#914336 (C++23) No.187 中華風 (Hard)

• 問題: No.187 中華風 (Hard)
• ユーザー: い
• 提出日時: 2023-09-21 12:46:37
• 言語: C++23 (gcc 12.3.0 + boost 1.83.0)
• 結果: AC
• 実行時間: 107 ms / 3,000 ms
• コード長: 8,415 bytes
• コンパイル時間: 3,726 ms
• コンパイル使用メモリ: 284,904 KB
• 実行使用メモリ: 5,376 KB
• 最終ジャッジ日時: 2024-07-07 06:33:18
• 合計ジャッジ時間: 5,544 ms
• ジャッジサーバーID （参考情報）: judge4 / judge1

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	2 ms; 5,248 KB
testcase_01	AC	3 ms; 5,376 KB
testcase_02	AC	28 ms; 5,376 KB
testcase_03	AC	26 ms; 5,376 KB
testcase_04	AC	67 ms; 5,376 KB
testcase_05	AC	64 ms; 5,376 KB
testcase_06	AC	66 ms; 5,376 KB
testcase_07	AC	65 ms; 5,376 KB
testcase_08	AC	105 ms; 5,376 KB
testcase_09	AC	107 ms; 5,376 KB
testcase_10	AC	106 ms; 5,376 KB
testcase_11	AC	67 ms; 5,376 KB
testcase_12	AC	68 ms; 5,376 KB
testcase_13	AC	73 ms; 5,376 KB
testcase_14	AC	60 ms; 5,376 KB
testcase_15	AC	13 ms; 5,376 KB
testcase_16	AC	14 ms; 5,376 KB
testcase_17	AC	2 ms; 5,376 KB
testcase_18	AC	2 ms; 5,376 KB
testcase_19	AC	2 ms; 5,376 KB
testcase_20	AC	55 ms; 5,376 KB
testcase_21	AC	2 ms; 5,376 KB
testcase_22	AC	64 ms; 5,376 KB
testcase_23	AC	2 ms; 5,376 KB
testcase_24	AC	2 ms; 5,376 KB

ソースコード

#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")

#include <bits/stdc++.h>
using namespace std;

using uint = unsigned int;
using ll = long long;
using ull = unsigned long long;
using ld = long double;
using i128 = __int128_t;

template <typename F>
using fn = function<F>;

#define all(a) a.begin(), a.end()
#define allr(a) a.rbegin(), a.rend()

template <class A>
int len(const A &a) {
  return a.size();
}

#define eb emplace_back
#define pb push_back
#define elif else if

template <typename T>
using vec = vector<T>;
template <typename T>
using vec2 = vec<vec<T>>;
template <typename T>
using vec3 = vec<vec2<T>>;
template <typename T>
using vec4 = vec<vec3<T>>;
template <typename T>
using vec5 = vec<vec4<T>>;

#define VEC(T, a, ...) \
  vec<T> a(__VA_ARGS__)

#define VEC2(T, a, n, ...) \
  vector a(n, vec<T>(__VA_ARGS__));

#define VEC3(T, a, n, m, ...) \
  vector a( \
    n, \
    vector(m, vec<T>(__VA_ARGS__)) \
  );

#define VEC4(T, a, n, m, l, ...) \
  vector a( \
    n, \
    vector( \
      m, \
      vector(l, vec<T>(__VA_ARGS__)) \
    ) \
  );

#define eval_4(a, b, c, d, e, ...) e

#define loop while (1)

#define rep(n) \
  for (int __ = 0; __ < n; __++)

#define range_1(i, n) \
  for (int i = 0; i < n; i++)
#define range_2(i, a, b) \
  for (ll i = a; i < b; i++)
#define range_3(i, a, b, c) \
  for (ll i = a; i < b; i += c)

#define range(...) \
  eval_4(__VA_ARGS__, range_3, range_2, range_1, rep)( \
    __VA_ARGS__ \
  )

#define ranger_1(i, n) \
  for (int i = n; i-- > 0;)
#define ranger_2(i, a, b) \
  for (ll i = b; i-- > a;)
#define ranger_3(i, a, b, c) \
  for (ll i = b - 1; i >= a; i -= c)

#define range_rev(...) \
  eval_4(__VA_ARGS__, ranger_3, ranger_2, ranger_1)( \
    __VA_ARGS__ \
  )

