#465109 (C++14) No.526 フィボナッチ数列の第N項をMで割った余りを求める

• 問題: No.526 フィボナッチ数列の第N項をMで割った余りを求める
• ユーザー: walkre
• 提出日時: 2020-04-17 08:54:26
• 言語: C++14 (gcc 12.3.0 + boost 1.83.0)
• 結果: AC
• 実行時間: 3 ms / 2,000 ms
• コード長: 8,670 bytes
• コンパイル時間: 1,821 ms
• コンパイル使用メモリ: 178,128 KB
• 実行使用メモリ: 5,248 KB
• 最終ジャッジ日時: 2024-10-03 10:07:45
• 合計ジャッジ時間: 2,526 ms
• ジャッジサーバーID （参考情報）: judge1 / 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; 5,248 KB
testcase_02	AC	2 ms; 5,248 KB
testcase_03	AC	2 ms; 5,248 KB
testcase_04	AC	2 ms; 5,248 KB
testcase_05	AC	2 ms; 5,248 KB
testcase_06	AC	2 ms; 5,248 KB
testcase_07	AC	3 ms; 5,248 KB
testcase_08	AC	2 ms; 5,248 KB
testcase_09	AC	2 ms; 5,248 KB
testcase_10	AC	2 ms; 5,248 KB
testcase_11	AC	2 ms; 5,248 KB
testcase_12	AC	2 ms; 5,248 KB
testcase_13	AC	2 ms; 5,248 KB
testcase_14	AC	2 ms; 5,248 KB

ソースコード

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

using i64 = int64_t;

#define rep(i, x, y) for (i64 i = i64(x), i##_max_for_repmacro = i64(y); i < i##_max_for_repmacro; ++i)
#define debug(x) #x << "=" << (x)

#ifdef DEBUG
#define _GLIBCXX_DEBUG
#define print(x) std::cerr << debug(x) << " (L:" << __LINE__ << ")" << std::endl
#else
#define print(x)
#endif

template <i64 p>
class fp {
    public:
    i64 x;
    fp() : x(0) {}
    fp(i64 x_) : x((x_ % p + p) % p) {}
    fp operator+() const { return fp(x); }
    fp operator-() const { return fp(-x); }
    fp& operator+=(const fp& y) {
        x += y.x;
        if (x >= p) x -= p;
        return *this;
    }
    fp& operator-=(const fp& y) { return *this += -y; }
    fp& operator*=(const fp& y) {
        x = x * y.x % p;
        return *this;
    }
    fp& operator/=(const fp& y) { return *this *= fp(inverse(y.x)); }
    fp operator+(const fp& y) const { return fp(x) += y; }
    fp operator-(const fp& y) const { return fp(x) -= y; }
    fp operator*(const fp& y) const { return fp(x) *= y; }
    fp operator/(const fp& y) const { return fp(x) /= y; }
    bool operator==(const fp& y) const { return x == y.x; }
    bool operator!=(const fp& y) const { return !(*this == y); }
    i64 extgcd(i64 a, i64 b, i64& x, i64& y) {
        i64 d = a;
        if (b != 0) {
            d = extgcd(b, a % b, y, x);
            y -= (a / b) * x;
        } else {
            x = 1;
            y = 0;
        }
        return d;
    }
    i64 inverse(i64 a) {
        i64 x, y;
        extgcd(a, p, x, y);
        return (x % p + p) % p;
    }
};

template <i64 p>
i64 abs(const fp<p>& x) { return x.x; }

template <i64 p>
istream& operator>>(istream& is, fp<p>& x) {
    is >> x.x;
    return is;
}

template <i64 p>
ostream& operator<<(ostream& os, const fp<p>& x) {
    os << x.x;
    return os;
}

template <typename T, typename U>
ostream& operator<<(ostream& os, const pair<T, U>& p) {
    os << "(" << p.first << ", " << p.second << ")";
    return os;
}

template <typename T>
ostream& operator<<(ostream& os, const vector<T>& vec) {
    os << "[";
    for (const auto& v : vec) {
        os << v << ",";
    }
    os << "]";
    return os;
}

template <typename T>
bool chmin(T& a, const T& b) {
    if (a > b) {
        a = b;
        return true;
    }
    return false;
}

template <typename T>
bool chmax(T& a, const T& b) {
    if (a < b) {
        a = b;
        return true;
    }
    return false;
}

template <typename A, typename T, size_t size>
void fill(A (&ary)[size], const T& val) {
    fill((T*)ary, (T*)(ary + size), val);
}

constexpr int inf = 1.01e9;
constexpr i64 inf64 = 4.01e18;
constexpr long double eps = 1e-9;

// double(64bit浮動小数)のn分探索のループ回数の上限(2分探索なら50でも十分かもしれない). long double(80ビットの x87 浮動小数点型?)だと, 2分探索であってもこれだと足りないケースがある気がするので, もうちょっと余裕を持たせた方が良さそう.
constexpr i64 max_loop = 100;

