#232888 (C++17) No.194 フィボナッチ数列の理解(1)

• 問題: No.194 フィボナッチ数列の理解(1)
• ユーザー: mai
• 提出日時: 2018-01-31 00:47:31
• 言語: C++17 (gcc 12.3.0 + boost 1.83.0)
• 結果: AC
• 実行時間: 15 ms / 5,000 ms
• コード長: 10,948 bytes
• コンパイル時間: 3,436 ms
• コンパイル使用メモリ: 222,976 KB
• 実行使用メモリ: 11,156 KB
• 最終ジャッジ日時: 2024-06-09 11:54:35
• 合計ジャッジ時間: 4,674 ms
• ジャッジサーバーID （参考情報）: judge1 / judge3

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	15 ms; 5,376 KB
testcase_03	AC	3 ms; 5,376 KB
testcase_04	AC	6 ms; 5,376 KB
testcase_05	AC	6 ms; 5,376 KB
testcase_06	AC	6 ms; 5,376 KB
testcase_07	AC	9 ms; 5,376 KB
testcase_08	AC	3 ms; 5,376 KB
testcase_09	AC	8 ms; 5,376 KB
testcase_10	AC	4 ms; 5,376 KB
testcase_11	AC	5 ms; 5,376 KB
testcase_12	AC	6 ms; 5,376 KB
testcase_13	AC	3 ms; 5,376 KB
testcase_14	AC	3 ms; 5,376 KB
testcase_15	AC	12 ms; 5,376 KB
testcase_16	AC	12 ms; 5,376 KB
testcase_17	AC	3 ms; 5,376 KB
testcase_18	AC	12 ms; 5,376 KB
testcase_19	AC	15 ms; 5,376 KB
testcase_20	AC	2 ms; 5,376 KB
testcase_21	AC	9 ms; 11,156 KB
testcase_22	AC	2 ms; 5,376 KB
testcase_23	AC	3 ms; 5,376 KB
testcase_24	AC	7 ms; 7,012 KB
testcase_25	AC	5 ms; 6,784 KB
testcase_26	AC	5 ms; 6,528 KB
testcase_27	AC	7 ms; 7,552 KB
testcase_28	AC	3 ms; 5,376 KB
testcase_29	AC	10 ms; 10,368 KB
testcase_30	AC	15 ms; 5,376 KB
testcase_31	AC	2 ms; 5,376 KB
testcase_32	AC	6 ms; 5,376 KB
testcase_33	AC	8 ms; 5,376 KB
testcase_34	AC	7 ms; 5,376 KB
testcase_35	AC	5 ms; 5,376 KB
testcase_36	AC	12 ms; 5,376 KB
testcase_37	AC	2 ms; 5,376 KB
testcase_38	AC	13 ms; 5,376 KB
testcase_39	AC	7 ms; 5,376 KB

ソースコード

#pragma GCC optimize ("O3")
#pragma GCC target ("avx")
#include "bits/stdc++.h" // define macro "/D__MAI"

using namespace std;
typedef long long int ll;

#define debugv(v) {printf("L%d %s > ",__LINE__,#v);for(auto e:v){cout<<e<<" ";}cout<<endl;}
#define debuga(m,w) {printf("L%d %s > ",__LINE__,#m);for(int x=0;x<(w);x++){cout<<(m)[x]<<" ";}cout<<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++){cout<<(m)[y][x]<<" ";}cout<<endl;}}
#define ALL(v) (v).begin(),(v).end()
#define repeat(cnt,l) for(auto cnt=0ll;(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))
#define MD 1000000007ll
#define PI 3.1415926535897932384626433832795
template<typename T1, typename T2> ostream& operator <<(ostream &o, const pair<T1, T2> p) { o << "(" << p.first << ":" << p.second << ")"; return o; }
template<typename T> T& maxset(T& to, const T& val) { return to = max(to, val); }
template<typename T> T& minset(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);
inline ll rand_range(ll l, ll h) {
    return uniform_int_distribution<ll>(l, h)(randdev);
}

#if defined(_WIN32) || defined(_WIN64)
#define getchar_unlocked _getchar_nolock
#define putchar_unlocked _putchar_nolock
#elif defined(__GNUC__)
#else
#define getchar_unlocked getchar
#define putchar_unlocked putchar
#endif
namespace {
#define isvisiblechar(c) (0x21<=(c)&&(c)<=0x7E)
    class MaiScanner {
    public:
        template<typename T> void input_integer(T& var) {
            var = 0; T sign = 1;
            int cc = getchar_unlocked();
            for (; cc<'0' || '9'<cc; cc = getchar_unlocked())
                if (cc == '-') sign = -1;
            for (; '0' <= cc && cc <= '9'; cc = getchar_unlocked())
                var = (var << 3) + (var << 1) + cc - '0';
            var = var * sign;
        }
        inline int c() { return getchar_unlocked(); }
        inline MaiScanner& operator>>(int& var) { input_integer<int>(var); return *this; }
        inline MaiScanner& operator>>(long long& var) { input_integer<long long>(var); return *this; }
        inline MaiScanner& operator>>(string& var) {
            int cc = getchar_unlocked();
            for (; !isvisiblechar(cc); cc = getchar_unlocked());
            for (; isvisiblechar(cc); cc = getchar_unlocked())
                var.push_back(cc);
            return *this;
        }
        template<typename IT> void in(IT begin, IT end) { for (auto it = begin; it != end; ++it) *this >> *it; }
    };
    class MaiPrinter {
    public:
        template<typename T>
        void output_integer(T var) {
            if (var == 0) { putchar_unlocked('0'); return; }
            if (var < 0)
                putchar_unlocked('-'),
                var = -var;
            char stack[32]; int stack_p = 0;
            while (var)
                stack[stack_p++] = '0' + (var % 10),
                var /= 10;
            while (stack_p)
                putchar_unlocked(stack[--stack_p]);
        }
        inline MaiPrinter& operator<<(char c) { putchar_unlocked(c); return *this; }
        inline MaiPrinter& operator<<(int var) { output_integer<int>(var); return *this; }
        inline MaiPrinter& operator<<(long long var) { output_integer<long long>(var); return *this; }
        inline MaiPrinter& operator<<(char* str_p) { while (*str_p) putchar_unlocked(*(str_p++)); return *this; }
        inline MaiPrinter& operator<<(const string& str) {
            const char* p = str.c_str();
            const char* l = p + str.size();
            while (p < l) putchar_unlocked(*p++);
            return *this;
        }
        template<typename IT> void join(IT begin, IT end, char sep = '\n') { for (auto it = begin; it != end; ++it) *this << *it << sep; }
    };
}
MaiScanner scanner;
MaiPrinter printer;




