#381678 (C++17) No.891 隣接3項間の漸化式

• 問題: No.891 隣接3項間の漸化式
• ユーザー: mai
• 提出日時: 2019-09-20 22:37:12
• 言語: C++17 (gcc 12.3.0 + boost 1.83.0)
• 結果: AC
• 実行時間: 3 ms / 2,000 ms
• コード長: 11,371 bytes
• コンパイル時間: 2,845 ms
• コンパイル使用メモリ: 216,420 KB
• 実行使用メモリ: 5,376 KB
• 最終ジャッジ日時: 2024-09-14 18:34:44
• 合計ジャッジ時間: 3,968 ms
• ジャッジサーバーID （参考情報）: judge4 / judge2

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	2 ms; 5,376 KB
testcase_06	AC	2 ms; 5,376 KB
testcase_07	AC	2 ms; 5,376 KB
testcase_08	AC	2 ms; 5,376 KB
testcase_09	AC	2 ms; 5,376 KB
testcase_10	AC	2 ms; 5,376 KB
testcase_11	AC	2 ms; 5,376 KB
testcase_12	AC	2 ms; 5,376 KB
testcase_13	AC	1 ms; 5,376 KB
testcase_14	AC	2 ms; 5,376 KB
testcase_15	AC	2 ms; 5,376 KB
testcase_16	AC	2 ms; 5,376 KB
testcase_17	AC	2 ms; 5,376 KB
testcase_18	AC	1 ms; 5,376 KB
testcase_19	AC	2 ms; 5,376 KB
testcase_20	AC	1 ms; 5,376 KB
testcase_21	AC	3 ms; 5,376 KB
testcase_22	AC	2 ms; 5,376 KB
testcase_23	AC	2 ms; 5,376 KB
testcase_24	AC	2 ms; 5,376 KB
testcase_25	AC	2 ms; 5,376 KB
testcase_26	AC	2 ms; 5,376 KB
testcase_27	AC	2 ms; 5,376 KB
testcase_28	AC	2 ms; 5,376 KB
testcase_29	AC	2 ms; 5,376 KB
testcase_30	AC	2 ms; 5,376 KB
testcase_31	AC	2 ms; 5,376 KB
testcase_32	AC	2 ms; 5,376 KB
testcase_33	AC	2 ms; 5,376 KB
testcase_34	AC	2 ms; 5,376 KB
testcase_35	AC	2 ms; 5,376 KB
testcase_36	AC	2 ms; 5,376 KB
testcase_37	AC	2 ms; 5,376 KB
testcase_38	AC	2 ms; 5,376 KB
testcase_39	AC	2 ms; 5,376 KB
testcase_40	AC	2 ms; 5,376 KB
testcase_41	AC	2 ms; 5,376 KB

ソースコード

#pragma GCC optimize ("O3")
#include "bits/stdc++.h"

using namespace std;
using ll = long long int;

