結果

問題 No.2262 Fractions
ユーザー maspymaspy
提出日時 2023-04-07 22:46:12
言語 C++23
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 385 ms / 2,000 ms
コード長 17,297 bytes
コンパイル時間 4,054 ms
コンパイル使用メモリ 287,944 KB
実行使用メモリ 5,376 KB
最終ジャッジ日時 2024-05-05 07:23:15
合計ジャッジ時間 14,936 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge2
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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 167 ms
5,248 KB
testcase_01 AC 108 ms
5,248 KB
testcase_02 AC 97 ms
5,376 KB
testcase_03 AC 99 ms
5,376 KB
testcase_04 AC 104 ms
5,376 KB
testcase_05 AC 93 ms
5,376 KB
testcase_06 AC 109 ms
5,376 KB
testcase_07 AC 100 ms
5,376 KB
testcase_08 AC 96 ms
5,376 KB
testcase_09 AC 101 ms
5,376 KB
testcase_10 AC 95 ms
5,376 KB
testcase_11 AC 201 ms
5,376 KB
testcase_12 AC 215 ms
5,376 KB
testcase_13 AC 205 ms
5,376 KB
testcase_14 AC 219 ms
5,376 KB
testcase_15 AC 196 ms
5,376 KB
testcase_16 AC 41 ms
5,376 KB
testcase_17 AC 42 ms
5,376 KB
testcase_18 AC 42 ms
5,376 KB
testcase_19 AC 351 ms
5,376 KB
testcase_20 AC 237 ms
5,376 KB
testcase_21 AC 300 ms
5,376 KB
testcase_22 AC 267 ms
5,376 KB
testcase_23 AC 281 ms
5,376 KB
testcase_24 AC 223 ms
5,376 KB
testcase_25 AC 307 ms
5,376 KB
testcase_26 AC 314 ms
5,376 KB
testcase_27 AC 333 ms
5,376 KB
testcase_28 AC 302 ms
5,376 KB
testcase_29 AC 296 ms
5,376 KB
testcase_30 AC 278 ms
5,376 KB
testcase_31 AC 347 ms
5,376 KB
testcase_32 AC 385 ms
5,376 KB
testcase_33 AC 324 ms
5,376 KB
testcase_34 AC 201 ms
5,376 KB
testcase_35 AC 99 ms
5,376 KB
testcase_36 AC 98 ms
5,376 KB
testcase_37 AC 7 ms
5,376 KB
testcase_38 AC 8 ms
5,376 KB
testcase_39 AC 228 ms
5,376 KB
testcase_40 AC 286 ms
5,376 KB
testcase_41 AC 306 ms
5,376 KB
testcase_42 AC 234 ms
5,376 KB
testcase_43 AC 207 ms
5,376 KB
testcase_44 AC 339 ms
5,376 KB
testcase_45 AC 340 ms
5,376 KB
権限があれば一括ダウンロードができます

ソースコード

diff # 

#line 1 "/home/maspy/compro/library/my_template.hpp"
#if defined(LOCAL)
#include <my_template_compiled.hpp>
#else
#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")

#include <bits/stdc++.h>

using namespace std;

using ll = long long;
using u32 = unsigned int;
using u64 = unsigned long long;
using i128 = __int128;

template <class T>
constexpr T infty = 0;
template <>
constexpr int infty<int> = 1'000'000'000;
template <>
constexpr ll infty<ll> = ll(infty<int>) * infty<int> * 2;
template <>
constexpr u32 infty<u32> = infty<int>;
template <>
constexpr u64 infty<u64> = infty<ll>;
template <>
constexpr i128 infty<i128> = i128(infty<ll>) * infty<ll>;
template <>
constexpr double infty<double> = infty<ll>;
template <>
constexpr long double infty<long double> = infty<ll>;

using pi = pair<ll, ll>;
using vi = vector<ll>;
template <class T>
using vc = vector<T>;
template <class T>
using vvc = vector<vc<T>>;
template <class T>
using vvvc = vector<vvc<T>>;
template <class T>
using vvvvc = vector<vvvc<T>>;
template <class T>
using vvvvvc = vector<vvvvc<T>>;
template <class T>
using pq = priority_queue<T>;
template <class T>
using pqg = priority_queue<T, vector<T>, greater<T>>;

