結果

問題 No.2262 Fractions
ユーザー siganaisiganai
提出日時 2023-04-08 19:21:37
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 227 ms / 2,000 ms
コード長 8,102 bytes
コンパイル時間 2,292 ms
コンパイル使用メモリ 211,360 KB
実行使用メモリ 7,044 KB
最終ジャッジ日時 2024-05-05 07:31:28
合計ジャッジ時間 10,815 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge1
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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 142 ms
5,760 KB
testcase_01 AC 48 ms
5,376 KB
testcase_02 AC 46 ms
5,376 KB
testcase_03 AC 45 ms
5,376 KB
testcase_04 AC 48 ms
5,376 KB
testcase_05 AC 43 ms
5,376 KB
testcase_06 AC 49 ms
5,376 KB
testcase_07 AC 47 ms
5,376 KB
testcase_08 AC 44 ms
5,376 KB
testcase_09 AC 48 ms
5,376 KB
testcase_10 AC 48 ms
5,376 KB
testcase_11 AC 127 ms
5,376 KB
testcase_12 AC 125 ms
5,376 KB
testcase_13 AC 126 ms
5,376 KB
testcase_14 AC 127 ms
5,376 KB
testcase_15 AC 125 ms
5,376 KB
testcase_16 AC 67 ms
5,376 KB
testcase_17 AC 65 ms
5,376 KB
testcase_18 AC 66 ms
5,376 KB
testcase_19 AC 196 ms
5,712 KB
testcase_20 AC 181 ms
5,396 KB
testcase_21 AC 197 ms
5,744 KB
testcase_22 AC 181 ms
5,384 KB
testcase_23 AC 155 ms
5,376 KB
testcase_24 AC 226 ms
6,896 KB
testcase_25 AC 223 ms
6,944 KB
testcase_26 AC 217 ms
6,784 KB
testcase_27 AC 223 ms
6,912 KB
testcase_28 AC 215 ms
6,884 KB
testcase_29 AC 223 ms
7,036 KB
testcase_30 AC 222 ms
7,036 KB
testcase_31 AC 227 ms
7,040 KB
testcase_32 AC 227 ms
6,912 KB
testcase_33 AC 221 ms
7,044 KB
testcase_34 AC 221 ms
6,912 KB
testcase_35 AC 227 ms
6,944 KB
testcase_36 AC 227 ms
6,916 KB
testcase_37 AC 6 ms
5,376 KB
testcase_38 AC 7 ms
5,376 KB
testcase_39 AC 195 ms
5,376 KB
testcase_40 AC 195 ms
5,376 KB
testcase_41 AC 199 ms
5,492 KB
testcase_42 AC 195 ms
5,376 KB
testcase_43 AC 195 ms
5,376 KB
testcase_44 AC 227 ms
6,944 KB
testcase_45 AC 222 ms
6,916 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 "main.cpp"
//#pragma GCC target("avx")
//#pragma GCC optimize("O3")
//#pragma GCC optimize("unroll-loops")
#include<bits/stdc++.h>