#define iter(x, a) \
  for (const auto &x : a)
#define iter_mut(x, a) \
  for (auto &&x : a)

template <typename T, typename U>
istream &
operator>>(istream &in, pair<T, U> &p) {
  return in >> p.first >> p.second;
}

template <typename T, typename U>
ostream &operator<<(
  ostream &out,
  pair<T, U> &p
) {
  out << p.first << ' ' << p.second;
  return out;
}

template <int k = 0, class T>
void read_tup(istream &in, T &x) {
  if constexpr (tuple_size<T>::value > k) {
    in >> get<k>(x);
    read_tup<k + 1>(in, x);
  }
}

template <class... T>
istream &operator>>(
  istream &in,
  tuple<T...> &x
) {
  read_tup(in, x);
  return in;
}

template <int k = 0, class T>
void out_tup(ostream &out, T &x) {
  if constexpr (tuple_size<T>::value > k) {
    if constexpr (k > 0) {
      out << ' ';
    }
    out << get<k>(x);
    out_tup<k + 1>(out, x);
  }
}

template <class... T>
ostream &operator<<(
  ostream &out,
  tuple<T...> &x
) {
  out_tup(out, x);
  return out;
}

template <typename T>
auto operator<<(ostream &out, vec<T> a)
  -> ostream & {
  range(i, len(a)) {
    if (i) {
      out << ' ';
    }
    out << a[i];
  }
  return out;
}

template <typename T>
auto operator<<(ostream &out, vec2<T> a)
  -> ostream & {
  iter_mut(x, a) out << x << '\n';
  return out;
}

template <typename T>
auto operator>>(istream &in, vec<T> &a)
  -> istream & {
  iter_mut(x, a) in >> x;
  return in;
}

template <typename... T>
void in(T &...a) {
  (cin >> ... >> a);
}

template <class T, class... U>
void out(T a, const U... b) {
  cout << a;
  ((cout << ' ' << b), ...);
  cout << '\n';
}

template <typename T = int>
vec<T> iota(int n, T v = 0) {
  vec<T> a(n);
  std::iota(all(a), v);
  return a;
}

template <class T>
using max_queue = priority_queue<T>;

template <class T>
using min_queue =
  priority_queue<T, vec<T>, greater<T>>;

template <typename T>
T pop(queue<T> &q) {
  T v = q.front();
  q.pop();
  return v;
}

template <typename T>
T pop(deque<T> &q) {
  T v = q.front();
  q.pop_front();
  return v;
}

template <typename T>
T pop(vec<T> &q) {
  T v = q.back();
  q.pop_back();
  return v;
}

template <typename T>
T pop(max_queue<T> &q) {
  T v = q.top();
  q.pop();
  return v;
}

template <typename T>
T pop(min_queue<T> &q) {
  T v = q.top();
  q.pop();
  return v;
}

template <typename T>
T max(const vec<T> &a) {
  return *max_element(all(a));
}

template <typename T>
T min(const vec<T> &a) {
  return *min_element(all(a));
}

int topbit(int x) {
  return 31 - __builtin_clz(x);
}

int popcnt(int x) {
  return __builtin_popcount(x);
}

template <class T>
int ctz(T n) {
  return __builtin_ctzll(n);
}

template <class T>
int bitlen(T n) {
  return 64 - __builtin_clzll(n);
}

template <class T>
bool operator==(
  const vec<T> &a,
  const vec<T> &b
) {
  int n = len(a);
  if (len(b) != n) {
    return false;
  }
  range(i, n) {
    if (a[i] != b[i]) {
      return false;
    }
  }
  return true;
}

template <class T, class U>
bool chmin(T &a, const U &b) {
  return b < a ? a = b, 1 : 0;
}

template <class T, class U>
bool chmax(T &a, const U &b) {
  return b > a ? a = b, 1 : 0;
}

template <class T, class U>
T sum(const vec<U> &a) {
  return accumulate(all(a), 0ll);
}

template <class T>
void unique(vec<T> &a) {
  sort(all(a));
  a.erase(std::unique(all(a)), a.end());
}

template <class T, class A>
int lb(const A &a, const T &x) {
  auto p = lower_bound(all(a), x);
  return distance(a.begin(), p);
}