#define debugos cout
#define debug(v) {printf("L%d %s > ",__LINE__,#v);debugos<<(v)<<endl;}
#define debugv(v) {printf("L%d %s > ",__LINE__,#v);for(auto e:(v)){debugos<<e<<" ";}debugos<<endl;}
#define debuga(m,w) {printf("L%d %s > ",__LINE__,#m);for(int x=0;x<(w);x++){debugos<<(m)[x]<<" ";}debugos<<endl;}
#define debugaa(m,h,w) {printf("L%d %s >\n",__LINE__,#m);for(int y=0;y<(h);y++){for(int x=0;x<(w);x++){debugos<<(m)[y][x]<<" ";}debugos<<endl;}}
#define all(v) (v).begin(),(v).end()
#define repeat(cnt,l) for(auto cnt=remove_reference<decltype(l)>::type();(cnt)<(l);++(cnt))
#define rrepeat(cnt,l) for(auto cnt=(l)-1;0<=(cnt);--(cnt))
#define iterate(cnt,b,e) for(auto cnt=(b);(cnt)!=(e);++(cnt))
#define diterate(cnt,b,e) for(auto cnt=(b);(cnt)!=(e);--(cnt))
const ll MD = 1000000007ll; const long double PI = 3.1415926535897932384626433832795L;
inline void assert_call(bool assertion, function<void()> f) { if (!assertion) { cerr << "assertion fault:" << endl; f(); abort(); } }
template<typename T1, typename T2> inline ostream& operator <<(ostream &o, const pair<T1, T2> p) { o << '(' << p.first << ':' << p.second << ')'; return o; }
template<typename Vec> inline ostream& _ostream_vecprint(ostream& os, const Vec& a) {
    os << '['; for (const auto& e : a) os << ' ' << e << ' '; os << ']'; return os; }
template<typename T> inline ostream& operator<<(ostream& o, const vector<T>& v) { return _ostream_vecprint(o, v); }
template<typename T, size_t S> inline ostream& operator<<(ostream& o, const array<T, S>& v) { return _ostream_vecprint(o, v); }
template<typename T> inline T& chmax(T& to, const T& val) { return to = max(to, val); }
template<typename T> inline T& chmin(T& to, const T& val) { return to = min(to, val); }
void bye(string s, int code = 0) { cout << s << endl; exit(code); }
mt19937_64 randdev(8901016);
template<typename T, typename Random = decltype(randdev), typename enable_if<is_integral<T>::value>::type* = nullptr>
inline T rand(T l, T h, Random& rand = randdev) { return uniform_int_distribution<T>(l, h)(rand); }
template<typename T, typename Random = decltype(randdev), typename enable_if<is_floating_point<T>::value>::type* = nullptr>
inline T rand(T l, T h, Random& rand = randdev) { return uniform_real_distribution<T>(l, h)(rand); }

#if defined(_WIN32) || defined(_WIN64)
#define getc_x _getc_nolock
#define putc_x _putc_nolock
#elif defined(__GNUC__)
#define getc_x getc_unlocked
#define putc_x putc_unlocked
#else
#define getc_x getc
#define putc_x putc
#endif
#define isvisiblechar(c) (0x21<=(c)&&(c)<=0x7E)
class MaiScanner {
    FILE* fp_;
public:
    inline MaiScanner(FILE* fp):fp_(fp){}
    template<typename T> void input_integer(T& var) noexcept {
        var = 0; T sign = 1;
        int cc = getc_x(fp_);
        for (; cc < '0' || '9' < cc; cc = getc_x(fp_))
            if (cc == '-') sign = -1;
        for (; '0' <= cc && cc <= '9'; cc = getc_x(fp_))
            var = (var << 3) + (var << 1) + cc - '0';
        var = var * sign;
    }
    inline int c() noexcept { return getc_x(fp_); }
    inline MaiScanner& operator>>(int& var) noexcept { input_integer<int>(var); return *this; }
    inline MaiScanner& operator>>(long long& var) noexcept { input_integer<long long>(var); return *this; }
    inline MaiScanner& operator>>(string& var) {
        int cc = getc_x(fp_);
        for (; !isvisiblechar(cc); cc = getc_x(fp_));
        for (; isvisiblechar(cc); cc = getc_x(fp_))
            var.push_back(cc);
        return *this;
    }
    template<typename IT> inline void in(IT begin, IT end) { for (auto it = begin; it != end; ++it) *this >> *it; }
};
class MaiPrinter {
    FILE* fp_;
public:
    inline MaiPrinter(FILE* fp):fp_(fp){}
    template<typename T>
    void output_integer(T var) noexcept {
        if (var == 0) { putc_x('0', fp_); return; }
        if (var < 0)
            putc_x('-', fp_),
            var = -var;
        char stack[32]; int stack_p = 0;
        while (var)
            stack[stack_p++] = '0' + (var % 10),
            var /= 10;
        while (stack_p)
            putc_x(stack[--stack_p], fp_);
    }
    inline MaiPrinter& operator<<(char c) noexcept { putc_x(c, fp_); return *this; }
    inline MaiPrinter& operator<<(int var) noexcept { output_integer<int>(var); return *this; }
    inline MaiPrinter& operator<<(long long var) noexcept { output_integer<long long>(var); return *this; }
    inline MaiPrinter& operator<<(char* str_p) noexcept { while (*str_p) putc_x(*(str_p++), fp_); return *this; }
    inline MaiPrinter& operator<<(const string& str) {
        const char* p = str.c_str();
        const char* l = p + str.size();
        while (p < l) putc_x(*p++, fp_);
        return *this;
    }
    template<typename IT> void join(IT begin, IT end, char sep = ' ') { for (bool b = 0; begin != end; ++begin, b = 1) b ? *this << sep << *begin : *this << *begin; }
};
MaiScanner scanner(stdin);
MaiPrinter printer(stdout);