#ifdef LOCAL
#include <debug.hpp>
#define debug(...) debug_print::multi_print(#__VA_ARGS__, __VA_ARGS__)
#else
#define debug(...) (static_cast<void>(0))
#endif
using namespace std;
using ll = long long;
using ld = long double;
using pll = pair<ll, ll>;
using pii = pair<int, int>;
using vi = vector<int>;
using vvi = vector<vi>;
using vvvi = vector<vvi>;
using vl = vector<ll>;
using vvl = vector<vl>;
using vvvl = vector<vvl>;
using vpii = vector<pii>;
using vpll = vector<pll>;
using vs = vector<string>;
template<class T> using pq = priority_queue<T, vector<T>, greater<T>>;
#define overload4(_1, _2, _3, _4, name, ...) name
#define overload3(a,b,c,name,...) name
#define rep1(n) for (ll UNUSED_NUMBER = 0; UNUSED_NUMBER < (n); ++UNUSED_NUMBER)
#define rep2(i, n) for (ll i = 0; i < (n); ++i)
#define rep3(i, a, b) for (ll i = (a); i < (b); ++i)
#define rep4(i, a, b, c) for (ll i = (a); i < (b); i += (c))
#define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__)
#define rrep1(n) for(ll i = (n) - 1;i >= 0;i--)
#define rrep2(i,n) for(ll i = (n) - 1;i >= 0;i--)
#define rrep3(i,a,b) for(ll i = (b) - 1;i >= (a);i--)
#define rrep4(i,a,b,c) for(ll i = (a) + ((b)-(a)-1) / (c) * (c);i >= (a);i -= c)
#define rrep(...) overload4(__VA_ARGS__, rrep4, rrep3, rrep2, rrep1)(__VA_ARGS__)
#define all1(i) begin(i) , end(i)
#define all2(i,a) begin(i) , begin(i) + a
#define all3(i,a,b) begin(i) + a , begin(i) + b
#define all(...) overload3(__VA_ARGS__, all3, all2, all1)(__VA_ARGS__)
#define sum(...) accumulate(all(__VA_ARGS__),0LL)
template<class T> bool chmin(T &a, const T &b){ if(a > b){ a = b; return 1; } else return 0; }
template<class T> bool chmax(T &a, const T &b){ if(a < b){ a = b; return 1; } else return 0; }
template<class T> auto min(const T& a){ return *min_element(all(a)); }
template<class T> auto max(const T& a){ return *max_element(all(a)); }
template<class... Ts> void in(Ts&... t);
#define INT(...) int __VA_ARGS__; in(__VA_ARGS__)
#define LL(...) ll __VA_ARGS__; in(__VA_ARGS__)
#define STR(...) string __VA_ARGS__; in(__VA_ARGS__)
#define CHR(...) char __VA_ARGS__; in(__VA_ARGS__)
#define DBL(...) double __VA_ARGS__; in(__VA_ARGS__)
#define LD(...) ld __VA_ARGS__; in(__VA_ARGS__)
#define VEC(type, name, size) vector<type> name(size); in(name)
#define VV(type, name, h, w) vector<vector<type>> name(h, vector<type>(w)); in(name)
ll intpow(ll a, ll b){ ll ans = 1; while(b){if(b & 1) ans *= a; a *= a; b /= 2;} return ans;}
ll modpow(ll a, ll b, ll p){ ll ans = 1; a %= p;if(a < 0) a += p;while(b){ if(b & 1) (ans *= a) %= p; (a *= a) %= p; b /= 2; } return ans; }
ll GCD(ll a,ll b) { if(a == 0 || b == 0) return 0; if(a % b == 0) return b; else return GCD(b,a%b);}
ll LCM(ll a,ll b) { if(a == 0) return b; if(b == 0) return a;return a / GCD(a,b) * b;}
namespace IO{
#define VOID(a) decltype(void(a))
struct setting{ setting(){cin.tie(nullptr); ios::sync_with_stdio(false);fixed(cout); cout.precision(30);}} setting;
template<int I> struct P : P<I-1>{};
template<> struct P<0>{};
template<class T> void i(T& t){ i(t, P<3>{}); }
void i(vector<bool>::reference t, P<3>){ int a; i(a); t = a; }
template<class T> auto i(T& t, P<2>) -> VOID(cin >> t){ cin >> t; }
template<class T> auto i(T& t, P<1>) -> VOID(begin(t)){ for(auto&& x : t) i(x); }
template<class T, size_t... idx> void ituple(T& t, index_sequence<idx...>){
    in(get<idx>(t)...);}
template<class T> auto i(T& t, P<0>) -> VOID(tuple_size<T>{}){
    ituple(t, make_index_sequence<tuple_size<T>::value>{});}
#undef VOID
}
#define unpack(a) (void)initializer_list<int>{(a, 0)...}
template<class... Ts> void in(Ts&... t){ unpack(IO :: i(t)); }
#undef unpack
static const double PI = 3.1415926535897932;
template <class F> struct REC {
    F f;
    REC(F &&f_) : f(forward<F>(f_)) {}
    template <class... Args> auto operator()(Args &&...args) const { return f(*this, forward<Args>(args)...); }};
//constexpr int mod = 1000000007;
constexpr int mod = 998244353;
vector< int > euler_phi_table(int n) {
  vector< int > euler(n + 1);
  for(int i = 0; i <= n; i++) {
    euler[i] = i;
  }
  for(int i = 2; i <= n; i++) {
    if(euler[i] == i) {
      for(int j = i; j <= n; j += i) {
        euler[j] = euler[j] / i * (i - 1);
      }
    }
  }
  return euler;
}
#line 2 "library/prime/prime_enumerate.hpp"
vector<int> prime_enumerate(int N) {
    vector<bool> sieve(N / 3 + 1, 1);
    for (int p = 5, d = 4, i = 1, sqn = sqrt(N); p <= sqn; p += d = 6 - d, i++) {
        if (!sieve[i]) continue;
        for (int q = p * p / 3, r = d * p / 3 + (d * p % 3 == 2), s = 2 * p,
                qe = sieve.size();
            q < qe; q += r = s - r)
        sieve[q] = 0;
    }
    vector<int> ret{2, 3};
    for (int p = 5, d = 4, i = 1; p <= N; p += d = 6 - d, i++)
        if (sieve[i]) ret.push_back(p);
    while (!ret.empty() && ret.back() > N) ret.pop_back();
    return ret;
}
#line 3 "library/multiplicative-function/divisor-multiple-transform.hpp"
struct divisor_transform {
    template <typename T>
    static void zeta_transform(vector<T> &a) {
        int N = a.size() - 1;
        auto sieve = prime_enumerate(N);
        for (auto &p : sieve) for (int k = 1; k * p <= N; ++k) a[k * p] += a[k];
    }
    template <typename T>
    static void mobius_transform(vector<T> &a) {
        int N = a.size() - 1;
        auto sieve = prime_enumerate(N);
        for (auto &p : sieve) for (int k = N / p; k > 0; --k) a[k * p] -= a[k];
    }