#define vv(type, name, h, ...) \
  vector<vector<type>> name(h, vector<type>(__VA_ARGS__))
#define vvv(type, name, h, w, ...)   \
  vector<vector<vector<type>>> name( \
      h, vector<vector<type>>(w, vector<type>(__VA_ARGS__)))
#define vvvv(type, name, a, b, c, ...)       \
  vector<vector<vector<vector<type>>>> name( \
      a, vector<vector<vector<type>>>(       \
             b, vector<vector<type>>(c, vector<type>(__VA_ARGS__))))

// https://trap.jp/post/1224/
#define FOR1(a) for (ll _ = 0; _ < ll(a); ++_)
#define FOR2(i, a) for (ll i = 0; i < ll(a); ++i)
#define FOR3(i, a, b) for (ll i = a; i < ll(b); ++i)
#define FOR4(i, a, b, c) for (ll i = a; i < ll(b); i += (c))
#define FOR1_R(a) for (ll i = (a)-1; i >= ll(0); --i)
#define FOR2_R(i, a) for (ll i = (a)-1; i >= ll(0); --i)
#define FOR3_R(i, a, b) for (ll i = (b)-1; i >= ll(a); --i)
#define overload4(a, b, c, d, e, ...) e
#define overload3(a, b, c, d, ...) d
#define FOR(...) overload4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__)
#define FOR_R(...) overload3(__VA_ARGS__, FOR3_R, FOR2_R, FOR1_R)(__VA_ARGS__)

#define FOR_subset(t, s) \
  for (ll t = (s); t >= 0; t = (t == 0 ? -1 : (t - 1) & (s)))
#define all(x) x.begin(), x.end()
#define len(x) ll(x.size())
#define elif else if

#define eb emplace_back
#define mp make_pair
#define mt make_tuple
#define fi first
#define se second

#define stoi stoll

int popcnt(int x) { return __builtin_popcount(x); }
int popcnt(u32 x) { return __builtin_popcount(x); }
int popcnt(ll x) { return __builtin_popcountll(x); }
int popcnt(u64 x) { return __builtin_popcountll(x); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 1, 2)
int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(u32 x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
int topbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 0, 2)
int lowbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(u32 x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }
int lowbit(u64 x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }

template <typename T, typename U>
T ceil(T x, U y) {
  return (x > 0 ? (x + y - 1) / y : x / y);
}
template <typename T, typename U>
T floor(T x, U y) {
  return (x > 0 ? x / y : (x - y + 1) / y);
}
template <typename T, typename U>
pair<T, T> divmod(T x, U y) {
  T q = floor(x, y);
  return {q, x - q * y};
}

template <typename T, typename U>
T SUM(const vector<U> &A) {
  T sum = 0;
  for (auto &&a: A) sum += a;
  return sum;
}

#define MIN(v) *min_element(all(v))
#define MAX(v) *max_element(all(v))
#define LB(c, x) distance((c).begin(), lower_bound(all(c), (x)))
#define UB(c, x) distance((c).begin(), upper_bound(all(c), (x)))
#define UNIQUE(x) \
  sort(all(x)), x.erase(unique(all(x)), x.end()), x.shrink_to_fit()

template <typename T>
T POP(deque<T> &que) {
  T a = que.front();
  que.pop_front();
  return a;
}
template <typename T>
T POP(pq<T> &que) {
  T a = que.top();
  que.pop();
  return a;
}
template <typename T>
T POP(pqg<T> &que) {
  assert(!que.empty());
  T a = que.top();
  que.pop();
  return a;
}
template <typename T>
T POP(vc<T> &que) {
  assert(!que.empty());
  T a = que.back();
  que.pop_back();
  return a;
}

