr = (l * 2 + r * 1) / 3;
      T lrr = (l * 1 + r * 2) / 3;
      bool flag = f(llr) < f(lrr);
      if (flag != greater) {
        r = lrr;
      } else {
        l = llr;
      }
    }
    return (l + r) / 2;
  } else {
    for (int iter = 0; iter < 80; iter++) {
      T llr = (l * 2 + r * 1) / 3;
      T lrr = (l * 1 + r * 2) / 3;
      bool flag = f(llr) < f(lrr);
      if (flag != greater) {
        r = lrr;
      } else {
        l = llr;
      }
    }
    return (l + r) / 2;
  }
}

}  // namespace Nyaan

// bit operation
namespace Nyaan {
__attribute__((target("popcnt"))) inline int popcnt(const u64 &a) {
  return _mm_popcnt_u64(a);
}
inline int lsb(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }
inline int ctz(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }
inline int msb(const u64 &a) { return a ? 63 - __builtin_clzll(a) : -1; }
template <typename T>
inline int gbit(const T &a, int i) {
  return (a >> i) & 1;
}
template <typename T>
inline void sbit(T &a, int i, bool b) {
  if (gbit(a, i) != b) a ^= T(1) << i;
}
constexpr long long PW(int n) { return 1LL << n; }
constexpr long long MSK(int n) { return (1LL << n) - 1; }
}  // namespace Nyaan

// inout
namespace Nyaan {

template <typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &p) {
  os << p.first << " " << p.second;
  return os;
}
template <typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &p) {
  is >> p.first >> p.second;
  return is;
}

template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
  int s = (int)v.size();
  for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];
  return os;
}
template <typename T>
istream &operator>>(istream &is, vector<T> &v) {
  for (auto &x : v) is >> x;
  return is;
}

istream &operator>>(istream &is, __int128_t &x) {
  string S;
  is >> S;
  x = 0;
  int flag = 0;
  for (auto &c : S) {
    if (c == '-') {
      flag = true;
      continue;
    }
    x *= 10;
    x += c - '0';
  }
  if (flag) x = -x;
  return is;
}

istream &operator>>(istream &is, __uint128_t &x) {
  string S;
  is >> S;
  x = 0;
  for (auto &c : S) {
    x *= 10;
    x += c - '0';
  }
  return is;
}

ostream &operator<<(ostream &os, __int128_t x) {
  if (x == 0) return os << 0;
  if (x < 0) os << '-', x = -x;
  string S;
  while (x) S.push_back('0' + x % 10), x /= 10;
  reverse(begin(S), end(S));
  return os << S;
}
ostream &operator<<(ostream &os, __uint128_t x) {
  if (x == 0) return os << 0;
  string S;
  while (x) S.push_back('0' + x % 10), x /= 10;
  reverse(begin(S), end(S));
  return os << S;
}

void in() {}
template <typename T, class... U>
void in(T &t, U &...u) {
  cin >> t;
  in(u...);
}

void out() { cout << "\n"; }
template <typename T, class... U, char sep = ' '>
void out(const T &t, const U &...u) {
  cout << t;
  if (sizeof...(u)) cout << sep;
  out(u...);
}

void outr() {}
template <typename T, class... U, char sep = ' '>
void outr(const T &t, const U &...u) {
  cout << t;
  outr(u...);
}

struct IoSetupNya {
  IoSetupNya() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(15);
    cerr << fixed << setprecision(7);
  }
} iosetupnya;

}  // namespace Nyaan

// debug
namespace DebugImpl {

template <typename U, typename = void>
struct is_specialize : false_type {};
template <typename U>
struct is_specialize<
    U, typename conditional<false, typename U::iterator, void>::type>
    : true_type {};
template <typename U>
struct is_specialize<
    U, typename conditional<false, decltype(U::first), void>::type>
    : true_type {};
template <typename U>
struct is_specialize<U, enable_if_t<is_integral<U>::value, void>> : true_type {
};

void dump(const char& t) { cerr << t; }

void dump(const string& t) { cerr << t; }

void dump(const bool& t) { cerr << (t ? "true" : "false"); }

void dump(__int128_t t) {
  if (t == 0) cerr << 0;
  if (t < 0) cerr << '-', t = -t;
  string S;
  while (t) S.push_back('0' + t % 10), t /= 10;
  reverse(begin(S), end(S));
  cerr << S;
}

void dump(__uint128_t t) {
  if (t == 0) cerr << 0;
  string S;
  while (t) S.push_back('0' + t % 10), t /= 10;
  reverse(begin(S), end(S));
  cerr << S;
}

template <typename U,
          enable_if_t<!is_specialize<U>::value, nullptr_t> = nullptr>
void dump(const U& t) {
  cerr << t;
}

