#580441 (C++17) No.1287 えぬけー

提出ソース
結果

問題	No.1287 えぬけー
ユーザー	iiljj
提出日時	2020-11-15 18:14:17
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	273 ms / 2,000 ms
コード長	18,597 bytes
コンパイル時間	3,388 ms
コンパイル使用メモリ	238,464 KB
実行使用メモリ	4,380 KB
最終ジャッジ日時	2023-09-30 07:02:22
合計ジャッジ時間	5,660 ms
ジャッジサーバーID （参考情報）	judge15 / judge12
このコードへのチャレンジ
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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	1 ms 4,380 KB
testcase_01	AC	2 ms 4,376 KB
testcase_02	AC	1 ms 4,376 KB
testcase_03	AC	1 ms 4,380 KB
testcase_04	AC	2 ms 4,380 KB
testcase_05	AC	261 ms 4,380 KB
testcase_06	AC	264 ms 4,376 KB
testcase_07	AC	273 ms 4,376 KB
testcase_08	AC	250 ms 4,376 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

raw source code
/* #region Head */

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

using ll = long long;
using ull = unsigned long long;
using ld = long double;
using pll = pair<ll, ll>;
template <class T> using vc = vector<T>;
template <class T> using vvc = vc<vc<T>>;
using vll = vc<ll>;
using vvll = vvc<ll>;
using vld = vc<ld>;
using vvld = vvc<ld>;
using vs = vc<string>;
using vvs = vvc<string>;
template <class T, class U> using um = unordered_map<T, U>;
template <class T> using pq = priority_queue<T>;
template <class T> using pqa = priority_queue<T, vc<T>, greater<T>>;
template <class T> using us = unordered_set<T>;

#define REP(i, m, n) for (ll i = (m), i##_len = (ll)(n); i < i##_len; ++(i))
#define REPM(i, m, n) for (ll i = (m), i##_max = (ll)(n); i <= i##_max; ++(i))
#define REPR(i, m, n) for (ll i = (m), i##_min = (ll)(n); i >= i##_min; --(i))
#define REPD(i, m, n, d) for (ll i = (m), i##_len = (ll)(n); i < i##_len; i += (d))
#define REPMD(i, m, n, d) for (ll i = (m), i##_max = (ll)(n); i <= i##_max; i += (d))
#define REPI(itr, ds) for (auto itr = ds.begin(); itr != ds.end(); itr++)
#define ALL(x) begin(x), end(x)
#define SIZE(x) ((ll)(x).size())
#define PERM(c)                                                                                                        \
    sort(ALL(c));                                                                                                      \
    for (bool c##p = 1; c##p; c##p = next_permutation(ALL(c)))
#define UNIQ(v) v.erase(unique(ALL(v)), v.end());
#define CEIL(a, b) (((a) + (b)-1) / (b))

constexpr ll INF = 1'010'000'000'000'000'017LL;
constexpr int IINF = 1'000'000'007LL;
constexpr ll MOD = 1'000'000'007LL; // 1e9 + 7
// constexpr ll MOD = 998244353;
constexpr ld EPS = 1e-12;
constexpr ld PI = 3.14159265358979323846;

template <typename T> istream &operator>>(istream &is, vc<T> &vec) { // vector 入力
    for (T &x : vec) is >> x;
    return is;
}
template <typename T> ostream &operator<<(ostream &os, vc<T> &vec) { // vector 出力 (for dump)
    os << "{";
    REP(i, 0, SIZE(vec)) os << vec[i] << (i == i_len - 1 ? "" : ", ");
    os << "}";
    return os;
}
template <typename T> ostream &operator>>(ostream &os, vc<T> &vec) { // vector 出力 (inline)
    REP(i, 0, SIZE(vec)) os << vec[i] << (i == i_len - 1 ? "\n" : " ");
    return os;
}

template <typename T, typename U> istream &operator>>(istream &is, pair<T, U> &pair_var) { // pair 入力
    is >> pair_var.first >> pair_var.second;
    return is;
}
template <typename T, typename U> ostream &operator<<(ostream &os, pair<T, U> &pair_var) { // pair 出力
    os << "(" << pair_var.first << ", " << pair_var.second << ")";
    return os;
}

