結果

問題 No.2262 Fractions
ユーザー 👑 rin204rin204
提出日時 2024-11-16 01:24:57
言語 C++23
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 1,486 ms / 2,000 ms
コード長 11,975 bytes
コンパイル時間 3,731 ms
コンパイル使用メモリ 267,428 KB
実行使用メモリ 85,600 KB
最終ジャッジ日時 2024-11-16 01:25:49
合計ジャッジ時間 50,043 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge2
このコードへのチャレンジ
（要ログイン）

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 975 ms
85,428 KB
testcase_01 AC 282 ms
85,272 KB
testcase_02 AC 307 ms
85,420 KB
testcase_03 AC 279 ms
85,448 KB
testcase_04 AC 285 ms
85,396 KB
testcase_05 AC 289 ms
85,400 KB
testcase_06 AC 324 ms
85,432 KB
testcase_07 AC 288 ms
85,504 KB
testcase_08 AC 290 ms
85,416 KB
testcase_09 AC 292 ms
85,428 KB
testcase_10 AC 322 ms
85,408 KB
testcase_11 AC 796 ms
85,272 KB
testcase_12 AC 811 ms
85,492 KB
testcase_13 AC 796 ms
85,440 KB
testcase_14 AC 835 ms
85,412 KB
testcase_15 AC 800 ms
85,460 KB
testcase_16 AC 528 ms
85,492 KB
testcase_17 AC 510 ms
85,424 KB
testcase_18 AC 518 ms
85,396 KB
testcase_19 AC 1,297 ms
85,516 KB
testcase_20 AC 1,186 ms
85,444 KB
testcase_21 AC 1,331 ms
85,460 KB
testcase_22 AC 1,212 ms
85,276 KB
testcase_23 AC 1,080 ms
85,500 KB
testcase_24 AC 1,415 ms
85,472 KB
testcase_25 AC 1,400 ms
85,268 KB
testcase_26 AC 1,367 ms
85,396 KB
testcase_27 AC 1,416 ms
85,468 KB
testcase_28 AC 1,347 ms
85,456 KB
testcase_29 AC 1,405 ms
85,496 KB
testcase_30 AC 1,433 ms
85,484 KB
testcase_31 AC 1,486 ms
85,432 KB
testcase_32 AC 1,429 ms
85,468 KB
testcase_33 AC 1,402 ms
85,400 KB
testcase_34 AC 1,390 ms
85,420 KB
testcase_35 AC 1,434 ms
85,272 KB
testcase_36 AC 1,431 ms
85,276 KB
testcase_37 AC 216 ms
85,384 KB
testcase_38 AC 193 ms
85,420 KB
testcase_39 AC 1,301 ms
85,600 KB
testcase_40 AC 1,301 ms
85,400 KB
testcase_41 AC 1,326 ms
85,408 KB
testcase_42 AC 1,293 ms
85,396 KB
testcase_43 AC 1,297 ms
85,424 KB
testcase_44 AC 1,444 ms
85,472 KB
testcase_45 AC 1,411 ms
85,496 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 # 

// #pragma GCC target("avx2")
// #pragma GCC optimize("O3")
// #pragma GCC optimize("unroll-loops")
#include <bits/stdc++.h>
using namespace std;
// #define INTERACTIVE

namespace templates {
// type
using ll  = long long;
using ull = unsigned long long;
using Pii = pair<int, int>;
using Pil = pair<int, ll>;
using Pli = pair<ll, int>;
using Pll = pair<ll, ll>;
template <class T>
using pq = priority_queue<T>;
template <class T>
using qp = priority_queue<T, vector<T>, greater<T>>;
// clang-format off
#define vec(T, A, ...) vector<T> A(__VA_ARGS__);
#define vvec(T, A, h, ...) vector<vector<T>> A(h, vector<T>(__VA_ARGS__));
#define vvvec(T, A, h1, h2, ...) vector<vector<vector<T>>> A(h1, vector<vector<T>>(h2, vector<T>(__VA_ARGS__)));
// clang-format on

