結果

問題 No.2262 Fractions
コンテスト
ユーザー miscalc
提出日時 2023-04-07 22:32:32
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
TLE  
実行時間 -
コード長 5,388 bytes
コンパイル時間 5,042 ms
コンパイル使用メモリ 265,228 KB
最終ジャッジ日時 2025-02-12 01:59:31
ジャッジサーバーID
（参考情報） 		judge5 / judge1
このコードへのチャレンジ
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ファイルパターン 結果
sample TLE * 1
other AC * 3 TLE * 42
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 # 

#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = double;
using pll = pair<ll, ll>;
using tlll = tuple<ll, ll, ll>;
constexpr ll INF = 1LL << 60;
template<class T> bool chmin(T& a, T b) {if (a > b) {a = b; return true;} return false;}
template<class T> bool chmax(T& a, T b) {if (a < b) {a = b; return true;} return false;}
ll safemod(ll A, ll M) {ll res = A % M; if (res < 0) res += M; return res;}
ll divfloor(ll A, ll B) {if (B < 0) A = -A, B = -B; return (A - safemod(A, B)) / B;}
ll divceil(ll A, ll B) {if (B < 0) A = -A, B = -B; return divfloor(A + B - 1, B);}
ll pow_ll(ll A, ll B) {if (A == 0 || A == 1) {return A;} if (A == -1) {return B & 1 ? -1 : 1;} ll res = 1; for (int i = 0; i < B; i++) {res *= A;} return res;}
ll mul_limited(ll A, ll B, ll M = INF) { return A > M / B ? M : A * B; }
ll pow_limited(ll A, ll B, ll M = INF) { if (A == 0 || A == 1) {return A;} ll res = 1; for (int i = 0; i < B; i++) {if (res > M / A) return M; res *= A;} return res;}
ll logfloor(ll A, ll B) {assert(A >= 2); ll res = 0; for (ll tmp = 1; tmp <= B / A; tmp *= A) {res++;} return res;}
ll logceil(ll A, ll B) {assert(A >= 2); ll res = 0; for (ll tmp = 1; tmp < B; tmp *= A) {res++;} return res;}
ll arisum_ll(ll a, ll d, ll n) { return n * a + (n & 1 ? ((n - 1) >> 1) * n : (n >> 1) * (n - 1)) * d; }
ll arisum2_ll(ll a, ll l, ll n) { return n & 1 ? ((a + l) >> 1) * n : (n >> 1) * (a + l); }
ll arisum3_ll(ll a, ll l, ll d) { assert((l - a) % d == 0); return arisum2_ll(a, l, (l - a) / d + 1); }
template<class T> void unique(vector<T> &V) {V.erase(unique(V.begin(), V.end()), V.end());}
template<class T> void sortunique(vector<T> &V) {sort(V.begin(), V.end()); V.erase(unique(V.begin(), V.end()), V.end());}
#define FINALANS(A) do {cout << (A) << '\n'; exit(0);} while (false)
template<class T> void printvec(const vector<T> &V) {int _n = V.size(); for (int i = 0; i < _n; i++) cout << V[i] << (i == _n - 1 ? "" : " ");cout << '\n';}
template<class T> void printvect(const vector<T> &V) {for (auto v : V) cout << v << '\n';}
template<class T> void printvec2(const vector<vector<T>> &V) {for (auto &v : V) printvec(v);}
//*
#include <atcoder/all>
using namespace atcoder;
using mint = modint998244353;
//using mint = modint1000000007;
//using mint = modint;
//*/

// https://qiita.com/drken/items/3beb679e54266f20ab63
class eratosthenes
{
public:
  int N;
  vector<bool> isprime;
  vector<int> primecount;
  vector<int> primes;
  vector<int> minfactor;
  vector<int> mobius;

  eratosthenes(int n)
  {
    N = n;
    isprime.assign(n + 1, true);
    primecount.assign(n + 1, 0);
    minfactor.assign(n + 1, -1);
    mobius.assign(n + 1, 1);
    isprime[0] = false, isprime[1] = false;
    minfactor[1] = 1;

    for (int p = 2; p <= n; p++)
    {
      primecount[p] = primecount[p - 1];
      if (!isprime[p])
        continue;
      primecount[p]++;

      primes.emplace_back(p);
      minfactor[p] = p;
      mobius[p] = -1;

      for (int k = 2, q = 2 * p; q <= n; k++, q += p)
      {
        isprime[q] = false;
        if (minfactor[q] == -1)
          minfactor[q] = p;
        if (k % p == 0)
          mobius[q] = 0;
        else
          mobius[q] = -mobius[q];
      }
    }
  }

  vector<pll> factorize(ll n)
  {
    vector<pll> ret;
    while (n > 1)
    {
      int p = minfactor[n];
      int e = 0;
      while (minfactor[n] == p)
      {
        n /= p;
        e++;
      }
      ret.emplace_back(make_pair(p, e));
    }
    return ret;
  }

  ll L;
  vector<vector<ll>> primefactors2;
  void rangesieve(ll l, ll r)
  {
    L = l;
    ll R = r;
    primefactors2.resize(R - L + 1);
    for (ll p = 2; p * p <= R; p++)
    {
      if (!isprime[p])
        continue;
      for (ll v = divceil(L, p) * p; v <= R; v += p)
      {
        primefactors2[v - L].emplace_back(p);
      }
    }
  }
  vector<pll> factorize2(ll v)
  {
    vector<pll> ret;
    ll vv = v;
    const auto &pfs = primefactors2[v - L];
    for (auto p : pfs)
    {
      ll e = 0;
      while (vv % p == 0)
      {
        vv /= p;
        e++;
      }
      ret.emplace_back(make_pair(p, e));
    }
    if (vv > 1)
      ret.emplace_back(make_pair(vv, 1));
    return ret;
  }
};

eratosthenes er(300010);
ll f(ll n, ll x)
{
  auto pes = er.factorize(x);
  ll k = pes.size();

  ll ans = 0;
  for (ll b = 0; b < (1LL << k); b++)
  {
    ll mul = 1;
    for (ll i = 0; i < k; i++)
    {
      if (b & (1LL << i))
        mul *= pes.at(i).first;
    }
    ans += (__builtin_popcount(b) % 2 == 0 ? 1 : -1) * (n / mul);
  }
  return ans;
}

string solve(ll N, ll K)
{
  if (K == 1)
    return "1/" + to_string(N);
  
  auto isok = [&](ld x) -> bool
  {
    ll cnt = 0;
    for (ll q = 1; q <= N; q++)
    {
      ll n = q * x;
      cnt += f(min(N, n), q);
    }
    return cnt >= K;
  };

  if (!isok(N))
    return "-1";
  ld ng = 1 / (ld)N, ok = N;
  for (int i = 0; i < 100; i++)
  {
    ld mid = (ok + ng) / 2;
    if (isok(mid))
      ok = mid;
    else
      ng = mid;
  }

  string ans = "";
  ld mn = INF;
  for (ll q = 1; q <= N; q++)
  {
    ll p = round(q * ok);
    if (!(1 <= p && p <= N))
      continue;
    ld tmp = abs(ok - (ld)p / (ld)q);
    if (chmin(mn, tmp))
      ans = to_string(p) + "/" + to_string(q);
  }
  return ans;
}

int main()
{
  ll T;
  cin >> T;
  while (T--)
  {
    ll N, K;
    cin >> N >> K;
    cout << solve(N, K) << endl;
  }
}
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