template <class T, class A>
int ub(const A &a, const T &x) {
  auto p = upper_bound(all(a), x);
  return distance(a.begin(), p);
}

template <class A>
vec<int> argsort(const A &a) {
  int n = len(a);
  auto b = iota(n);
  sort(all(b), [&](int i, int j) {
    return a[i] < a[j];
  });
  return b;
}

template <typename T>
auto divmod(T a, T b) -> pair<T, T> {
  T q = a / b;
  return {q, a - q * b};
}

template <typename T>
int argmax(const vec<T> &a) {
  int n = len(a);
  assert(n);
  int j = 0;
  range(i, 1, n) {
    if (a[i] > a[j]) {
      j = i;
    }
  }
  return j;
}

#ifdef DEBUG
#define dbg(...) out(__VA_ARGS__);
#else
#define dbg(...) ;
#endif

#ifdef DEBUG
#define dbg_assert(...) \
  assert(__VA_ARGS__);
#else
#define dbg_assert(...) ;
#endif

// define yes/no
#define yesno(y, n) \
  void yes(bool f = 1) { \
    out(f ? #y : #n); \
  } \
  void no() { \
    out(#n); \
  }

yesno(yes, no);

// yesno(Yes, No);
// yesno(YES, NO);

template <class T>
T norm(T m, T x) {
  assert(m > 0);
  if (x < -m || x >= m) {
    x %= m;
  }
  if (x < 0) {
    x += m;
  }
  return x;
}

template <class T>
tuple<T, T, T> egcd(T a, T b) {
  if (!b) {
    if (a < 0) {
      return {-a, -1, 0};
    }
    return {a, 1, 0};
  };
  T q = a / b;
  auto [g, x, y] = egcd(b, a - b * q);
  return {g, y, x - q * y};
}

template <class T>
auto factorize(T n)
  -> vec<pair<T, int>> {
  vec<pair<T, int>> f;
  for (T i = 2; i * i <= n; ++i) {
    if (n % i) {
      continue;
    }
    int e = 0;
    do {
      ++e;
      n /= i;
    } while (n % i == 0);
    f.eb(i, e);
  }
  if (n != 1) {
    f.eb(n, 1);
  }
  return f;
}

int crt_mod(
  vec<int> m,
  const vec<int> &r,
  int mod
) {
  int l = len(m);
  assert(len(r) == l);
  m.pb(mod);
  vec<ll> p(l + 1, 1), x(l + 1);
  range(i, l) {
    ll n = m[i];
    assert(n > 0);
    auto [g, ip, _] = egcd(p[i], n);
    assert(g == 1);
    ll t = (r[i] - x[i]) % n * ip;
    t = norm(n, t);
    range(j, i + 1, l + 1) {
      (x[j] += t * p[j]) %= m[j];
      (p[j] *= n) %= m[j];
    }
  }
  return x.back();
}

// inplace
template <class T>
void to_coprime(vec<pair<T, T>> &mr) {
  unordered_map<T, pair<T, T>> f;
  for (auto &&[m, r] : mr) {
    for (auto &&[p, e] : factorize(m)) {
      T n = 1;
      rep(e) n *= p;
      T b = r % n;
      if (!f.count(p)) {
        f[p] = {n, b};
        continue;
      }
      auto &[l, a] = f[p];
      if (l < n) {
        swap(l, n);
        swap(a, b);
      }
      if (a % n != b) {
        mr.clear();
        return;
      }
    }
  }
  mr.clear();
  mr.reserve(len(f));
  for (auto &&[p, x] : f) {
    mr.pb(x);
  }
}

void solve() {
  int n;
  in(n);
  vec<pair<int, int>> mr(n);
  range(i, n) {
    in(mr[i].second, mr[i].first);
  }
  to_coprime(mr);
  n = len(mr);
  if (!n) {
    out(-1);
    return;
  }
  vec<int> r(n), m(n);
  range(i, n) {
    auto [l, a] = mr[i];
    m[i] = l;
    r[i] = a;
  }
  const int mod = 1'000'000'007;
  if (max(r) != 0) {
    out(crt_mod(m, r, mod));
    return;
  }
  ll l = 1;
  iter(x, m) {
    l *= x;
    l %= mod;
  }
  out(l);
}

int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  // cout << setprecision(16);
  int t = 1;
  // in(t);
  while (t--) {
    solve();
  }
}