template <typename T>
void dump(const T& t, enable_if_t<is_integral<T>::value>* = nullptr) {
  string res;
  if (t == Nyaan::inf) res = "inf";
  if constexpr (is_signed<T>::value) {
    if (t == -Nyaan::inf) res = "-inf";
  }
  if constexpr (sizeof(T) == 8) {
    if (t == Nyaan::infLL) res = "inf";
    if constexpr (is_signed<T>::value) {
      if (t == -Nyaan::infLL) res = "-inf";
    }
  }
  if (res.empty()) res = to_string(t);
  cerr << res;
}

template <typename T, typename U>
void dump(const pair<T, U>&);
template <typename T>
void dump(const pair<T*, int>&);

template <typename T>
void dump(const T& t,
          enable_if_t<!is_void<typename T::iterator>::value>* = nullptr) {
  cerr << "[ ";
  for (auto it = t.begin(); it != t.end();) {
    dump(*it);
    cerr << (++it == t.end() ? "" : ", ");
  }
  cerr << " ]";
}

template <typename T, typename U>
void dump(const pair<T, U>& t) {
  cerr << "( ";
  dump(t.first);
  cerr << ", ";
  dump(t.second);
  cerr << " )";
}

template <typename T>
void dump(const pair<T*, int>& t) {
  cerr << "[ ";
  for (int i = 0; i < t.second; i++) {
    dump(t.first[i]);
    cerr << (i == t.second - 1 ? "" : ", ");
  }
  cerr << " ]";
}

void trace() { cerr << endl; }
template <typename Head, typename... Tail>
void trace(Head&& head, Tail&&... tail) {
  cerr << " ";
  dump(head);
  if (sizeof...(tail) != 0) cerr << ",";
  trace(forward<Tail>(tail)...);
}

}  // namespace DebugImpl

#ifdef NyaanDebug
#define trc(...)                            \
  do {                                      \
    cerr << "## " << #__VA_ARGS__ << " = "; \
    DebugImpl::trace(__VA_ARGS__);          \
  } while (0)
#else
#define trc(...) (void(0))
#endif

// macro
#define each(x, v) for (auto&& x : v)
#define each2(x, y, v) for (auto&& [x, y] : v)
#define all(v) (v).begin(), (v).end()
#define rep(i, N) for (long long i = 0; i < (long long)(N); i++)
#define repr(i, N) for (long long i = (long long)(N)-1; i >= 0; i--)
#define rep1(i, N) for (long long i = 1; i <= (long long)(N); i++)
#define repr1(i, N) for (long long i = (N); (long long)(i) > 0; i--)
#define reg(i, a, b) for (long long i = (a); i < (b); i++)
#define regr(i, a, b) for (long long i = (b)-1; i >= (a); i--)
#define fi first
#define se second
#define ini(...)   \
  int __VA_ARGS__; \
  in(__VA_ARGS__)
#define inl(...)         \
  long long __VA_ARGS__; \
  in(__VA_ARGS__)
#define ins(...)      \
  string __VA_ARGS__; \
  in(__VA_ARGS__)
#define in2(s, t)                           \
  for (int i = 0; i < (int)s.size(); i++) { \
    in(s[i], t[i]);                         \
  }
#define in3(s, t, u)                        \
  for (int i = 0; i < (int)s.size(); i++) { \
    in(s[i], t[i], u[i]);                   \
  }
#define in4(s, t, u, v)                     \
  for (int i = 0; i < (int)s.size(); i++) { \
    in(s[i], t[i], u[i], v[i]);             \
  }
#define die(...)             \
  do {                       \
    Nyaan::out(__VA_ARGS__); \
    return;                  \
  } while (0)

namespace Nyaan {
void solve();
}
int main() { Nyaan::solve(); }

//

struct Point {
  using T = __int128_t;
  T x, y;
  Point() : x(0), y(0) {}
  Point(T x_, T y_) : x(x_), y(y_) {}

  Point &operator+=(const Point &p) {
    this->x += p.x;
    this->y += p.y;
    return *this;
  }

  Point &operator-=(const Point &p) {
    this->x -= p.x;
    this->y -= p.y;
    return *this;
  }

  int pos() const {
    if (y < 0) return -1;
    if (y == 0 && 0 <= x) return 0;
    return 1;
  }

  Point operator+(const Point &p) const { return Point(*this) += p; }
  Point operator-(const Point &p) const { return Point(*this) -= p; }
  Point operator-() const { return Point(-this->x, -this->y); }
  bool operator==(const Point &p) const { return x == p.x && y == p.y; }
  bool operator!=(const Point &p) const { return x != p.x || y != p.y; }
  bool operator<(const Point &p) const { return x == p.x ? y < p.y : x < p.x; }

  friend istream &operator>>(istream &is, Point &p) {
    long long x, y;
    is >> x >> y;
    p.x = x, p.y = y;
    return is;
  }

  friend ostream &operator<<(ostream &os, const Point &p) {
    os << (long long)(p.x) << " " << (long long)(p.y);
    return os;
  }
};
using Points = vector<Point>;

