#579980 (C++17) No.1287 えぬけー

• 問題: No.1287 えぬけー
• ユーザー: r1933
• 提出日時: 2020-11-14 01:47:47
• 言語: C++17 (gcc 12.3.0 + boost 1.83.0)
• 結果: AC
• 実行時間: 97 ms / 2,000 ms
• コード長: 8,623 bytes
• コンパイル時間: 2,636 ms
• コンパイル使用メモリ: 212,240 KB
• 実行使用メモリ: 5,376 KB
• 最終ジャッジ日時: 2024-07-22 22:35:17
• 合計ジャッジ時間: 3,755 ms
• ジャッジサーバーID （参考情報）: judge2 / judge4

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	2 ms; 5,248 KB
testcase_01	AC	2 ms; 5,376 KB
testcase_02	AC	2 ms; 5,376 KB
testcase_03	AC	2 ms; 5,376 KB
testcase_04	AC	2 ms; 5,376 KB
testcase_05	AC	92 ms; 5,376 KB
testcase_06	AC	94 ms; 5,376 KB
testcase_07	AC	97 ms; 5,376 KB
testcase_08	AC	90 ms; 5,376 KB

ソースコード

#pragma GCC optimize("Ofast")
#include "bits/stdc++.h"

// Begin Header {{{
using namespace std;

#ifndef DEBUG
#define dump(...)
#endif

#define all(x) begin(x), end(x)
#define rall(x) rbegin(x), rend(x)
#define rep(i, b, e) for (intmax_t i = (b), i##_limit = (e); i < i##_limit; ++i)
#define repc(i, b, e) for (intmax_t i = (b), i##_limit = (e); i <= i##_limit; ++i)
#define repr(i, b, e) for (intmax_t i = (b), i##_limit = (e); i >= i##_limit; --i)
#define var(Type, ...) Type __VA_ARGS__; input(__VA_ARGS__)

constexpr size_t    operator""_zu(unsigned long long value) { return value; };
constexpr intmax_t  operator""_jd(unsigned long long value) { return value; };
constexpr uintmax_t operator""_ju(unsigned long long value) { return value; };

constexpr int INF = 0x3f3f3f3f;
constexpr intmax_t LINF = 0x3f3f3f3f3f3f3f3f_jd;

template <class T, class Compare = less<>>
using MaxHeap = priority_queue<T, vector<T>, Compare>;
template <class T, class Compare = greater<>>
using MinHeap = priority_queue<T, vector<T>, Compare>;

inline void input() {}
template <class Head, class... Tail>
inline void input(Head&& head, Tail&&... tail) {
    cin >> head;
    input(forward<Tail>(tail)...);
}

template <class Container, class Value = typename Container::value_type,
enable_if_t<!is_same<Container, string>::value, nullptr_t> = nullptr>
inline istream& operator>>(istream &is, Container &vs) {
    for (auto &v: vs) is >> v;
    return is;
}

inline void output() { cout << "\n"; }
template <class Head, class... Tail>
inline void output(Head&& head, Tail&&... tail) {
    cout << head;
    if (sizeof...(tail)) cout << " ";
    output(forward<Tail>(tail)...);
}

template <class Container, class Value = typename Container::value_type,
enable_if_t<!is_same<Container, string>::value, nullptr_t> = nullptr>
inline ostream& operator<<(ostream &os, const Container &vs) {
    static constexpr const char *delim[] = {" ", ""};
    for (auto it = begin(vs); it != end(vs); ++it) {
        os << delim[it == begin(vs)] << *it;
    }
    return os;
}

template <class Iterator>
inline void join(const Iterator &Begin, const Iterator &End, const string &delim = "\n", const string &last = "\n") {
    for (auto it = Begin; it != End; ++it) {
        cout << ((it == Begin) ? "" : delim) << *it;
    }
    cout << last;
}

template <class T>
inline vector<T> makeVector(const T &init_value, size_t sz) {
    return vector<T>(sz, init_value);
}

template <class T, class... Args>
inline auto makeVector(const T &init_value, size_t sz, Args... args) {
    return vector<decltype(makeVector<T>(init_value, args...))>(sz, makeVector<T>(init_value, args...));
}

template <class Func>
class FixPoint : Func {
public:
    explicit constexpr FixPoint(Func&& f) noexcept : Func(forward<Func>(f)) {}

    template <class... Args>
    constexpr decltype(auto) operator()(Args&&... args) const {
        return Func::operator()(*this, std::forward<Args>(args)...);
    }
};

template <class Func>
static inline constexpr decltype(auto) makeFixPoint(Func&& f) noexcept {
    return FixPoint<Func>{forward<Func>(f)};
}

template <class Container>
struct reverse_t {
    Container &c;
    reverse_t(Container &c) : c(c) {}
    auto begin() { return c.rbegin(); }
    auto end() { return c.rend(); }
};

template <class Container>
auto reversed(Container &c) {
    return reverse_t<Container>(c);
}

template <class T>
inline bool chmax(T &a, const T &b) noexcept {
    return b > a && (a = b, true);
}

template <class T>
inline bool chmin(T &a, const T &b) noexcept {
    return b < a && (a = b, true);
}

template <class T>
inline T diff(const T &a, const T &b) noexcept {
    return a < b ? b - a : a - b;
}

void operator|=(vector<bool>::reference lhs, const bool rhs) {
    lhs = lhs | rhs;
}

void ioinit() {
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);
    cout << fixed << setprecision(10);
    cerr << fixed << setprecision(10);
    clog << fixed << setprecision(10);
}
// }}} End Header