template<typename T>
// using T = double;
class Matrix {
public:
    size_t height_, width_;
    valarray<T> data_;
    Matrix(size_t height = 1, size_t width = 1) :height_(height), width_(width), data_(height*width) {}
    template <typename V>
    Matrix(size_t height, size_t width, const V& data) : height_(height), width_(width), data_(data) {}
    Matrix(size_t height, size_t width, initializer_list<T> init) : height_(height), width_(width), data_(init) {}

    inline T& operator()(size_t y, size_t x) { return data_[y*width_ + x]; }
    inline T operator() (size_t y, size_t x) const { return data_[y*width_ + x]; }
    inline T& at(size_t y, size_t x) { return data_[y*width_ + x]; }
    inline T at(size_t y, size_t x) const { return data_[y*width_ + x]; }
    inline void resize(size_t h, size_t w) { height_ = h; width_ = w; data_.resize(h*w); }
    inline void resize(size_t h, size_t w, T val) { height_ = h; width_ = w; data_.resize(h*w, val); }
    inline void fill(T val) { data_ = val; }
    Matrix<T>& setDiag(T val) { for (size_t i = 0, en = min(width_, height_); i < en; ++i)at(i, i) = val; return *this; }

    void print(ostream& os) {
        os << "- - -" << endl; //  << setprecision(3)
        for (size_t y = 0; y < height_; ++y) {
            for (size_t x = 0; x < width_; ++x) {
                os << setw(7) << at(y, x) << ' ';
            }os << endl;
        }
    }
};
template<typename T> inline ostream& operator << (ostream& os, Matrix<T> mat) { mat.print(os); return os; }

template<typename T> Matrix<T> multiply(const Matrix<T>& mat1, const Matrix<T>& mat2) {
    assert(mat1.width_ == mat2.height_);
    Matrix<T> result(mat1.height_, mat2.width_);
    for (size_t i = 0; i < mat1.height_; ++i)
        for (size_t j = 0; j < mat2.width_; ++j)
            for (size_t k = 0; k < mat1.width_; ++k)
                result(i, j) += mat1(i, k) * mat2(k, j);
    return result;
}
template<typename T, typename V> V multiply(const Matrix<T>& mat1, const V& vec2) {
    assert(mat1.width_ == vec2.size());
    V result(mat1.height_);
    for (size_t i = 0, j; i < mat1.height_; ++i)
        for (j = 0; j < mat1.width_; ++j)
            result[i] += mat1(i, j) * vec2[j];
    return result;
}