class mint {
public:
    i64 x, m;
    mint() = default;
    mint(i64 m_, i64 x_) : m(m_), x((x_ % m_ + m_) % m_) {}
    mint operator+() const { return mint(m, x); }
    mint operator-() const { return mint(m, -x); }
    mint& operator+=(const mint& y) {
        if (m == 0) {
            assert(y.m != 0);
            m = y.m;
        }
        assert(m == y.m);
        x = ((x + y.x) % m + m) % m;
        return *this;
    }
    mint& operator-=(const mint& y) { return *this += -y; }
    mint& operator*=(const mint& y) {
        if (m == 0) {
            assert(y.m != 0);
            m = y.m;
        }
        assert(m == y.m);
        x = x * y.x % m;
        return *this;
    }
    mint& operator/=(const mint& y) { return *this *= mint(m, inverse(y.x)); }
    mint operator+(const mint& y) const { return mint(m, x) += y; }
    mint operator-(const mint& y) const { return mint(m, x) -= y; }
    mint operator*(const mint& y) const { return mint(m, x) *= y; }
    mint operator/(const mint& y) const { return mint(m, x) /= y; }
    bool operator==(const mint& y) const { return x == y.x; }
    bool operator!=(const mint& y) const { return !(*this == y); }
    i64 extgcd(i64 a, i64 b, i64& x, i64& y) {
        i64 d = a;
        if (b != 0) {
            d = extgcd(b, a % b, y, x);
            y -= (a / b) * x;
        } else {
            x = 1;
            y = 0;
        }
        return d;
    }
    i64 inverse(i64 a) {
        i64 x, y;
        extgcd(a, m, x, y);
        return (x % m + m) % m;
    }
};

ostream& operator<<(ostream& os, const mint& x) {
    os << x.x;
    return os;
}

template<class K> class matrix {
public:
    int m, n;
    vector<vector<K>> a;
    matrix(int m_, int n_) : m(m_), n(n_), a(m_, vector<K>(n_)) {}
    matrix(const vector<vector<K>>& v) : m(v.size()), n((v.size() == 0 or v[0].size() == 0) ? 0 : v[0].size()), a(v) {}
    //matrix(const matrix<K>& other)=default;
    //~matrix()=default;

    vector<K>& operator[](int i) {
        assert(0 <= i);
        assert(i < m);
        return a[i];
    }
    matrix<K> operator+() const { return *this; }
    matrix<K> operator-() const { return K(-1) * *this; }
    K at(int i, int j) const { return a[i][j]; }

    matrix<K>& operator=(const matrix<K>& other) = default;
    matrix<K>& operator+=(const matrix<K>& other) {
        assert(m == other.m);
        assert(n == other.n);
        for (int i = 0; i < m; ++i)
            for (int j = 0; j < n; ++j) (*this)[i][j] += other[i][j];
        return *this;
    }
    matrix<K>& operator-=(const matrix<K>& other) { return (*this) += -other; }
    matrix<K>& operator*=(const matrix<K>& other) {
        assert(n == other.m);
        vector<vector<K>> b(m, vector<K>(other.n));
        for (int i = 0; i < m; ++i)
            for (int j = 0; j < other.n; ++j)
                for (int k = 0; k < n; ++k) b[i][j] += (*this)[i][k] * other.at(k, j);
        a = b;
        n = other.n;
        return *this;
    }
    matrix<K>& operator/=(const K& k) {
        assert(k != K(0));
        for (int i = 0; i < m; ++i)
            for (int j = 0; j < n; ++j) (*this)[i][j] /= k;
        return *this;
    }
    matrix<K>& operator%=(const K& k) {
        assert(k != K(0));
        for (int i = 0; k < m; ++i)
            for (int j = 0; j < n; ++j) (*this)[i][j] = ((*this)[i][j] + k) % k;
        return *this;
    }
    matrix<K> operator+(const matrix<K>& other) const { return matrix<K>(*this) += other; }
    matrix<K> operator-(const matrix<K>& other) const { return matrix<K>(*this) -= other; }
    matrix<K> operator*(const matrix<K>& other) const { return matrix<K>(*this) *= other; }
    matrix<K> operator/(const K& k) const { return matrix(*this) /= k; }
    matrix<K> operator%(const K& k) const { return matrix(*this) %= k; }

    bool operator==(const matrix<K>& other) const {
        if (m != other.m or n != other.n) return false;
        for (int i = 0; i < m; ++i)
            for (int j = 0; j < n; ++j)
                if ((*this)[i][j] != other[i][j]) return false;
        return true;
    }
    bool operator!=(const matrix<K>& other) const { return !((*this) == other); }

    static matrix<K> E(int m) {
        assert(0 <= m);
        matrix<K> E_(m, m);
        for (int i = 0; i < m; ++i) E_[i][i] = K(1);
        return E_;
    }

    static matrix<K> e(int m, int i) {
        assert(0 <= i);
        assert(i < m);
        matrix<K> e_;
        e_[i][0] = K(1);
        return e_;
    }
};


template <class K>
matrix<K> rep_pow(matrix<K> x, const K e /* = Kの単位元 */, int n, int64_t y) {
    assert(x.m == x.n);
    assert(x.m == n);

    matrix<K> res(n, n);
    for (int i = 0; i < n; ++i) {
        for (int j = 0; j < n; ++j) {
            if (i == j)
                res[i][j] = e;
            else
                res[i][j] = e - e;
        }
    }

    while (y > 0) {
        if (y & 1) res *= x;
        x *= x;
        y >>= 1;
    }
    return res;
}


void solve() {
    //constexpr i64 mod = 1'000'000'007;
    i64 N,M;
    cin >> N >> M;

    if(N==1){
        cout << 0 << endl;
        return;
    }
    if(N==2){
        cout << 1 << endl;
        return;
    }

    matrix<mint> a(2, 2);
    a[0][0]=mint(M, 0);
    a[0][1]=mint(M, 1);
    a[1][0]=mint(M, 1);
    a[1][1]=mint(M, 1);

    auto a_pow=rep_pow(a,mint(M,1),2,N-2);

    matrix<mint> v(2,1);
    v[0][0]=mint(M,0);
    v[1][0]=mint(M,1);

    auto b=a_pow*v;

    cout << b[1][0] << endl;
}

int main() {
    std::cin.tie(0);
    std::ios::sync_with_stdio(false);
    cout.setf(ios::fixed);
    cout.precision(16);
    solve();
    return 0;
}