結果

問題 No.1275 綺麗な式
ユーザー kcvlexkcvlex
提出日時 2020-10-30 23:33:33
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 2 ms / 2,000 ms
コード長 8,655 bytes
コンパイル時間 1,393 ms
コンパイル使用メモリ 150,412 KB
最終ジャッジ日時 2025-01-15 18:07:15
ジャッジサーバーID
（参考情報） 		judge5 / judge5
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ファイルパターン 結果
sample AC * 2
other AC * 60
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 <limits>
#include <initializer_list>
#include <utility>
#include <bitset>
#include <tuple>
#include <type_traits>
#include <functional>
#include <string>
#include <array>
#include <deque>
#include <list>
#include <queue>
#include <stack>
#include <vector>
#include <map>
#include <set>
#include <unordered_map>
#include <unordered_set>
#include <iterator>
#include <algorithm>
#include <complex>
#include <random>
#include <numeric>
#include <iostream>
#include <iomanip>
#include <sstream>
#include <regex>
#include <cassert>
#include <cstddef>
#include <variant>

#define endl codeforces

#define ALL(v) std::begin(v), std::end(v)
#define ALLR(v) std::rbegin(v), std::rend(v)

using ll = std::int64_t;
using ull = std::uint64_t;
using pii = std::pair<int, int>;
using tii = std::tuple<int, int, int>;
using pll = std::pair<ll, ll>;
using tll = std::tuple<ll, ll, ll>;
using size_type = ssize_t;
template <typename T> using vec = std::vector<T>;
template <typename T> using vvec = vec<vec<T>>;

template <typename T> const T& var_min(const T &t) { return t; }
template <typename T> const T& var_max(const T &t) { return t; }
template <typename T, typename... Tail> const T& var_min(const T &t, const Tail&... tail) { return std::min(t, var_min(tail...)); }
template <typename T, typename... Tail> const T& var_max(const T &t, const Tail&... tail) { return std::max(t, var_max(tail...)); }
template <typename T, typename... Tail> void chmin(T &t, const Tail&... tail) { t = var_min(t, tail...); }
template <typename T, typename... Tail> void chmax(T &t, const Tail&... tail) { t = var_max(t, tail...); }

template <typename T, std::size_t Head, std::size_t... Tail> 
struct multi_dim_array { using type = std::array<typename multi_dim_array<T, Tail...>::type, Head>; };

template <typename T, std::size_t Head> 
struct multi_dim_array<T, Head> { using type = std::array<T, Head>; };

template <typename T, std::size_t... Args> using mdarray = typename multi_dim_array<T, Args...>::type;

template <typename T, typename F, typename... Args> 
void fill_seq(T &t, F f, Args... args) { 
    if constexpr (std::is_invocable<F, Args...>::value) { 
        t = f(args...); 
    } else { 
        for (size_type i = 0; i < t.size(); i++) fill_seq(t[i], f, args..., i); 
    } 
}

template <typename T> vec<T> make_v(size_type sz) { return vec<T>(sz); }

template <typename T, typename... Tail> 
auto make_v(size_type hs, Tail&&... ts) { 
    auto v = std::move(make_v<T>(std::forward<Tail>(ts)...)); 
    return vec<decltype(v)>(hs, v); 
}

namespace init__ { 
struct InitIO { 
    InitIO() { 
        std::cin.tie(nullptr); 
        std::ios_base::sync_with_stdio(false); 
        std::cout << std::fixed << std::setprecision(30); 
    } 
} init_io; 
}

template <typename T>
T ceil_pow2(T bound) {
    T ret = 1;
    while (ret < bound) ret *= 2;
    return ret;
}

template <typename T>
T ceil_div(T a, T b) { return a / b + !!(a % b); }


namespace math {

template <typename T>
constexpr T mul_id_ele() {
    if constexpr (std::is_fundamental<T>::value) {
        return T(1);
    } else {
        return T::mul_id_ele();
    }
}

template <typename T>
constexpr T add_id_ele() {
    if constexpr (std::is_fundamental<T>::value) {
        return T(0);
    } else {
        return T::add_id_ele();
    }
}

template <typename T>
constexpr T pow(const T &n, ll k) {
    T ret = mul_id_ele<T>();
    T cur = n;
    while (k) {
        if (k & 1) ret *= cur;
        cur *= cur;
        k /= 2;
    }
    return ret;
}


template <typename T>
typename std::enable_if<std::is_integral<T>::value, T>::type
gcd(T a, T b) { return b ? gcd(a % b, b) : a; }

