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 rniya
提出日時 2020-09-22 13:38:48
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 2 ms / 2,000 ms
コード長 9,038 bytes
コンパイル時間 1,983 ms
コンパイル使用メモリ 173,012 KB
実行使用メモリ 6,944 KB
最終ジャッジ日時 2024-06-26 01:50:59
合計ジャッジ時間 2,466 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge5
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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 # 

#include <bits/stdc++.h>
using namespace std;
#define LOCAL
#pragma region Macros
typedef long long ll;
#define ALL(x) (x).begin(),(x).end()
const long long MOD=1000000007;
// const long long MOD=998244353;
const int INF=1e9;
const long long IINF=1e18;
const int dx[4]={1,0,-1,0},dy[4]={0,1,0,-1};
const char dir[4]={'D','R','U','L'};

template<typename T>
istream &operator>>(istream &is,vector<T> &v){
    for (T &x:v) is >> x;
    return is;
}
template<typename T>
ostream &operator<<(ostream &os,const vector<T> &v){
    for (int i=0;i<v.size();++i){
        os << v[i] << (i+1==v.size()?"": " ");
    }
    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,typename U>
ostream &operator<<(ostream &os,const map<T,U> &m){
    os << '{';
    for (auto itr=m.begin();itr!=m.end();++itr){
        os << '(' << itr->first << ',' << itr->second << ')';
        if (++itr!=m.end()) os << ',';
        --itr;
    }
    os << '}';
    return os;
}
template<typename T>
ostream &operator<<(ostream &os,const set<T> &s){
    os << '{';
    for (auto itr=s.begin();itr!=s.end();++itr){
        os << *itr;
        if (++itr!=s.end()) os << ',';
        --itr;
    }
    os << '}';
    return os;
}

void debug_out(){cerr << '\n';}
template<class Head,class... Tail>
void debug_out(Head&& head,Tail&&... tail){
    cerr << head;
    if (sizeof...(Tail)>0) cerr << ", ";
    debug_out(move(tail)...);
}
#ifdef LOCAL
#define debug(...) cerr << " ";\
cerr << #__VA_ARGS__ << " :[" << __LINE__ << ":" << __FUNCTION__ << "]" << '\n';\
cerr << " ";\
debug_out(__VA_ARGS__)
#else
#define debug(...) 42
#endif

template<typename T> T gcd(T x,T y){return y!=0?gcd(y,x%y):x;}
template<typename T> T lcm(T x,T y){return x/gcd(x,y)*y;}

template<class T1,class T2> inline bool chmin(T1 &a,T2 b){
    if (a>b){a=b; return true;} return false;
}
template<class T1,class T2> inline bool chmax(T1 &a,T2 b){
    if (a<b){a=b; return true;} return false;
}
#pragma endregion

class dynamic_modint{
    using i64=int64_t;
    using u32=uint32_t;
    using u64=uint64_t;
    static u32 &mod(){
        static u32 mod_=0;
        return mod_;
    }
public:
    u32 v;
    static void set_mod(const u32 x){
        assert(x<(u32(1)<<31));
        mod()=x;
    }
    static u32 get_mod(){return mod();}
    dynamic_modint(const i64 x=0):v(x<0?get_mod()-1-(-(x+1)%get_mod()):x%get_mod()){}
    u32 &value() noexcept {return v;}
    const u32 &value() const noexcept {return v;}
    dynamic_modint operator+(const dynamic_modint &rhs) const {return dynamic_modint(*this)+=rhs;}
    dynamic_modint operator-(const dynamic_modint &rhs) const {return dynamic_modint(*this)-=rhs;}
    dynamic_modint operator*(const dynamic_modint &rhs) const {return dynamic_modint(*this)*=rhs;}
    dynamic_modint operator/(const dynamic_modint &rhs) const {return dynamic_modint(*this)/=rhs;}
    dynamic_modint &operator+=(const dynamic_modint &rhs){
        v+=rhs.v;
        if (v>=get_mod()) v-=get_mod();
        return *this;
    }
    dynamic_modint &operator-=(const dynamic_modint &rhs){
        if (v<rhs.v) v+=get_mod();
        v-=rhs.v;
        return *this;
    }
    dynamic_modint &operator*=(const dynamic_modint &rhs){
        v=(u64)v*rhs.v%get_mod();
        return *this;
    }
    dynamic_modint &operator/=(const dynamic_modint &rhs){
        return *this*=rhs.pow(get_mod()-2);
    }
    dynamic_modint pow(u64 exp) const {
        dynamic_modint self(*this),res(1);
        while (exp>0){
            if (exp&1) res*=self;
            self*=self; exp>>=1;
        }
        return res;
    }
    dynamic_modint &operator++(){if (++v==get_mod()) v=0; return *this;}
    dynamic_modint &operator--(){if (v==0) v=get_mod(); return --v,*this;}
    dynamic_modint operator++(int){dynamic_modint t=*this; return ++*this,t;}
    dynamic_modint operator--(int){dynamic_modint t=*this; return --*this,t;}
    template<class T> friend dynamic_modint operator+(T x,dynamic_modint y){return dynamic_modint(x)+y;}
    template<class T> friend dynamic_modint operator-(T x,dynamic_modint y){return dynamic_modint(x)-y;}
    template<class T> friend dynamic_modint operator*(T x,dynamic_modint y){return dynamic_modint(x)*y;}
    template<class T> friend dynamic_modint operator/(T x,dynamic_modint y){return dynamic_modint(x)/y;}
    bool operator==(const dynamic_modint &rhs){return v==rhs.v;}
    bool operator!=(const dynamic_modint &rhs){return v!=rhs.v;}
    bool operator!(){return !v;}
    friend istream &operator>>(istream &s,dynamic_modint &rhs){
        i64 v; rhs=dynamic_modint{(s>>v,v)}; return s;
    }
    friend ostream &operator<<(ostream &s,dynamic_modint &rhs){
        return s<<rhs.v;
    }
};