template<typename T> inline Matrix<T>& operator+=(Matrix<T>& mat, T val) { mat.data_ += val; return mat; }
template<typename T> inline Matrix<T>& operator-=(Matrix<T>& mat, T val) { mat.data_ -= val; return mat; }
template<typename T> inline Matrix<T>& operator*=(Matrix<T>& mat, T val) { mat.data_ *= val; return mat; }
template<typename T> inline Matrix<T>& operator/=(Matrix<T>& mat, T val) { mat.data_ /= val; return mat; }
template<typename T> inline Matrix<T>& operator^=(Matrix<T>& mat, T val) { mat.data_ ^= val; return mat; }
template<typename T> inline Matrix<T>& operator+=(Matrix<T>& mat1, const Matrix<T>& mat2) { mat1.data_ += mat2.data_; return mat1; }
template<typename T> inline Matrix<T> operator+(Matrix<T>& mat1, const Matrix<T>& mat2) { return Matrix<T>(mat1.height_, mat1.width_, mat1.data_ + mat2.data_); }
template<typename T> inline Matrix<T>& operator-=(Matrix<T>& mat1, const Matrix<T>& mat2) { mat1.data_ -= mat2.data_; return mat1; }
template<typename T> inline Matrix<T> operator-(Matrix<T>& mat1, const Matrix<T>& mat2) { return Matrix<T>(mat1.height_, mat1.width_, mat1.data_ - mat2.data_); }
template<typename T> inline Matrix<T>& operator*=(Matrix<T>& mat1, const Matrix<T>& mat2) { mat1 = multiply(mat1, mat2); return mat1; }
template<typename T> inline Matrix<T> operator*(const Matrix<T>& mat1, const Matrix<T>& mat2) { return multiply(mat1, mat2); }
template<typename T, typename V> inline V operator*(const Matrix<T>& mat1, const V& vec2) { return multiply(mat1, vec2); }

template<typename T> Matrix<T> pow(Matrix<T> a, long long p) {
    assert(a.height_ == a.width_);
    Matrix<T> b(a.height_, a.height_); b.setDiag(1);
    while (0 < p) {
        if (p & 1) b *= a;
        a *= a; p >>= 1;
    }
    return b;
}

class llmod {
private:
    using value_type = long long;
    value_type val_;
    // inline ll cut(ll v) const { return ((v%MOD) + MOD) % MOD; } // safe
public:
    static const value_type MOD = MD; // <= 

    llmod() : val_(0) {}
    llmod(value_type num) :val_(((num % MOD) + MOD) % MOD) {}

    inline operator value_type() const { return val_; }
    inline value_type operator *() const { return val_; }
    inline llmod& operator=(const llmod& lm) { val_ = lm.val_; return *this; }
    inline llmod& operator=(value_type v) { val_ = (v) % MOD; return *this; }

    inline llmod& operator+=(value_type v) { val_ = (val_ + v) % MOD; return *this; }
    inline llmod& operator+=(const llmod& l) { val_ = (val_ + l.val_) % MOD; return *this; }
    inline llmod& operator-=(value_type v) { val_ = (val_ - v + MOD) % MOD; return *this; }
    inline llmod& operator-=(const llmod& l) { val_ = (val_ - l.val_ + MOD) % MOD; return *this; }
    inline llmod& operator*=(value_type v) { val_ = (val_ * v) % MOD; return *this; }
    inline llmod& operator*=(const llmod& l) { val_ = (val_ * l.val_) % MOD; return *this; }
    inline llmod& operator++() { val_ = (val_ + 1) % MOD; return *this; }
    inline llmod operator++(int) { llmod t = *this; val_ = (val_ + 1) % MOD; return t; }
    inline llmod& justify() { val_ = ((val_ % MOD) + MOD) % MOD; return *this; }
    friend llmod pow(llmod, long long);
};
inline ostream& operator<<(ostream& os, const llmod& l) { os << *l; return os; }

inline llmod operator+(llmod t, const llmod& r) { return t += r; }
inline llmod operator-(llmod t, const llmod& r) { return t -= r; }
inline llmod operator*(llmod t, const llmod& r) { return t *= r; }

// MEMO : 逆元...pow(n,MD-2)
llmod pow(llmod x, long long p) {
    llmod::value_type y = 1;
    llmod::value_type xval = x.justify();
    while (0 < p) {
        if (p & 1) y = (xval * y) % llmod::MOD;
        xval = (xval * xval) % llmod::MOD;
        p >>= 1;
    }
    return llmod(y);
}

inline llmod& operator/=(llmod& l, const llmod& r) { return l *= pow(r, llmod::MOD - 2); }

//

ll A, B, N;

//


int main() {
    scanner >> A >> B >> N;
    Matrix<llmod> mat(2, 2, {
        A, B,
        1, 0
    });
    
    auto m = pow(mat, N);
    
    vector<llmod> v = {1, 0};
    
    llmod ans = (m*v)[1];
    
    cout << *ans << endl;
    
    return 0;
}