// map, um, set, us 出力
template <class T> ostream &out_iter(ostream &os, T &map_var) {
    os << "{";
    REPI(itr, map_var) {
        os << *itr;
        auto itrcp = itr;
        if (++itrcp != map_var.end()) os << ", ";
    }
    return os << "}";
}
template <typename T, typename U> ostream &operator<<(ostream &os, map<T, U> &map_var) { return out_iter(os, map_var); }
template <typename T, typename U> ostream &operator<<(ostream &os, um<T, U> &map_var) {
    os << "{";
    REPI(itr, map_var) {
        auto [key, value] = *itr;
        os << "(" << key << ", " << value << ")";
        auto itrcp = itr;
        if (++itrcp != map_var.end()) os << ", ";
    }
    os << "}";
    return os;
}
template <typename T> ostream &operator<<(ostream &os, set<T> &set_var) { return out_iter(os, set_var); }
template <typename T> ostream &operator<<(ostream &os, us<T> &set_var) { return out_iter(os, set_var); }
template <typename T> ostream &operator<<(ostream &os, pq<T> &pq_var) {
    pq<T> pq_cp(pq_var);
    os << "{";
    if (!pq_cp.empty()) {
        os << pq_cp.top(), pq_cp.pop();
        while (!pq_cp.empty()) os << ", " << pq_cp.top(), pq_cp.pop();
    }
    return os << "}";
}

void pprint() { cout << endl; }
template <class Head, class... Tail> void pprint(Head &&head, Tail &&... tail) {
    cout << head;
    if (sizeof...(Tail) > 0) cout << ' ';
    pprint(move(tail)...);
}

// dump
#define DUMPOUT cerr
void dump_func() { DUMPOUT << endl; }
template <class Head, class... Tail> void dump_func(Head &&head, Tail &&... tail) {
    DUMPOUT << head;
    if (sizeof...(Tail) > 0) DUMPOUT << ", ";
    dump_func(move(tail)...);
}

// chmax (更新「される」かもしれない値が前)
template <typename T, typename U, typename Comp = less<>> bool chmax(T &xmax, const U &x, Comp comp = {}) {
    if (comp(xmax, x)) {
        xmax = x;
        return true;
    }
    return false;
}

// chmin (更新「される」かもしれない値が前)
template <typename T, typename U, typename Comp = less<>> bool chmin(T &xmin, const U &x, Comp comp = {}) {
    if (comp(x, xmin)) {
        xmin = x;
        return true;
    }
    return false;
}

// ローカル用
#ifndef ONLINE_JUDGE
#define DEBUG_
#endif

#ifdef DEBUG_
#define DEB
#define dump(...)                                                                                                      \
    DUMPOUT << "  " << string(#__VA_ARGS__) << ": "                                                                    \
            << "[" << to_string(__LINE__) << ":" << __FUNCTION__ << "]" << endl                                        \
            << "    ",                                                                                                 \
        dump_func(__VA_ARGS__)
#else
#define DEB if (false)
#define dump(...)
#endif

#define VAR(type, ...)                                                                                                 \
    type __VA_ARGS__;                                                                                                  \
    cin >> __VA_ARGS__;

template <typename T> istream &operator,(istream &is, T &rhs) { return is >> rhs; }
template <typename T> ostream &operator,(ostream &os, const T &rhs) { return os << ' ' << rhs; }

struct AtCoderInitialize {
    static constexpr int IOS_PREC = 15;
    static constexpr bool AUTOFLUSH = false;
    AtCoderInitialize() {
        ios_base::sync_with_stdio(false), cin.tie(nullptr), cout.tie(nullptr);
        cout << fixed << setprecision(IOS_PREC);
        if (AUTOFLUSH) cout << unitbuf;
    }
} ATCODER_INITIALIZE;

void Yn(bool p) { cout << (p ? "Yes" : "No") << endl; }
void YN(bool p) { cout << (p ? "YES" : "NO") << endl; }

/* #endregion */

// #include <atcoder/all>
// using namespace atcoder;

/* #region kth_root */

// 以下から拝借
// Submitted https://judge.yosupo.jp/submission/23481

namespace inner {

using i32 = int32_t;
using u32 = uint32_t;
using i64 = int64_t;
using u64 = uint64_t;

template <typename T> T gcd(T a, T b) {
    while (b) swap(a %= b, b);
    return a;
}

template <typename T> T inv(T a, T p) {
    T b = p, x = 1, y = 0;
    while (a) {
        T q = b / a;
        swap(a, b %= a);
        swap(x, y -= q * x);
    }
    assert(b == 1);
    return y < 0 ? y + p : y;
}

template <typename T, typename U> T modpow(T a, U n, T p) {
    T ret = 1 % p;
    for (; n; n >>= 1, a = U(a) * a % p)
        if (n & 1) ret = U(ret) * a % p;
    return ret;
}