// for loop
#define fori1(a) for (ll _ = 0; _ < (a); _++)
#define fori2(i, a) for (ll i = 0; i < (a); i++)
#define fori3(i, a, b) for (ll i = (a); i < (b); i++)
#define fori4(i, a, b, c) for (ll i = (a); ((c) > 0 || i > (b)) && ((c) < 0 || i < (b)); i += (c))
#define overload4(a, b, c, d, e, ...) e
#define fori(...) overload4(__VA_ARGS__, fori4, fori3, fori2, fori1)(__VA_ARGS__)

// declare and input
// clang-format off
#define INT(...) int __VA_ARGS__; inp(__VA_ARGS__);
#define LL(...) ll __VA_ARGS__; inp(__VA_ARGS__);
#define STRING(...) string __VA_ARGS__; inp(__VA_ARGS__);
#define CHAR(...) char __VA_ARGS__; inp(__VA_ARGS__);
#define DOUBLE(...) double __VA_ARGS__; STRING(str___); __VA_ARGS__ = stod(str___);
#define VEC(T, A, n) vector<T> A(n); inp(A);
#define VVEC(T, A, n, m) vector<vector<T>> A(n, vector<T>(m)); inp(A);
// clang-format on

// const value
const ll MOD1   = 1000000007;
const ll MOD9   = 998244353;
const double PI = acos(-1);

// other macro
#if !defined(RIN__LOCAL) && !defined(INTERACTIVE)
#define endl "\n"
#endif
#define spa ' '
#define len(A) ll(A.size())
#define all(A) begin(A), end(A)

// function
vector<char> stoc(string &S) {
    int n = S.size();
    vector<char> ret(n);
    for (int i = 0; i < n; i++) ret[i] = S[i];
    return ret;
}
string ctos(vector<char> &S) {
    int n      = S.size();
    string ret = "";
    for (int i = 0; i < n; i++) ret += S[i];
    return ret;
}

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 T, class S>
auto clamp(T &a, const S &l, const S &r) {
    return (a > r ? r : a < l ? l : a);
}
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);
}
template <class T, class S>
inline bool chclamp(T &a, const S &l, const S &r) {
    auto b = clamp(a, l, r);
    return (a != b ? a = b, 1 : 0);
}

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

template <typename T>
vector<T> compression(vector<T> X) {
    sort(all(X));
    X.erase(unique(all(X)), X.end());
    return X;
}

// input and output
namespace io {
// __int128_t
std::ostream &operator<<(std::ostream &dest, __int128_t value) {
    std::ostream::sentry s(dest);
    if (s) {
        __uint128_t tmp = value < 0 ? -value : value;
        char buffer[128];
        char *d = std::end(buffer);
        do {
            --d;
            *d = "0123456789"[tmp % 10];
            tmp /= 10;
        } while (tmp != 0);
        if (value < 0) {
            --d;
            *d = '-';
        }
        int len = std::end(buffer) - d;
        if (dest.rdbuf()->sputn(d, len) != len) {
            dest.setstate(std::ios_base::badbit);
        }
    }
    return dest;
}

// vector<T>
template <typename T>
istream &operator>>(istream &is, vector<T> &A) {
    for (auto &a : A) is >> a;
    return is;
}
template <typename T>
ostream &operator<<(ostream &os, vector<T> &A) {
    for (size_t i = 0; i < A.size(); i++) {
        os << A[i];
        if (i != A.size() - 1) os << ' ';
    }
    return os;
}

// vector<vector<T>>
template <typename T>
istream &operator>>(istream &is, vector<vector<T>> &A) {
    for (auto &a : A) is >> a;
    return is;
}
template <typename T>
ostream &operator<<(ostream &os, vector<vector<T>> &A) {
    for (size_t i = 0; i < A.size(); i++) {
        os << A[i];
        if (i != A.size() - 1) os << endl;
    }
    return os;
}

// pair<S, T>
template <typename S, typename T>
istream &operator>>(istream &is, pair<S, T> &A) {
    is >> A.first >> A.second;
    return is;
}
template <typename S, typename T>
ostream &operator<<(ostream &os, pair<S, T> &A) {
    os << A.first << ' ' << A.second;
    return os;
}