template<class K>
struct Matrix{
    vector<vector<K>> dat;
    Matrix(size_t r,size_t c):dat(r,vector<K>(c,K())){}
    Matrix(size_t n):dat(n,vector<K>(n,K())){}
    Matrix(vector<vector<K>> dat):dat(dat){}
    size_t size() const{return dat.size();}
    vector<K> &operator[](int i){return dat[i];}
    const vector<K> &operator[](int i) const{return dat[i];}
    static Matrix I(size_t n){
        Matrix res(n);
        for (int i=0;i<n;++i) res[i][i]=K(1);
        return res;
    }
    Matrix &operator+=(const Matrix &B){
        for (int i=0;i<dat.size();++i)
            for (int j=0;j<dat[0].size();++j)
                (*this)[i][j]+=B[i][j];
        return (*this);
    }
    Matrix operator+(const Matrix &B) const{
        return Matrix(*this)+=B;
    }
    Matrix &operator-=(const Matrix &B){
        for (int i=0;i<dat.size();++i)
            for (int j=0;j<dat[0].size();++j)
                (*this)[i][j]-=B[i][j];
        return (*this);
    }
    Matrix operator-(const Matrix &B) const{
        return Matrix(*this)-=B;
    }
    Matrix &operator*=(const Matrix &B){
        vector<vector<K>> res(dat.size(),vector<K>(B[0].size(),K()));
        for (int i=0;i<dat.size();++i)
            for (int j=0;j<B[0].size();++j)
                for (int k=0;k<B.size();++k)
                    res[i][j]+=(*this)[i][k]*B[k][j];
        dat.swap(res);
        return (*this);
    }
    Matrix operator*(const Matrix &B) const{
        return Matrix(*this)*=B;
    }
    Matrix &operator^=(long long k){
        Matrix res=Matrix::I(size());
        while(k){
            if (k&1LL) res*=*this;
            *this*=*this; k>>=1LL;
        }
        dat.swap(res.dat);
        return (*this);
    }
    Matrix operator^(long long k) const{
        return Matrix(*this)^=k;
    }
    static Matrix Gauss_Jordan(const Matrix &A,const Matrix &B){
        int n=A.size(),l=B[0].size();
        Matrix C(n,n+l);
        for (int i=0;i<n;++i){
            for (int j=0;j<n;++j)
                C[i][j]=A[i][j];
            for (int j=0;j<l;++j)
                C[i][j+n]=B[i][j];
        }
        for (int i=0;i<n;++i){
            int p=i;
            for (int j=i;j<n;++j){
                if (abs(C[p][i])<abs(C[j][i])) p=j;
            }
            swap(C[i],C[p]);
            if (abs(C[i][i])<1e-9) return Matrix(0,0);
            for (int j=i+1;j<n+l;++j) C[i][j]/=C[i][i];
            for (int j=0;j<n;++j){
                if (i!=j) for (int k=i+1;k<n+l;++k){
                    C[j][k]-=C[j][i]*C[i][k];
                }
            }
        }
        Matrix res(n,l);
        for (int i=0;i<n;++i)
            for (int j=0;j<n;++j)
                res[i][j]=C[i][j+n];
        return res;
    }
    Matrix inv() const{
        Matrix res=I(size());
        return Gauss_Jordan(*this,res);
    }
    K determinant() const{
        Matrix A(dat);
        K res(1);
        int n=size();
        for (int i=0;i<n;++i){
            int p=i;
            for (int j=i;j<n;++j){
                if (abs(A[p][i])<abs(A[j][i])) p=j;
            }
            if (i!=p) swap(A[i],A[p]),res=-res;
            if (abs(A[i][i])<1e-9) return K(0);
            res*=A[i][i];
            for (int j=i+1;j<n;++j) A[i][j]/=A[i][i];
            for (int j=i+1;j<n;++j)
                for (int k=i+1;k<n;++k)
                    A[j][k]-=A[j][i]*A[i][k];
        }
        return res;
    }
    //sum_{k=0}^{n-1} x^k
    static K geometric_sum(K x,long long n){
        Matrix A(2);
        A[0][0]=x; A[0][1]=0;
        A[1][0]=1; A[1][1]=1;
        return (A^n)[1][0];
    }
    //sum_{k=0}^{n-1} A^k
    Matrix powsum(long long k) const{
        int n=size();
        Matrix B(n<<1),res(n);
        for (int i=0;i<n;++i){
            for (int j=0;j<n;++j)
                B[i][j]=dat[i][j];
            B[i+n][i]=B[i+n][i+n]=K(1);
        }
        B^=k;
        for (int i=0;i<n;++i)
            for (int j=0;j<n;++j)
                res[i][j]=B[i+n][j];
        return res;
    }
};

using mint=dynamic_modint;

int main(){
    cin.tie(0);
    ios::sync_with_stdio(false);
    int N,M; cin >> N >> M;

    mint::set_mod(M);
    Matrix<mint> m(2);
    m[0][1]=m[1][0]=m[1][1]=1;
    m^=N;

    cout << m[0][0] << '\n';
}
0