} // namespace inner
using namespace std;

struct ArbitraryLazyMontgomeryModInt {
    using mint = ArbitraryLazyMontgomeryModInt;
    using i32 = int32_t;
    using u32 = uint32_t;
    using u64 = uint64_t;

    static u32 mod;
    static u32 r;
    static u32 n2;

    static u32 get_r() {
        u32 ret = mod;
        for (i32 i = 0; i < 4; ++i) ret *= 2 - mod * ret;
        return ret;
    }

    static void set_mod(u32 m) {
        assert(m < (1 << 30));
        assert((m & 1) == 1);
        mod = m;
        n2 = -u64(m) % m;
        r = get_r();
        assert(r * mod == 1);
    }

    u32 a;

    ArbitraryLazyMontgomeryModInt() : a(0) {}
    ArbitraryLazyMontgomeryModInt(const int64_t &b) : a(reduce(u64(b % mod + mod) * n2)){};

    static u32 reduce(const u64 &b) { return (b + u64(u32(b) * u32(-r)) * mod) >> 32; }

    mint &operator+=(const mint &b) {
        if (i32(a += b.a - 2 * mod) < 0) a += 2 * mod;
        return *this;
    }

    mint &operator-=(const mint &b) {
        if (i32(a -= b.a) < 0) a += 2 * mod;
        return *this;
    }

    mint &operator*=(const mint &b) {
        a = reduce(u64(a) * b.a);
        return *this;
    }

    mint &operator/=(const mint &b) {
        *this *= b.inverse();
        return *this;
    }

    mint operator+(const mint &b) const { return mint(*this) += b; }
    mint operator-(const mint &b) const { return mint(*this) -= b; }
    mint operator*(const mint &b) const { return mint(*this) *= b; }
    mint operator/(const mint &b) const { return mint(*this) /= b; }
    bool operator==(const mint &b) const { return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a); }
    bool operator!=(const mint &b) const { return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a); }
    mint operator-() const { return mint() - mint(*this); }

    mint pow(u64 n) const {
        mint ret(1), mul(*this);
        while (n > 0) {
            if (n & 1) ret *= mul;
            mul *= mul;
            n >>= 1;
        }
        return ret;
    }

    friend ostream &operator<<(ostream &os, const mint &b) { return os << b.get(); }

    friend istream &operator>>(istream &is, mint &b) {
        int64_t t;
        is >> t;
        b = ArbitraryLazyMontgomeryModInt(t);
        return (is);
    }

    mint inverse() const { return pow(mod - 2); }

    u32 get() const {
        u32 ret = reduce(a);
        return ret >= mod ? ret - mod : ret;
    }

    static u32 get_mod() { return mod; }
};
typename ArbitraryLazyMontgomeryModInt::u32 ArbitraryLazyMontgomeryModInt::mod;
typename ArbitraryLazyMontgomeryModInt::u32 ArbitraryLazyMontgomeryModInt::r;
typename ArbitraryLazyMontgomeryModInt::u32 ArbitraryLazyMontgomeryModInt::n2;

struct montgomery64 {
    using mint = montgomery64;
    using i64 = int64_t;
    using u64 = uint64_t;
    using u128 = __uint128_t;

    static u64 mod;
    static u64 r;
    static u64 n2;

    static u64 get_r() {
        u64 ret = mod;
        for (i64 i = 0; i < 5; ++i) ret *= 2 - mod * ret;
        return ret;
    }

    static void set_mod(u64 m) {
        assert(m < (1LL << 62));
        assert((m & 1) == 1);
        mod = m;
        n2 = -u128(m) % m;
        r = get_r();
        assert(r * mod == 1);
    }

    u64 a;

    montgomery64() : a(0) {}
    montgomery64(const int64_t &b) : a(reduce((u128(b) + mod) * n2)){};

    static u64 reduce(const u128 &b) { return (b + u128(u64(b) * u64(-r)) * mod) >> 64; }

    mint &operator+=(const mint &b) {
        if (i64(a += b.a - 2 * mod) < 0) a += 2 * mod;
        return *this;
    }

    mint &operator-=(const mint &b) {
        if (i64(a -= b.a) < 0) a += 2 * mod;
        return *this;
    }

    mint &operator*=(const mint &b) {
        a = reduce(u128(a) * b.a);
        return *this;
    }

    mint &operator/=(const mint &b) {
        *this *= b.inverse();
        return *this;
    }