Point::T dot(const Point &a, const Point &b) { return a.x * b.x + a.y * b.y; }
Point::T cross(const Point &a, const Point &b) { return a.x * b.y - a.y * b.x; }

// sort by argument (-Pi ~ Pi)
void ArgumentSort(Points &v) {
  sort(begin(v), end(v), [](Point a, Point b) {
    if (a.pos() != b.pos()) return a.pos() < b.pos();
    return cross(a, b) > 0;
  });
}

// 1 ... counterclockwise / 0 straight / -1 clockwise
int ccw(const Point &a, const Point &b, const Point &c) {
  Point::T t = cross(b - a, c - a);
  return t < 0 ? -1 : t == 0 ? 0 : 1;
}

// v must have sorted by x-coordinate
Points LowerHull(const Points &ps) {
  int N = (int)ps.size();
  for (int i = 0; i < N - 1; i++) assert(ps[i].x <= ps[i + 1].x);
  if (N <= 2) return ps;
  Points convex(N);
  int k = 0;
  for (int i = 0; i < N; convex[k++] = ps[i++]) {
    while (k >= 2 && ccw(convex[k - 2], convex[k - 1], ps[i]) <= 0) --k;
  }
  convex.resize(k);
  return convex;
}

Points UpperHull(const Points &ps) {
  int N = (int)ps.size();
  for (int i = 0; i < N - 1; i++) assert(ps[i].x <= ps[i + 1].x);
  if (N <= 2) return ps;
  Points convex(N);
  int k = 0;
  for (int i = 0; i < N; convex[k++] = ps[i++]) {
    while (k >= 2 && ccw(convex[k - 2], convex[k - 1], ps[i]) >= 0) --k;
  }
  convex.resize(k);
  return convex;
}

Points ConvexHull(const Points &ps) {
  int N = (int)ps.size();
  for (int i = 0; i < N - 1; i++) assert(ps[i].x <= ps[i + 1].x);
  if (N <= 2) return ps;
  Points convex(2 * N);
  int k = 0;
  for (int i = 0; i < N; convex[k++] = ps[i++]) {
    while (k >= 2 && ccw(convex[k - 2], convex[k - 1], ps[i]) <= 0) --k;
  }
  for (int i = N - 2, t = k + 1; i >= 0; convex[k++] = ps[i--]) {
    while (k >= t && ccw(convex[k - 2], convex[k - 1], ps[i]) <= 0) --k;
  }
  convex.resize(k - 1);
  return convex;
}



template <uint32_t mod>
struct LazyMontgomeryModInt {
  using mint = LazyMontgomeryModInt;
  using i32 = int32_t;
  using u32 = uint32_t;
  using u64 = uint64_t;

  static constexpr u32 get_r() {
    u32 ret = mod;
    for (i32 i = 0; i < 4; ++i) ret *= 2 - mod * ret;
    return ret;
  }

  static constexpr u32 r = get_r();
  static constexpr u32 n2 = -u64(mod) % mod;
  static_assert(r * mod == 1, "invalid, r * mod != 1");
  static_assert(mod < (1 << 30), "invalid, mod >= 2 ^ 30");
  static_assert((mod & 1) == 1, "invalid, mod % 2 == 0");

  u32 a;

  constexpr LazyMontgomeryModInt() : a(0) {}
  constexpr LazyMontgomeryModInt(const int64_t &b)
      : a(reduce(u64(b % mod + mod) * n2)){};

  static constexpr u32 reduce(const u64 &b) {
    return (b + u64(u32(b) * u32(-r)) * mod) >> 32;
  }

  constexpr mint &operator+=(const mint &b) {
    if (i32(a += b.a - 2 * mod) < 0) a += 2 * mod;
    return *this;
  }

  constexpr mint &operator-=(const mint &b) {
    if (i32(a -= b.a) < 0) a += 2 * mod;
    return *this;
  }

  constexpr mint &operator*=(const mint &b) {
    a = reduce(u64(a) * b.a);
    return *this;
  }

  constexpr mint &operator/=(const mint &b) {
    *this *= b.inverse();
    return *this;
  }

  constexpr mint operator+(const mint &b) const { return mint(*this) += b; }
  constexpr mint operator-(const mint &b) const { return mint(*this) -= b; }
  constexpr mint operator*(const mint &b) const { return mint(*this) *= b; }
  constexpr mint operator/(const mint &b) const { return mint(*this) /= b; }
  constexpr bool operator==(const mint &b) const {
    return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a);
  }
  constexpr bool operator!=(const mint &b) const {
    return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a);
  }
  constexpr mint operator-() const { return mint() - mint(*this); }