// ModInt {{{
template <intmax_t Modulo>
class ModInt {
public:
    using value_type = intmax_t;

private:
    static constexpr value_type cmod = Modulo; // compile-time
    static value_type rmod; // runtime
    value_type value = 0;

    static constexpr value_type inverse(value_type n, value_type m) {
        value_type a = n;
        value_type b = m;
        value_type x = 0;
        value_type y = 1;
        for (value_type u = y, v = x; a;) {
            const value_type t = b / a;
            swap(x -= t * u, u);
            swap(y -= t * v, v);
            swap(b -= t * a, a);
        }
        if ((x %= m) < 0) x += m;
        return x;
    }

    static value_type normalize(intmax_t n, value_type m) {
        if (n >= m) {
            n %= m;
        } else if (n < 0) {
            if ((n %= m) < 0) n += m;
        }
        return n;
    }

public:
    ModInt() = default;
    ModInt(intmax_t n) : value(normalize(n, getModulo())) {}

    template <typename T>
        constexpr explicit operator T() const { return static_cast<T>(value); }

    ModInt& operator=(intmax_t n) {
        value = normalize(n, getModulo());
        return *this;
    }

    ModInt& operator+=(const ModInt& other) {
        if ((value += other.value) >= getModulo()) value -= getModulo();
        return *this;
    }
    ModInt& operator-=(const ModInt& other) {
        if ((value -= other.value) < 0) value += getModulo();
        return *this;
    }
    ModInt& operator*=(const ModInt& other) {
        value = (value * other.value) % getModulo();
        return *this;
    }
    ModInt& operator/=(const ModInt& other) {
        value = (value * inverse(other.value, getModulo())) % getModulo();
        return *this;
    }

    ModInt& operator++() {
        if (++value == getModulo()) value = 0;
        return *this;
    }
    ModInt& operator--() {
        if (value-- == 0) value = getModulo() - 1;
        return *this;
    }

    ModInt operator++(int) {
        const ModInt tmp(*this);
        ++*this;
        return tmp;
    }
    ModInt operator--(int) {
        const ModInt tmp(*this);
        --*this;
        return tmp;
    }

    friend ModInt operator+(ModInt lhs, const ModInt& rhs) { return lhs += rhs; }
    friend ModInt operator-(ModInt lhs, const ModInt& rhs) { return lhs -= rhs; }
    friend ModInt operator*(ModInt lhs, const ModInt& rhs) { return lhs *= rhs; }
    friend ModInt operator/(ModInt lhs, const ModInt& rhs) { return lhs /= rhs; }

    ModInt operator+() const { return *this; }
    ModInt operator-() const {
        if (value == 0) return *this;
        return ModInt(getModulo() - value);
    }

    friend bool operator==(const ModInt& lhs, const ModInt& rhs) {
        return lhs.value == rhs.value;
    }
    friend bool operator!=(const ModInt& lhs, const ModInt& rhs) {
        return !(lhs == rhs);
    }

    friend ostream& operator<<(ostream& os, const ModInt& n) {
        return os << n.value;
    }
    friend istream& operator>>(istream& is, ModInt& n) {
        is >> n.value;
        n.value = normalize(n.value, getModulo());
        return is;
    }

    static value_type getModulo() { return ((cmod > 0) ? cmod : rmod); }

    template <int M = Modulo, typename T = typename enable_if<(M <= 0)>::type>
        static T setModulo(value_type m) { rmod = m; }
};

template <intmax_t M>
constexpr typename ModInt<M>::value_type ModInt<M>::cmod;
template <intmax_t M>
typename ModInt<M>::value_type ModInt<M>::rmod;
// }}}

constexpr intmax_t p = intmax_t(1e9) + 7;
using Mint = ModInt<p>;

template <class T>
T extgcd(T a, T b, T &x, T &y) {
    T g = a;
    x = 1, y = 0;
    if (b != 0) {
        g = extgcd(b, a % b, y, x);
        y -= (a / b) * x;
    }
    return g;
}

template <class T>
T power(const T& b, const intmax_t& e) {
    T ret = 1;
    T n = b;
    for (intmax_t p = abs(e); p > 0; p >>= 1) {
        if (p & 1) ret *= n;
        n *= n;
    }
    if (e < 0) return T(1) / ret;
    return ret;
}

// N^K = X (mod p) を満たす N を求める
// フェルマーの小定理より N^{p - 1} = 1 (mod p)
// よって N^{a(p - 1) + 1} = N (mod p)
// ここで a(p - 1) + 1 = bK とする
// N^{bK} = N (mod p)
// よって X^b = N (mod p)
// したがって a(p - 1) + 1 = bK
//           a(p - 1) - bK = -1
//          -a(p - 1) + bK = 1
// を満たす b を求めればよい

int test_case() {
    var(intmax_t, X, K);
    intmax_t a, b;
    const auto g = extgcd(p - 1, K, a, b);
    output(power<Mint>(X, b));
    return 0;
}

int main() {
    ioinit();

    var(size_t, T);

    while (T--) {
        test_case();
    }
    return 0;
}