}

namespace math {

template <ull Mod>
struct Modint {

    constexpr Modint(ll x) noexcept : x((Mod + x % static_cast<ll>(Mod)) % Mod) { }
    constexpr Modint() noexcept : Modint(0) { }
    
    constexpr static Modint add_id_ele() { 
        return Modint(0); 
    }
    
    constexpr static Modint mul_id_ele() {
        return Modint(1);
    }
    
    constexpr ll value() const noexcept { 
        return static_cast<ll>(x);
    }

    constexpr Modint& operator+=(const Modint &oth) noexcept {
        x += oth.value();
        if (Mod <= x) x -= Mod;
        return *this;
    }

    constexpr Modint& operator-=(const Modint &oth) noexcept {
        x += Mod - oth.value();
        if (Mod <= x) x -= Mod;
        return *this;
    }

    constexpr Modint& operator*=(const Modint &oth) noexcept {
        x *= oth.value();
        x %= Mod;
        return *this;
    }

    constexpr Modint& operator/=(const Modint &oth) noexcept {
        x *= oth.inv().value();
        x %= Mod;
        return *this;
    }

    constexpr Modint operator+(const Modint &oth) const noexcept {
        return Modint(x) += oth;
    }

    constexpr Modint operator-(const Modint &oth) const noexcept {
        return Modint(x) -= oth;
    }

    constexpr Modint operator*(const Modint &oth) const noexcept {
        return Modint(x) *= oth;
    }

    constexpr Modint operator/(const Modint &oth) const noexcept {
        return Modint(x) /= oth;
    }

    constexpr Modint operator-() const noexcept {
        return Modint((x != 0) * (Mod - x)); 
    }

    constexpr bool operator==(const Modint &oth) const noexcept {
        return value() == oth.value();
    }

    template <typename T>
    constexpr typename std::enable_if<std::is_integral<T>::value, const Modint&>::type
    operator=(T t) noexcept {
        (*this) = Modint(std::forward<T>(t)); 
        return *this;
    }

    constexpr Modint inv() const noexcept {
        return ::math::pow(*this, Mod - 2);
    }

    constexpr ull mod() const noexcept {
        return Mod;
    }

private:
    ull x;
};

template <ull Mod>
Modint<Mod> inv(Modint<Mod> m) {
    return m.inv();
}

template <ull Mod>
std::istream& operator>>(std::istream &is, Modint<Mod> &m) {
    ll v;
    is >> v;
    m = v;
    return is;
}

template <ull Mod>
std::ostream& operator<<(std::ostream &os, Modint<Mod> m) {
    os << m.value();
    return os;
}

}


namespace math {

template <typename T, size_type M, size_type N>
struct Matrix : mdarray<T, M, N> {
    using mdarray<T, M, N>::mdarray;

    constexpr Matrix& operator+=(const Matrix<T, M, N> &rhs) {
        for (size_type i = 0; i < M; i++) for (size_type j = 0; j < N; j++) (*this)[i][j] += rhs[i][j];
    }

    constexpr Matrix operator+(const Matrix<T, M, N> &rhs) const {
        return Matrix(*this) += rhs;
    }
    
    template <size_type L>
    constexpr Matrix<T, M, L> operator*(const Matrix<T, N, L> &rhs) const {
        Matrix<T, M, L> ret;
        for (size_type i = 0; i < M; i++) for (size_type j = 0; j < L; j++) ret[i][j] = T();
        for (size_type i = 0; i < M; i++) {
            for (size_type j = 0; j < N; j++) {
                for (size_type k = 0; k < L; k++) {
                    ret[i][k] += (*this)[i][j] * rhs[j][k];
                }
            }
        }
        return ret;
    }

    constexpr Matrix& operator*=(const T &c) {
        for (size_type i = 0; i < M; i++) for (size_type j = 0; j < N; j++) (*this)[i][j] *= c;
        return *this;
    }

    constexpr Matrix operator*(const T &c) const {
        return Matrix(*this) *= c;
    }

    size_type row() const noexcept {
        return M;
    }

    size_type col() const noexcept {
        return N;
    }

    static Matrix add_id_ele() {
        Matrix ret;
        fill_seq(ret, [&](size_type, size_type) { return T(0); });
        return ret;
    }

    static Matrix mul_id_ele() {
        static_assert(M == N, "Matrix must be square.");
        Matrix ret;
        fill_seq(ret, [&](size_type i, size_type j) { 
            return i == j ? T(1) : T(0);  // TODO : is this correct ??
        });
        return ret;
    }
};

template <typename T, size_type M, size_type N>
std::ostream& operator<<(std::ostream &os, const Matrix<T, M, N> &mat) {
    for (size_type i = 0; i < M; i++) {
        os << (i == 0 ? "[ " : "  ");
        for (size_type j = 0; j < N; j++) os << mat[i][j] << ", ";
        os << (i + 1 == M ? " ]" : "\n");
    }
    return os;
}

}

constexpr ll mod = 1e9 + 7;
using mint = math::Modint<mod>;
using matrix_t = math::Matrix<mint, 2, 2>;

int main() {
    mint a, b;
    ll n;
    std::cin >> a >> b >> n;
    auto mat = matrix_t::add_id_ele();
    mat[0][0] = a;
    mat[0][1] = 1;
    mat[1][0] = b;
    mat[1][1] = a;

    auto res = matrix_t::mul_id_ele(), cur = mat;
    while (n) {
        if (n & 1) res = cur * res;
        cur = cur * cur;
        n /= 2;
    }
    auto ans = res[1][1];
    ans *= 2;
    std::cout << ans << '\n';
    return 0;
}
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