// vector<pair<S, T>>
template <typename S, typename T>
istream &operator>>(istream &is, vector<pair<S, T>> &A) {
    for (size_t i = 0; i < A.size(); i++) {
        is >> A[i];
    }
    return is;
}
template <typename S, typename T>
ostream &operator<<(ostream &os, vector<pair<S, T>> &A) {
    for (size_t i = 0; i < A.size(); i++) {
        os << A[i];
        if (i != A.size() - 1) os << endl;
    }
    return os;
}

// tuple
template <typename T, size_t N>
struct TuplePrint {
    static ostream &print(ostream &os, const T &t) {
        TuplePrint<T, N - 1>::print(os, t);
        os << ' ' << get<N - 1>(t);
        return os;
    }
};
template <typename T>
struct TuplePrint<T, 1> {
    static ostream &print(ostream &os, const T &t) {
        os << get<0>(t);
        return os;
    }
};
template <typename... Args>
ostream &operator<<(ostream &os, const tuple<Args...> &t) {
    TuplePrint<decltype(t), sizeof...(Args)>::print(os, t);
    return os;
}

// io functions
void FLUSH() {
    cout << flush;
}

void print() {
    cout << endl;
}
template <class Head, class... Tail>
void print(Head &&head, Tail &&...tail) {
    cout << head;
    if (sizeof...(Tail)) cout << spa;
    print(std::forward<Tail>(tail)...);
}

template <typename T, typename S>
void prisep(vector<T> &A, S sep) {
    int n = A.size();
    for (int i = 0; i < n; i++) {
        cout << A[i];
        if (i != n - 1) cout << sep;
    }
    cout << endl;
}
template <typename T, typename S>
void priend(T A, S end) {
    cout << A << end;
}
template <typename T>
void prispa(T A) {
    priend(A, spa);
}
template <typename T, typename S>
bool printif(bool f, T A, S B) {
    if (f)
        print(A);
    else
        print(B);
    return f;
}

template <class... T>
void inp(T &...a) {
    (cin >> ... >> a);
}

} // namespace io
using namespace io;

// read graph
vector<vector<int>> read_edges(int n, int m, bool direct = false, int indexed = 1) {
    vector<vector<int>> edges(n, vector<int>());
    for (int i = 0; i < m; i++) {
        INT(u, v);
        u -= indexed;
        v -= indexed;
        edges[u].push_back(v);
        if (!direct) edges[v].push_back(u);
    }
    return edges;
}
vector<vector<int>> read_tree(int n, int indexed = 1) {
    return read_edges(n, n - 1, false, indexed);
}

template <typename T = long long>
vector<vector<pair<int, T>>> read_wedges(int n, int m, bool direct = false, int indexed = 1) {
    vector<vector<pair<int, T>>> edges(n, vector<pair<int, T>>());
    for (int i = 0; i < m; i++) {
        INT(u, v);
        T w;
        inp(w);
        u -= indexed;
        v -= indexed;
        edges[u].push_back({v, w});
        if (!direct) edges[v].push_back({u, w});
    }
    return edges;
}
template <typename T = long long>
vector<vector<pair<int, T>>> read_wtree(int n, int indexed = 1) {
    return read_wedges<T>(n, n - 1, false, indexed);
}

// yes / no
namespace yesno {

// yes
inline bool yes(bool f = true) {
    cout << (f ? "yes" : "no") << endl;
    return f;
}
inline bool Yes(bool f = true) {
    cout << (f ? "Yes" : "No") << endl;
    return f;
}
inline bool YES(bool f = true) {
    cout << (f ? "YES" : "NO") << endl;
    return f;
}

// no
inline bool no(bool f = true) {
    cout << (!f ? "yes" : "no") << endl;
    return f;
}
inline bool No(bool f = true) {
    cout << (!f ? "Yes" : "No") << endl;
    return f;
}
inline bool NO(bool f = true) {
    cout << (!f ? "YES" : "NO") << endl;
    return f;
}