template <typename F>
ll binary_search(F check, ll ok, ll ng, bool check_ok = true) {
  if (check_ok) assert(check(ok));
  while (abs(ok - ng) > 1) {
    auto x = (ng + ok) / 2;
    tie(ok, ng) = (check(x) ? mp(x, ng) : mp(ok, x));
  }
  return ok;
}
template <typename F>
double binary_search_real(F check, double ok, double ng, int iter = 100) {
  FOR(iter) {
    double x = (ok + ng) / 2;
    tie(ok, ng) = (check(x) ? mp(x, ng) : mp(ok, x));
  }
  return (ok + ng) / 2;
}

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

// ? は -1
vc<int> s_to_vi(const string &S, char first_char) {
  vc<int> A(S.size());
  FOR(i, S.size()) { A[i] = (S[i] != '?' ? S[i] - first_char : -1); }
  return A;
}

template <typename T, typename U>
vector<T> cumsum(vector<U> &A, int off = 1) {
  int N = A.size();
  vector<T> B(N + 1);
  FOR(i, N) { B[i + 1] = B[i] + A[i]; }
  if (off == 0) B.erase(B.begin());
  return B;
}

// stable sort
template <typename T>
vector<int> argsort(const vector<T> &A) {
  vector<int> ids(len(A));
  iota(all(ids), 0);
  sort(all(ids),
       [&](int i, int j) { return (A[i] == A[j] ? i < j : A[i] < A[j]); });
  return ids;
}

// A[I[0]], A[I[1]], ...
template <typename T>
vc<T> rearrange(const vc<T> &A, const vc<int> &I) {
  vc<T> B(len(I));
  FOR(i, len(I)) B[i] = A[I[i]];
  return B;
}
#endif
#line 1 "/home/maspy/compro/library/other/io.hpp"
// based on yosupo's fastio
#include <unistd.h>

namespace fastio {
#define FASTIO
// クラスが read(), print() を持っているかを判定するメタ関数
struct has_write_impl {
  template <class T>
  static auto check(T &&x) -> decltype(x.write(), std::true_type{});

  template <class T>
  static auto check(...) -> std::false_type;
};

template <class T>
class has_write : public decltype(has_write_impl::check<T>(std::declval<T>())) {
};

struct has_read_impl {
  template <class T>
  static auto check(T &&x) -> decltype(x.read(), std::true_type{});

  template <class T>
  static auto check(...) -> std::false_type;
};

template <class T>
class has_read : public decltype(has_read_impl::check<T>(std::declval<T>())) {};

