結果

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
コンテスト
ユーザー minato
提出日時 2020-10-10 11:18:48
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 7,366 bytes
コンパイル時間 3,402 ms
コンパイル使用メモリ 221,456 KB
最終ジャッジ日時 2025-01-15 06:16:26
ジャッジサーバーID
（参考情報） 		judge3 / judge3
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ファイルパターン 結果
sample AC * 3
other AC * 12
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 # 

#ifdef ONLINE_JUDGE
#pragma GCC target("avx2,avx")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#endif
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ull = unsigned long long;
using i128 = __int128_t;
using pii = pair<int, int>;
using pll = pair<long long, long long>;
#define rep(i, n) for (int i = 0; i < (n); i++)
#define all(x) (x).begin(), (x).end()
constexpr char ln = '\n';
template<class T1, class T2> inline bool chmax(T1& a, T2 b) { if (a < b) {a = b; return true ;} return false ;}
template<class T1, class T2> inline bool chmin(T1& a, T2 b) { if (a > b) {a = b; return true ;} return false ;}
struct fast_ios { fast_ios() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(20); }; } fast_ios_;
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////

template<typename Int, int sz>
struct SquareMatrix {
    using arr = array<Int, sz>;
   	using mat = array<arr, sz>;
    mat A;
	int N;

   	SquareMatrix() : SquareMatrix(sz) {}
   	SquareMatrix(int N) : N(N) {
        for (int i = 0; i < N; i++) {
            for (int j = 0; j < N; j++) {
                A[i][j] = 0;
            }
        }
    }

    int size() { return N; }
	const arr& operator[](int k) const { return A[k]; }
  	arr& operator[](int k) { return A[k]; }

    static SquareMatrix add_identity(int N) { return SquareMatrix(N); }
  	static SquareMatrix mul_identity(int N) {
        SquareMatrix I(N);
    	for(int i = 0; i < N; i++) I[i][i] = 1;
    	return I;
  	}

  	SquareMatrix& operator+=(const SquareMatrix &B) {
    	for(int i = 0; i < N; i++) {
      	    for(int j = 0; j < N; j++) {
        	    (*this)[i][j] += B[i][j];
            }
        }
    	return *this;
  	}

  	SquareMatrix& operator-=(const SquareMatrix &B) {
    	for(int i = 0; i < N; i++) {
      		for(int j = 0; j < N; j++) {
				(*this)[i][j] -= B[i][j];
			}
		}
    	return *this;
  	}

    SquareMatrix& operator*=(const SquareMatrix &B) {
        SquareMatrix C(N);
        for(int i = 0; i < N; i++) {
            for(int k = 0; k < N; k++) {
                for(int j = 0; j < N; j++) {
                    C[i][j] += (*this)[i][k] * B[k][j];
                }
            }
        }
        A.swap(C.A);
        return *this;
    }

    SquareMatrix& operator^=(long long k) {
        SquareMatrix B = SquareMatrix::mul_identity(N);
        while(k) {
            if(k & 1) B *= *this;
            *this *= *this;
            k >>= 1;
        }
        A.swap(B.A);
        return *this;
    }

    SquareMatrix pow(long long k) {
        SquareMatrix ret = A;
        ret ^= k;
        return ret;
    }

    SquareMatrix operator+(const SquareMatrix& B) const { return (SquareMatrix(*this) += B); }
    SquareMatrix operator-(const SquareMatrix& B) const { return (SquareMatrix(*this) -= B); }
    SquareMatrix operator*(const SquareMatrix& B) const { return (SquareMatrix(*this) *= B); }
    SquareMatrix operator^(long long k) const { return (SquareMatrix(*this) ^= k); }
    bool operator==(const SquareMatrix& B) const { return A == B.A; }
    bool operator!=(const SquareMatrix& B) const { return A != B.A; }

    friend ostream& operator<<(ostream& os, SquareMatrix& B) {
        for(int i = 0; i < B.size(); i++) {
            os << "[";
            for(int j = 0; j < B.size(); j++) {
                os << B[i][j] << (j == B.size()-1 ? "]\n" : ",");
            }
        }
        return os;
    }
};