  constexpr mint pow(u64 n) const {
    mint ret(1), mul(*this);
    while (n > 0) {
      if (n & 1) ret *= mul;
      mul *= mul;
      n >>= 1;
    }
    return ret;
  }
  
  constexpr mint inverse() const { return pow(mod - 2); }

  friend ostream &operator<<(ostream &os, const mint &b) {
    return os << b.get();
  }

  friend istream &operator>>(istream &is, mint &b) {
    int64_t t;
    is >> t;
    b = LazyMontgomeryModInt<mod>(t);
    return (is);
  }
  
  constexpr u32 get() const {
    u32 ret = reduce(a);
    return ret >= mod ? ret - mod : ret;
  }

  static constexpr u32 get_mod() { return mod; }
};

template <typename T>
struct Binomial {
  vector<T> f, g, h;
  Binomial(int MAX = 0) {
    assert(T::get_mod() != 0 && "Binomial<mint>()");
    f.resize(1, T{1});
    g.resize(1, T{1});
    h.resize(1, T{1});
    while (MAX >= (int)f.size()) extend();
  }

  void extend() {
    int n = f.size();
    int m = n * 2;
    f.resize(m);
    g.resize(m);
    h.resize(m);
    for (int i = n; i < m; i++) f[i] = f[i - 1] * T(i);
    g[m - 1] = f[m - 1].inverse();
    h[m - 1] = g[m - 1] * f[m - 2];
    for (int i = m - 2; i >= n; i--) {
      g[i] = g[i + 1] * T(i + 1);
      h[i] = g[i] * f[i - 1];
    }
  }

  T fac(int i) {
    if (i < 0) return T(0);
    while (i >= (int)f.size()) extend();
    return f[i];
  }

  T finv(int i) {
    if (i < 0) return T(0);
    while (i >= (int)g.size()) extend();
    return g[i];
  }

  T inv(int i) {
    if (i < 0) return -inv(-i);
    while (i >= (int)h.size()) extend();
    return h[i];
  }

  T C(int n, int r) {
    if (n < 0 || n < r || r < 0) return T(0);
    return fac(n) * finv(n - r) * finv(r);
  }

  inline T operator()(int n, int r) { return C(n, r); }

  template <typename I>
  T multinomial(const vector<I>& r) {
    static_assert(is_integral<I>::value == true);
    int n = 0;
    for (auto& x : r) {
      if (x < 0) return T(0);
      n += x;
    }
    T res = fac(n);
    for (auto& x : r) res *= finv(x);
    return res;
  }

  template <typename I>
  T operator()(const vector<I>& r) {
    return multinomial(r);
  }

  T C_naive(int n, int r) {
    if (n < 0 || n < r || r < 0) return T(0);
    T ret = T(1);
    r = min(r, n - r);
    for (int i = 1; i <= r; ++i) ret *= inv(i) * (n--);
    return ret;
  }

  T P(int n, int r) {
    if (n < 0 || n < r || r < 0) return T(0);
    return fac(n) * finv(n - r);
  }

  T H(int n, int r) {
    if (n < 0 || r < 0) return T(0);
    return r == 0 ? 1 : C(n + r - 1, r);
  }
};

//
using namespace Nyaan;
using mint = LazyMontgomeryModInt<1000000007>;
using vm = vector<mint>;
using vvm = vector<vm>;
Binomial<mint> C;

void Nyaan::solve() {
  ini(N);
  vp v(N);
  in(v);
  vp c, d;
  Points ps;
  each2(x, y, v) {
    if (x == 0 and y == 0) continue;
    if (y < 0) x = -x, y = -y;
    ps.emplace_back(x, y);
  }
  ArgumentSort(ps);
  Points ps2;
  {
    ll x = 0, y = 0;
    rep(i, sz(ps)) {
      ps2.emplace_back(x, y);
      x += ps[i].x;
      y += ps[i].y;
    }
    rep(i, sz(ps)) {
      ps2.emplace_back(x, y);
      x -= ps[i].x;
      y -= ps[i].y;
    }
  }
  trc(ps2);
  auto cross = [&](Point a, Point b) {
    return mint(a.x) * b.y - mint(b.x) * a.y;
  };
  mint area = 0;
  rep(i, sz(ps2)) { area += cross(ps2[i], ps2[(i + 1) % sz(ps2)]); }
  area /= 2;
  trc(area);

  mint kousi = sz(ps);
  rep(i, sz(ps)) kousi += mint(gcd(abs<ll>(ps[i].x), abs<ll>(ps[i].y)) - 1);
  kousi *= 2;
  trc(kousi);
  mint i = area - kousi / 2 + 1;
  out(kousi + i);
}
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