struct Scanner {
  FILE *fp;
  char line[(1 << 15) + 1];
  size_t st = 0, ed = 0;
  void reread() {
    memmove(line, line + st, ed - st);
    ed -= st;
    st = 0;
    ed += fread(line + ed, 1, (1 << 15) - ed, fp);
    line[ed] = '\0';
  }
  bool succ() {
    while (true) {
      if (st == ed) {
        reread();
        if (st == ed) return false;
      }
      while (st != ed && isspace(line[st])) st++;
      if (st != ed) break;
    }
    if (ed - st <= 50) {
      bool sep = false;
      for (size_t i = st; i < ed; i++) {
        if (isspace(line[i])) {
          sep = true;
          break;
        }
      }
      if (!sep) reread();
    }
    return true;
  }
  template <class T, enable_if_t<is_same<T, string>::value, int> = 0>
  bool read_single(T &ref) {
    if (!succ()) return false;
    while (true) {
      size_t sz = 0;
      while (st + sz < ed && !isspace(line[st + sz])) sz++;
      ref.append(line + st, sz);
      st += sz;
      if (!sz || st != ed) break;
      reread();
    }
    return true;
  }
  template <class T, enable_if_t<is_integral<T>::value, int> = 0>
  bool read_single(T &ref) {
    if (!succ()) return false;
    bool neg = false;
    if (line[st] == '-') {
      neg = true;
      st++;
    }
    ref = T(0);
    while (isdigit(line[st])) { ref = 10 * ref + (line[st++] & 0xf); }
    if (neg) ref = -ref;
    return true;
  }
  template <typename T,
            typename enable_if<has_read<T>::value>::type * = nullptr>
  inline bool read_single(T &x) {
    x.read();
    return true;
  }
  bool read_single(double &ref) {
    string s;
    if (!read_single(s)) return false;
    ref = std::stod(s);
    return true;
  }
  bool read_single(char &ref) {
    string s;
    if (!read_single(s) || s.size() != 1) return false;
    ref = s[0];
    return true;
  }
  template <class T>
  bool read_single(vector<T> &ref) {
    for (auto &d: ref) {
      if (!read_single(d)) return false;
    }
    return true;
  }
  template <class T, class U>
  bool read_single(pair<T, U> &p) {
    return (read_single(p.first) && read_single(p.second));
  }
  template <size_t N = 0, typename T>
  void read_single_tuple(T &t) {
    if constexpr (N < std::tuple_size<T>::value) {
      auto &x = std::get<N>(t);
      read_single(x);
      read_single_tuple<N + 1>(t);
    }
  }
  template <class... T>
  bool read_single(tuple<T...> &tpl) {
    read_single_tuple(tpl);
    return true;
  }
  void read() {}
  template <class H, class... T>
  void read(H &h, T &... t) {
    bool f = read_single(h);
    assert(f);
    read(t...);
  }
  Scanner(FILE *fp) : fp(fp) {}
};

struct Printer {
  Printer(FILE *_fp) : fp(_fp) {}
  ~Printer() { flush(); }

  static constexpr size_t SIZE = 1 << 15;
  FILE *fp;
  char line[SIZE], small[50];
  size_t pos = 0;
  void flush() {
    fwrite(line, 1, pos, fp);
    pos = 0;
  }
  void write(const char val) {
    if (pos == SIZE) flush();
    line[pos++] = val;
  }
  template <class T, enable_if_t<is_integral<T>::value, int> = 0>
  void write(T val) {
    if (pos > (1 << 15) - 50) flush();
    if (val == 0) {
      write('0');
      return;
    }
    if (val < 0) {
      write('-');
      val = -val; // todo min
    }
    size_t len = 0;
    while (val) {
      small[len++] = char(0x30 | (val % 10));
      val /= 10;
    }
    for (size_t i = 0; i < len; i++) { line[pos + i] = small[len - 1 - i]; }
    pos += len;
  }
  void write(const string s) {
    for (char c: s) write(c);
  }
  void write(const char *s) {
    size_t len = strlen(s);
    for (size_t i = 0; i < len; i++) write(s[i]);
  }
  void write(const double x) {
    ostringstream oss;
    oss << fixed << setprecision(15) << x;
    string s = oss.str();
    write(s);
  }
  void write(const long double x) {
    ostringstream oss;
    oss << fixed << setprecision(15) << x;
    string s = oss.str();
    write(s);
  }
  template <typename T,
            typename enable_if<has_write<T>::value>::type * = nullptr>
  inline void write(T x) {
    x.write();
  }
  template <class T>
  void write(const vector<T> val) {
    auto n = val.size();
    for (size_t i = 0; i < n; i++) {
      if (i) write(' ');
      write(val[i]);
    }
  }
  template <class T, class U>
  void write(const pair<T, U> val) {
    write(val.first);
    write(' ');
    write(val.second);
  }
  template <size_t N = 0, typename T>
  void write_tuple(const T t) {
    if constexpr (N < std::tuple_size<T>::value) {
      if constexpr (N > 0) { write(' '); }
      const auto x = std::get<N>(t);
      write(x);
      write_tuple<N + 1>(t);
    }
  }
  template <class... T>
  bool write(tuple<T...> tpl) {
    write_tuple(tpl);
    return true;
  }
  template <class T, size_t S>
  void write(const array<T, S> val) {
    auto n = val.size();
    for (size_t i = 0; i < n; i++) {
      if (i) write(' ');
      write(val[i]);
    }
  }
  void write(i128 val) {
    string s;
    bool negative = 0;
    if (val < 0) {
      negative = 1;
      val = -val;
    }
    while (val) {
      s += '0' + int(val % 10);
      val /= 10;
    }
    if (negative) s += "-";
    reverse(all(s));
    if (len(s) == 0) s = "0";
    write(s);
  }
};
Scanner scanner = Scanner(stdin);
Printer printer = Printer(stdout);
void flush() { printer.flush(); }
void print() { printer.write('\n'); }
template <class Head, class... Tail>
void print(Head &&head, Tail &&... tail) {
  printer.write(head);
  if (sizeof...(Tail)) printer.write(' ');
  print(forward<Tail>(tail)...);
}