    template <typename T>
    static void zeta_transform(map<long long, T> &a) {
        for (auto p = rbegin(a); p != rend(a); p++) for (auto &x : a) {
            if (p->first == x.first) break;
            if (p->first % x.first == 0) p->second += x.second;
        }
  }
    template <typename T>
    static void mobius_transform(map<long long, T> &a) {
        for (auto &x : a) for (auto p = rbegin(a); p != rend(a); p++) {
            if (x.first == p->first) break;
            if (p->first % x.first == 0) p->second -= x.second;
        }
    }
};

struct multiple_transform {
    template <typename T>
    static void zeta_transform(vector<T> &a) {
        int N = a.size() - 1;
        auto sieve = prime_enumerate(N);
        for (auto &p : sieve) for (int k = N / p; k > 0; --k) a[k] += a[k * p];
    }
    template <typename T>
    static void mobius_transform(vector<T> &a) {
        int N = a.size() - 1;
        auto sieve = prime_enumerate(N);
        for (auto &p : sieve) for (int k = 1; k * p <= N; ++k) a[k] -= a[k * p];
    }

    template <typename T>
    static void zeta_transform(map<long long, T> &a) {
        for (auto &x : a) 
            for (auto p = rbegin(a); p->first != x.first; p++) 
                if (p->first % x.first == 0) x.second += p->second;
    }
    template <typename T>
    static void mobius_transform(map<long long, T> &a) {
        for (auto p1 = rbegin(a); p1 != rend(a); p1++)
            for (auto p2 = rbegin(a); p2 != p1; p2++) 
                if (p2->first % p1->first == 0) p1->second -= p2->second;
    }
};
#line 101 "main.cpp"
void solve() {
    INT(n);
    LL(k);
    auto ret = euler_phi_table(n);
    ll cnt = 0;
    rep(i,1,n+1) cnt += ret[i];
    if(2 * cnt - 1 < k) {
        cout << -1 << '\n';
        return;
    }
    int rv_flg = 0;
    if(cnt < k) {
        rv_flg = 1;
        k = 2 * cnt - k;
    }
    ll ng = 0,ok = 1LL * n * n;
    while(ok - ng > 1) {
        ll mid = (ok + ng) / 2;
        vl C(n+1);
        rep(i,1,n+1) {
            C[i] = mid * i / (1LL * n * n);
        }
        divisor_transform::mobius_transform(C);
        ll SU = sum(C);
        if(SU >= k) ok = mid;
        else ng = mid;
    }
    ll num = 0,den = n;
    rep(i,1,n+1) {
        ll tmp = ok * i / (1LL * n * n);
        if(num * i < den * tmp) {
            num = tmp;
            den = i;
        }
    }
    if(rv_flg) cout << den << "/" << num << '\n';
    else cout << num << "/" << den << '\n';
}
 
int main() {
    INT(TT);
    while(TT--) solve();
}
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