    mint operator+(const mint &b) const { return mint(*this) += b; }
    mint operator-(const mint &b) const { return mint(*this) -= b; }
    mint operator*(const mint &b) const { return mint(*this) *= b; }
    mint operator/(const mint &b) const { return mint(*this) /= b; }
    bool operator==(const mint &b) const { return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a); }
    bool operator!=(const mint &b) const { return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a); }
    mint operator-() const { return mint() - mint(*this); }

    mint pow(u128 n) const {
        mint ret(1), mul(*this);
        while (n > 0) {
            if (n & 1) ret *= mul;
            mul *= mul;
            n >>= 1;
        }
        return ret;
    }

    friend ostream &operator<<(ostream &os, const mint &b) { return os << b.get(); }

    friend istream &operator>>(istream &is, mint &b) {
        int64_t t;
        is >> t;
        b = montgomery64(t);
        return (is);
    }

    mint inverse() const { return pow(mod - 2); }

    u64 get() const {
        u64 ret = reduce(a);
        return ret >= mod ? ret - mod : ret;
    }

    static u64 get_mod() { return mod; }
};
typename montgomery64::u64 montgomery64::mod, montgomery64::r, montgomery64::n2;

unsigned long long rng() {
    static unsigned long long x_ = 88172645463325252ULL;
    x_ = x_ ^ (x_ << 7);
    return x_ = x_ ^ (x_ >> 9);
}
namespace fast_factorize {
using u64 = uint64_t;

template <typename mint> bool miller_rabin(u64 n, vector<u64> as) {
    if (mint::get_mod() != n) mint::set_mod(n);
    u64 d = n - 1;
    while (~d & 1) d >>= 1;
    mint e{1}, rev{int64_t(n - 1)};
    for (u64 a : as) {
        if (n <= a) break;
        u64 t = d;
        mint y = mint(a).pow(t);
        while (t != n - 1 && y != e && y != rev) {
            y *= y;
            t *= 2;
        }
        if (y != rev && t % 2 == 0) return false;
    }
    return true;
}

bool is_prime(u64 n) {
    if (~n & 1) return n == 2;
    if (n <= 1) return false;
    if (n < (1LL << 30))
        return miller_rabin<ArbitraryLazyMontgomeryModInt>(n, {2, 7, 61});
    else
        return miller_rabin<montgomery64>(n, {2, 325, 9375, 28178, 450775, 9780504, 1795265022});
}

template <typename mint, typename T> T pollard_rho(T n) {
    if (~n & 1) return 2;
    if (is_prime(n)) return n;
    if (mint::get_mod() != n) mint::set_mod(n);
    mint R, one = 1;
    auto f = [&](mint x) { return x * x + R; };
    auto rnd = [&]() { return rng() % (n - 2) + 2; };
    while (1) {
        mint x, y, ys, q = one;
        R = rnd(), y = rnd();
        T g = 1;
        constexpr int m = 128;
        for (int r = 1; g == 1; r <<= 1) {
            x = y;
            for (int i = 0; i < r; ++i) y = f(y);
            for (int k = 0; g == 1 && k < r; k += m) {
                ys = y;
                for (int i = 0; i < m && i < r - k; ++i) q *= x - (y = f(y));
                g = inner::gcd<T>(q.get(), n);
            }
        }
        if (g == n) do
                g = inner::gcd<T>((x - (ys = f(ys))).get(), n);
            while (g == 1);
        if (g != n) return g;
    }
    exit(1);
}

vector<u64> inner_factorize(u64 n) {
    if (n <= 1) return {};
    u64 p;
    if (n <= (1LL << 30))
        p = pollard_rho<ArbitraryLazyMontgomeryModInt, uint32_t>(n);
    else
        p = pollard_rho<montgomery64, uint64_t>(n);
    if (p == n) return {p};
    auto l = inner_factorize(p);
    auto r = inner_factorize(n / p);
    copy(begin(r), end(r), back_inserter(l));
    return l;
}

vector<u64> factorize(u64 n) {
    auto ret = inner_factorize(n);
    sort(begin(ret), end(ret));
    return ret;
}

} // namespace fast_factorize
using fast_factorize::factorize;
using fast_factorize::is_prime;