void read() {}
template <class Head, class... Tail>
void read(Head &head, Tail &... tail) {
  scanner.read(head);
  read(tail...);
}
} // namespace fastio
using fastio::print;
using fastio::flush;
using fastio::read;

#define INT(...)   \
  int __VA_ARGS__; \
  read(__VA_ARGS__)
#define LL(...)   \
  ll __VA_ARGS__; \
  read(__VA_ARGS__)
#define STR(...)      \
  string __VA_ARGS__; \
  read(__VA_ARGS__)
#define CHAR(...)   \
  char __VA_ARGS__; \
  read(__VA_ARGS__)
#define DBL(...)      \
  double __VA_ARGS__; \
  read(__VA_ARGS__)

#define VEC(type, name, size) \
  vector<type> name(size);    \
  read(name)
#define VV(type, name, h, w)                     \
  vector<vector<type>> name(h, vector<type>(w)); \
  read(name)

void YES(bool t = 1) { print(t ? "YES" : "NO"); }
void NO(bool t = 1) { YES(!t); }
void Yes(bool t = 1) { print(t ? "Yes" : "No"); }
void No(bool t = 1) { Yes(!t); }
void yes(bool t = 1) { print(t ? "yes" : "no"); }
void no(bool t = 1) { yes(!t); }
#line 2 "/home/maspy/compro/library/nt/primetable.hpp"

template <typename T = long long>
vc<T> primetable(int LIM) {
  ++LIM;
  const int S = 32768;
  static int done = 2;
  static vc<T> primes = {2}, sieve(S + 1);

  if (done < LIM) {
    done = LIM;

    primes = {2}, sieve.assign(S + 1, 0);
    const int R = LIM / 2;
    primes.reserve(int(LIM / log(LIM) * 1.1));
    vc<pair<int, int>> cp;
    for (int i = 3; i <= S; i += 2) {
      if (!sieve[i]) {
        cp.eb(i, i * i / 2);
        for (int j = i * i; j <= S; j += 2 * i) sieve[j] = 1;
      }
    }
    for (int L = 1; L <= R; L += S) {
      array<bool, S> block{};
      for (auto& [p, idx]: cp)
        for (int i = idx; i < S + L; idx = (i += p)) block[i - L] = 1;
      FOR(i, min(S, R - L)) if (!block[i]) primes.eb((L + i) * 2 + 1);
    }
  }
  int k = LB(primes, LIM + 1);
  return {primes.begin(), primes.begin() + k};
}
#line 3 "/home/maspy/compro/library/nt/zeta.hpp"

template <typename T>
void divisor_zeta(vc<T>& A) {
  assert(A[0] == 0);
  int N = len(A) - 1;
  auto P = primetable(N);
  for (auto&& p: P) { FOR3(x, 1, N / p + 1) A[p * x] += A[x]; }
}