/////////////////////////////////////////////////////////////////////////////////////

template<int& m> 
struct ModInt {
  public:
    static constexpr int mod() { return m; }
    static ModInt raw(int v) {
        ModInt x;
        x._v = v;
        return x;
    }

    ModInt() : _v(0) {}
    ModInt(long long v) {
        long long x = (long long)(v % (long long)(umod()));
        if (x < 0) x += umod();
        _v = (unsigned int)(x);
    }

    unsigned int val() const { return _v; }

    ModInt& operator++() {
        _v++;
        if (_v == umod()) _v = 0;
        return *this;
    }
    ModInt& operator--() {
        if (_v == 0) _v = umod();
        _v--;
        return *this;
    }
    ModInt operator++(int) {
        ModInt result = *this;
        ++*this;
        return result;
    }
    ModInt operator--(int) {
        ModInt result = *this;
        --*this;
        return result;
    }

    ModInt& operator+=(const ModInt& rhs) {
        _v += rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    ModInt& operator-=(const ModInt& rhs) {
        _v -= rhs._v;
        if (_v >= umod()) _v += umod();
        return *this;
    }
    ModInt& operator*=(const ModInt& rhs) {
        unsigned long long z = _v;
        z *= rhs._v;
        _v = (unsigned int)(z % umod());
        return *this;
    }
    ModInt& operator^=(long long n) {
        ModInt x = *this;
        *this = 1;
        if (n < 0) x = x.inv(), n = -n;
        while (n) {
            if (n & 1) *this *= x;
            x *= x;
            n >>= 1;
        }
        return *this;
    }
    ModInt& operator/=(const ModInt& rhs) { return *this = *this * rhs.inv(); }

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

    ModInt pow(long long n) const {
        ModInt r = *this;
        r ^= n;
        return r;
    }
    ModInt inv() const {
        int a = _v, b = umod(), y = 1, z = 0, t;
        for (; ; ) {
            t = a / b; a -= t * b;
            if (a == 0) {
                assert(b == 1 || b == -1);
                return ModInt(b * z);
            }
            y -= t * z;
            t = b / a; b -= t * a;
            if (b == 0) {
                assert(a == 1 || a == -1);
                return ModInt(a * y);
            }
            z -= t * y;
        }
    }

    friend ModInt operator+(const ModInt& lhs, const ModInt& rhs) { return ModInt(lhs) += rhs; }
    friend ModInt operator-(const ModInt& lhs, const ModInt& rhs) { return ModInt(lhs) -= rhs; }
    friend ModInt operator*(const ModInt& lhs, const ModInt& rhs) { return ModInt(lhs) *= rhs; }
    friend ModInt operator/(const ModInt& lhs, const ModInt& rhs) { return ModInt(lhs) /= rhs; }
    friend ModInt operator^(const ModInt& lhs, long long rhs) { return ModInt(lhs) ^= rhs; }
    friend bool operator==(const ModInt& lhs, const ModInt& rhs) { return lhs._v == rhs._v; }
    friend bool operator!=(const ModInt& lhs, const ModInt& rhs) { return lhs._v != rhs._v; }
    friend ModInt operator+(long long lhs, const ModInt& rhs) { return (ModInt(lhs) += rhs); }
    friend ModInt operator-(long long lhs, const ModInt& rhs) { return (ModInt(lhs) -= rhs); }
    friend ModInt operator*(long long lhs, const ModInt& rhs) { return (ModInt(lhs) *= rhs); }
    friend ostream &operator<<(ostream& os, const ModInt& rhs) { return os << rhs._v; }

  private:
    unsigned int _v;
    static constexpr unsigned int umod() { return m; }
};

static int MOD;
using mint = ModInt<MOD>;

void yuki526() {
    long long N; cin >> N >> MOD;

    SquareMatrix<mint,2> mat(2);

    mat[0][0] = mat[0][1] = mat[1][0] = 1;
    mat ^= N-1;

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

int main() {
    yuki526();
}

/*
  verified on 2020/10/10
  https://yukicoder.me/problems/no/526
*/
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