/**
 * @brief 高速素因数分解(Miller Rabin/Pollard's Rho)
 * @docs docs/prime/fast-factorize.md
 */

namespace kth_root_mod {

// fast BS-GS
template <typename T> struct Memo {
    Memo(const T &g, int s, int period)
        : size(1 << __lg(min(s, period))), mask(size - 1), period(period), vs(size), os(size + 1) {
        T x(1);
        for (int i = 0; i < size; ++i, x *= g) os[x.get() & mask]++;
        for (int i = 1; i < size; ++i) os[i] += os[i - 1];
        x = 1;
        for (int i = 0; i < size; ++i, x *= g) vs[--os[x.get() & mask]] = {x, i};
        gpow = x;
        os[size] = size;
    }
    int find(T x) const {
        for (int t = 0; t < period; t += size, x *= gpow) {
            for (int m = (x.get() & mask), i = os[m]; i < os[m + 1]; ++i) {
                if (x == vs[i].first) {
                    int ret = vs[i].second - t;
                    return ret < 0 ? ret + period : ret;
                }
            }
        }
        assert(0);
    }
    T gpow;
    int size, mask, period;
    vector<pair<T, int>> vs;
    vector<int> os;
};

using inner::gcd;
using inner::inv;
using inner::modpow;
template <typename INT, typename LINT, typename mint> mint pe_root(INT c, INT pi, INT ei, INT p) {
    if (mint::get_mod() != decltype(mint::a)(p)) mint::set_mod(p);
    INT s = p - 1, t = 0;
    while (s % pi == 0) s /= pi, ++t;
    INT pe = 1;
    for (INT _ = 0; _ < ei; ++_) pe *= pi;

    INT u = inv(pe - s % pe, pe);
    mint mc = c, one = 1;
    mint z = mc.pow((s * u + 1) / pe);
    mint zpe = mc.pow(s * u);
    if (zpe == one) return z;

    assert(t > ei);
    mint vs;
    {
        INT ptm1 = 1;
        for (INT _ = 0; _ < t - 1; ++_) ptm1 *= pi;
        for (mint v = 2;; v += one) {
            vs = v.pow(s);
            if (vs.pow(ptm1) != one) break;
        }
    }

    mint vspe = vs.pow(pe);
    INT vs_e = ei;
    mint base = vspe;
    for (INT _ = 0; _ < t - ei - 1; _++) base = base.pow(pi);
    Memo<mint> memo(base, (INT)(sqrt(t - ei) * sqrt(pi)) + 1, pi);

    while (zpe != one) {
        mint tmp = zpe;
        INT td = 0;
        while (tmp != 1) ++td, tmp = tmp.pow(pi);
        INT e = t - td;
        while (vs_e != e) {
            vs = vs.pow(pi);
            vspe = vspe.pow(pi);
            ++vs_e;
        }

        // BS-GS ... find (zpe * ( vspe ^ n ) ) ^( p_i ^ (td - 1) ) = 1
        mint base_zpe = zpe.inverse();
        for (INT _ = 0; _ < td - 1; _++) base_zpe = base_zpe.pow(pi);
        INT bsgs = memo.find(base_zpe);

        z *= vs.pow(bsgs);
        zpe *= vspe.pow(bsgs);
    }
    return z;
}

template <typename INT, typename LINT, typename mint> INT inner_kth_root(INT a, INT k, INT p) {
    a %= p;
    if (k == 0) return a == 1 ? a : -1;
    if (a <= 1 || k <= 1) return a;

    assert(p > 2);
    if (mint::get_mod() != decltype(mint::a)(p)) mint::set_mod(p);
    INT g = gcd(p - 1, k);
    if (modpow<INT, LINT>(a, (p - 1) / g, p) != 1) return -1;
    a = mint(a).pow(inv(k / g, (p - 1) / g)).get();
    unordered_map<INT, int> fac;
    for (auto &f : factorize(g)) fac[f]++;
    if (mint::get_mod() != decltype(mint::a)(p)) mint::set_mod(p);
    for (auto pp : fac) a = pe_root<INT, LINT, mint>(a, pp.first, pp.second, p).get();
    return a;
}

int64_t kth_root(int64_t a, int64_t k, int64_t p) {
    if (max({a, k, p}) < (1LL << 30))
        return inner_kth_root<int32_t, int64_t, ArbitraryLazyMontgomeryModInt>(a, k, p);
    else
        return inner_kth_root<int64_t, __int128_t, montgomery64>(a, k, p);
}

} // namespace kth_root_mod
using kth_root_mod::kth_root;

/* #endregion */

// Problem
void solve() {
    VAR(int, t);

    REP(i, 0, t) {
        VAR(ll, x, k);
        pprint(kth_root(x, k, MOD));
    }
}

// entry point
int main() {
    solve();
    return 0;
}
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結果

テストケース

ソースコード