template <typename T>
void divisor_mobius(vc<T>& A) {
  assert(A[0] == 0);
  int N = len(A) - 1;
  auto P = primetable(N);
  for (auto&& p: P) { FOR3_R(x, 1, N / p + 1) A[p * x] -= A[x]; }
}

template <typename T>
void multiplier_zeta(vc<T>& A) {
  assert(A[0] == 0);
  int N = len(A) - 1;
  auto P = primetable(N);
  for (auto&& p: P) { FOR3_R(x, 1, N / p + 1) A[x] += A[p * x]; }
}

template <typename T>
void multiplier_mobius(vc<T>& A) {
  assert(A[0] == 0);
  int N = len(A) - 1;
  auto P = primetable(N);
  for (auto&& p: P) { FOR3(x, 1, N / p + 1) A[x] -= A[p * x]; }
}
#line 2 "/home/maspy/compro/library/nt/mobius_table.hpp"

template<typename T>
vc<T> mobius_table(int N){
  vc<T> mu(N + 1);
  mu[1] = T(1);
  divisor_mobius(mu);
  return mu;
}
#line 2 "/home/maspy/compro/library/mod/floor_sum_of_linear.hpp"

// sum_{x in [L,R)} floor(ax + b, mod)
i128 floor_sum_of_linear(ll L, ll R, ll a, ll b, ll mod) {
  assert(L <= R);
  i128 res = 0;
  b += L * a;
  ll N = R - L;

  if (b < 0) {
    ll k = ceil(-b, mod);
    b += k * mod;
    res -= i128(N) * k;
  }

  while (N) {
    ll q;
    tie(q, a) = divmod(a, mod);
    res += i128(N) * (N - 1) / 2 * q;
    if (b >= mod) {
      tie(q, b) = divmod(b, mod);
      res += i128(N) * q;
    }
    tie(N, b) = divmod(a * N + b, mod);
    tie(a, mod) = mp(mod, a);
  }
  return res;
}
#line 5 "main.cpp"

void solve() {
  LL(N, K);
  vc<int> mu = mobius_table<int>(N);

  auto out = [&](ll a, ll b) -> void {
    string s;
    s += to_string(a);
    s += "/";
    s += to_string(b);
    print(s);
  };

  auto count = [&](ll a, ll b) -> ll {
    // a/b 以下の数え上げ
    assert(a <= b);
    ll ans = 0;
    ll pre_lim = 0;
    ll pre_f = 0;
    FOR(d, 1, N + 1) {
      if (mu[d] == 0) continue;
      ll lim = N / d;
      ll f = pre_f;
      if (lim != pre_lim) { f = floor_sum_of_linear(1, lim + 1, a, 0, b); }
      pre_lim = lim;
      pre_f = f;
      ans += mu[d] * f;
    }
    return ans;
  };

  ll base = count(1, 1) - 1;

  if (K == base + 1) { return out(1, 1); }
  if (K > 2 * base + 1) return print(-1);

  auto solve = [&](ll K) -> pi {
    assert(K <= base);
    ll a = 0, b = 1, c = 1, d = 1;
    // a/b 以下：K 未満
    // c/d 以下：K 以上
    while (1) {
      if (b + d > N) { break; }
      // (a/b,c/d) -> (a/b,a+kc/b+kd)
      ll k = binary_search(
          [&](ll k) -> bool { return count(a + k * c, b + k * d) < K; }, 0,
          (N - b) / d + 1);
      a += k * c, b += k * d;
      k = binary_search(
          [&](ll k) -> bool { return count(k * a + c, k * b + d) >= K; }, 0,
          (N - d) / b + 1);
      c += k * a;
      d += k * b;
    }
    return {c, d};
  };

  if (K <= base) {
    auto [a, b] = solve(K);
    return out(a, b);
  } else {
    K = 2 * base + 2 - K;
    auto [a, b] = solve(K);
    return out(b, a);
  }
}

signed main() {
  INT(T);
  FOR(T) solve();
  return 0;
}
0