// possible
inline bool possible(bool f = true) {
    cout << (f ? "possible" : "impossible") << endl;
    return f;
}
inline bool Possible(bool f = true) {
    cout << (f ? "Possible" : "Impossible") << endl;
    return f;
}
inline bool POSSIBLE(bool f = true) {
    cout << (f ? "POSSIBLE" : "IMPOSSIBLE") << endl;
    return f;
}

// impossible
inline bool impossible(bool f = true) {
    cout << (!f ? "possible" : "impossible") << endl;
    return f;
}
inline bool Impossible(bool f = true) {
    cout << (!f ? "Possible" : "Impossible") << endl;
    return f;
}
inline bool IMPOSSIBLE(bool f = true) {
    cout << (!f ? "POSSIBLE" : "IMPOSSIBLE") << endl;
    return f;
}

// Alice Bob
inline bool Alice(bool f = true) {
    cout << (f ? "Alice" : "Bob") << endl;
    return f;
}
inline bool Bob(bool f = true) {
    cout << (f ? "Bob" : "Alice") << endl;
    return f;
}

// Takahashi Aoki
inline bool Takahashi(bool f = true) {
    cout << (f ? "Takahashi" : "Aoki") << endl;
    return f;
}
inline bool Aoki(bool f = true) {
    cout << (f ? "Aoki" : "Takahashi") << endl;
    return f;
}

} // namespace yesno
using namespace yesno;

} // namespace templates
using namespace templates;

void solve() {
    const time_t start = clock();
    auto elapsed       = [&] { return (double)(clock() - start) / CLOCKS_PER_SEC; };

    const int N = 300300;
    vec(bool, isPrime, N, true);
    vvec(int, P, N);
    fori(i, 2, N) {
        if (!isPrime[i]) continue;
        fori(j, i, N, i) {
            isPrime[j] = false;
            P[j].push_back(i);
        }
    }
    vec(ll, phi, N);
    fori(i, 2, N) {
        phi[i] = i;
        for (int p : P[i]) {
            phi[i] -= phi[i] / p;
        }
    }
    vvec(ll, prods, N);
    vvec(ll, pms, N);
    fori(i, 2, N) {
        int le = len(P[i]);
        prods[i].resize(1 << le);
        pms[i].resize(1 << le);
        fori(bit, 1 << le) {
            ll prod = 1;
            ll pm   = 1;
            fori(j, le) {
                if ((bit >> j) & 1) {
                    prod *= P[i][j];
                    pm *= -1;
                }
            }
            prods[i][bit] = prod;
            pms[i][bit]   = pm;
        }
    }

    auto f = [&](ll n, ll upp) -> ll {
        ll ret = 0;
        int le = len(P[n]);
        fori(bit, 1 << le) {
            ll prod = prods[n][bit];
            ll pm   = pms[n][bit];

            ret += pm * (upp / prod);
        }

        return ret;
    };

    INT(T);
    fori(T) {
        LL(n, k);
        ll tot = 0;
        fori(j, 2, n + 1) tot += phi[j];
        if (2 * tot + 1 < k) {
            print(-1);
            continue;
        } else if (tot + 1 == k) {
            print("1/1");
            continue;
        }
        bool rev = false;
        if (tot + 1 < k) {
            k   = 2 * tot + 2 - k;
            rev = true;
        }

        auto cnt = [&](Pll x) -> ll {
            ll ret = 0;
            fori(j, 2, n + 1) {
                ll upp = x.first * j / x.second;
                ret += f(j, upp);
            }
            return ret;
        };

        ll l = 0;
        ll r = n * n;
        while (r - l > 1) {
            ll mid = (l + r) / 2;
            auto c = cnt({mid, n * n});
            if (c >= k)
                r = mid;
            else
                l = mid;
        }

        fori(i, 1, n + 1) {
            ll t = i * r / (n * n);
            if (i * l < n * n * t) {
                Pll ans = {t, i};
                if (rev) swap(ans.first, ans.second);
                cout << ans.first << '/' << ans.second << endl;
                break;
            }
        }
    }
}

int main() {
#ifndef INTERACTIVE
    cin.tie(0)->sync_with_stdio(0);
#endif
    // cout << fixed << setprecision(12);
    int t;
    t = 1;
    // cin >> t;
    while (t--) solve();
    return 0;
}
0