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

    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;
        }
    }
    valarray<valarray<T>> to_valarray() const {
        valarray<valarray<T>> work(height_);
        for (size_t i = 0; i < height_; ++i) {
            auto &v = work[i]; v.resize(height_);
            for (size_t j = 0; j < width_; ++j)
                v[j] = at(i, j);
        } return work;
    }
    // mathematics
    Matrix<T> pow(long long);
    double det() const; T tr();
    Matrix<T>& transpose_self(); Matrix<T> transpose() const;
    struct LU {
        size_t size;
        vector<int> pivot;
        vector<T> elem;
    };
};

// IO
template<typename T> inline ostream& operator << (ostream& os, Matrix<T> mat) { mat.print(os); return os; }

// 掛け算
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> valarray<T> multiply(const Matrix<T>& mat1, const valarray<T>& vec2) {
    assert(mat1.width_ == vec2.size());
    valarray<T> 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>& mat1, Matrix<T>& mat2) { mat1 = multiply(mat1, mat2); return mat1; }
template<typename T> inline Matrix<T> operator*(Matrix<T>& mat1, Matrix<T>& mat2) { return multiply(mat1, mat2); }


// スカラー
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; }

// 行列
template<typename T> inline Matrix<T>& operator+=(Matrix<T>& mat1, Matrix<T>& mat2) { mat1.data_ += mat2.data_; return mat1; }
template<typename T> inline Matrix<T> operator+(Matrix<T>& mat1, Matrix<T>& mat2) { return Matrix<T>(mat1.height_, mat1.width_, mat1.data_ + mat2.data_); }


template<typename T> Matrix<T> Matrix<T>::pow(long long p) {
    assert(height_ == width_);
    Matrix<T> a = *this;
    Matrix<T> b(height_, height_); b.setDiag(1);

    while (0 < p) {
        if (p % 2) {
            b *= a;
        }
        a *= a; p /= 2;
    }
    return b;
}


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

    llmod() : val_(0) {}
    llmod(ll num) :val_(cut(num)) {}
    llmod(const llmod& lm) : val_(lm.val_) {}

    inline operator ll() const { return val_; }
    inline ll operator *() const { return val_; }
    inline llmod& operator=(const llmod& lm) { val_ = lm.val_; return *this; }
    inline llmod& operator=(ll v) { val_ = cut(v); return *this; }

    inline llmod& operator+=(ll v) { val_ = cut(val_ + v); return *this; }
    inline llmod& operator+=(const llmod& l) { val_ = cut(val_ + l.val_); return *this; }
    inline llmod& operator-=(ll v) { val_ = cut(val_ - v); return *this; }
    inline llmod& operator-=(const llmod& l) { val_ = cut(val_ - l.val_); return *this; }
    inline llmod& operator*=(ll v) { val_ = cut(val_ * v); return *this; }
    inline llmod& operator*=(const llmod& l) { val_ = cut(val_ * l.val_); 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 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...powm(n,MD-2)
llmod pow(llmod x, ll p) {
    llmod y = 1;
    while (0 < p) {
        if (p % 2)
            y *= x;
        x *= x;
        p /= 2;
    }
    return y;
}

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






ll m, n, kei;

ll aa[10010];




int main() {
    scanner >> n >> kei;
    scanner.in(aa, aa + n);
    --kei;

    if (40 < n) {
        vector<ll> sum(kei+10);
        repeat(i, n)
            sum[i + 1] = (sum[i] + aa[i]) % MD;
        iterate(i, n, kei+1) {
            sum[i + 1] = (sum[i] + sum[i] - sum[i - n] + MD) % MD;
        }
        cout << ((sum[kei] - sum[kei-n]+MD)%MD) << ' ' << sum[kei+1] << endl;
    }
    else {
        m = n + 1;
        Matrix<llmod> mat(m, m);
        valarray<llmod> v(m);

        repeat(i, n)
            v[i] = aa[i];

        repeat(i, n) {
            iterate(j, i, n) {
                mat(i, j) = 1;
            }
            repeat(j, n) {
                repeat(k, i)
                    mat(i, j) += mat(k, j);
            }
        }
        repeat(i, m)
            mat(n, i) = 1;

        auto p = mat.pow(kei / n);
        auto u = multiply(p, v);
        auto r = u[kei%n];
        
        llmod s = u[n];
        if ((kei%n)+1 < n)
            repeat(i, (kei+1)%n) s += u[i];
        else {
            p *= mat;
            s = multiply(p, v)[n] ;
        }

        cout << r << ' ' << s << endl;
    }

    return 0;
}