結果

問題 No.194 フィボナッチ数列の理解(1)
ユーザー cureskolcureskol
提出日時 2022-08-26 14:07:56
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 136 ms / 5,000 ms
コード長 6,269 bytes
コンパイル時間 3,263 ms
コンパイル使用メモリ 229,660 KB
最終ジャッジ日時 2025-01-31 04:04:42
ジャッジサーバーID
（参考情報） 		judge4 / judge3
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 37
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 # 

#pragma region template
#pragma GCC optimize("Ofast")
#include <bits/stdc++.h>
using namespace std;
#ifdef __LOCAL
 #include <debug>
#else
 #define debug(...) void(0)
#endif

using ll=long long;
using ld=long double;
using vi=vector<int>;
using vll=vector<ll>;
using pi=pair<int,int>;
using pll=pair<ll,ll>;

#define overload2(a,b,c,...) c
#define overload3(a,b,c,d,...) d
#define overload4(a,b,c,d,e,...) e
#define overload5(a,b,c,d,e,f,...) f

#define TYPE1(T) template<typename T>
#define TYPE2(T,U) template<typename T,typename U>
#define TYPE(...) overload2(__VA_ARGS__,TYPE2,TYPE1)(__VA_ARGS__)
#define TYPES1(T) template<typename... T>
#define TYPES2(H,T) template<typename H,typename... T>
#define TYPES(...) overload2(__VA_ARGS__,TYPES2,TYPES1)(__VA_ARGS__)

#define REP4(i,s,n,d) for(int i=(s);i<(n);i+=(d))
#define REP3(i,s,n) REP4(i,s,n,1)
#define REP2(i,n) REP3(i,0,n)
#define REP1(n) REP2(tomato,n)
#define REP(...) overload4(__VA_ARGS__,REP4,REP3,REP2,REP1)(__VA_ARGS__)

#define RREP4(i,s,n,d) for(int i=(n)-1;i>=s;i-=d)
#define RREP3(i,s,n) RREP4(i,s,n,1)
#define RREP2(i,n) RREP3(i,0,n)
#define RREP1(n) RREP2(tomato,n)
#define RREP(...) overload4(__VA_ARGS__,RREP4,RREP3,RREP2,RREP1)(__VA_ARGS__)

#define ALL(v) v.begin(),v.end()
#define RALL(v) v.rbegin(),v.rend()
#define SORT(v) sort(ALL(v))
#define RSORT(v) sort(RALL(v))
#define REVERSE(v) reverse(ALL(v))
#define UNIQUE(v) SORT(v),v.erase(unique(ALL(v)),v.end())

TYPES(T) void input(T&... a){ (cin>>...>>a); }
#define DECLARE(T,...) T __VA_ARGS__;input(__VA_ARGS__);
#define INT(...) DECLARE(int,__VA_ARGS__)
#define STR(...) DECLARE(string,__VA_ARGS__)
#define LL(...) DECLARE(long long,__VA_ARGS__)
#define CHR(...) DECLARE(char,__VA_ARGS__)
#define DBL(...) DECLARE(double,__VA_ARGS__)
#define VI(n,v) vi v(n);cin>>v;
#define VLL(n,v) vll v(n);cin>>v;

TYPE(T) istream&operator>>(istream&is,vector<T>&v){
  for(auto&a:v)cin>>a;
  return is;
}
TYPE(T) ostream&operator<<(ostream&os,const vector<T>&v){
  if(&os==&cerr)os<<"[";
  REP(i,v.size()){
    os<<v[i];
    if(i+1<v.size())os<<(&os==&cerr?",":" ");
  }
  if(&os==&cerr)os<<"]";
  return os;
}
TYPE(T,S) istream&operator>>(istream&is,pair<T,S>&p){
  cin>>p.first>>p.second;
  return is;
}

TYPE(T) using pq=priority_queue<T>;
TYPE(T) using pqg=priority_queue<T,vector<T>,greater<T>>;
TYPE(T) T pick(queue<T>& que){assert(que.size()); T a=que.front();que.pop();return a;}
TYPE(T) T pick(pq<T>& que){assert(que.size()); T a=que.top();que.pop();return a;}
TYPE(T) T pick(pqg<T>& que){assert(que.size()); T a=que.top();que.pop();return a;}
TYPE(T) T pick(stack<T>& sta){assert(sta.size()); T a=sta.top();sta.pop();return a;}

string YES(bool f=true){return (f?"YES":"NO");}
string Yes(bool f=true){return (f?"Yes":"No");}
string yes(bool f=true){return (f?"yes":"no");}

constexpr int INF=1e9+7;
constexpr ll LINF=ll(1e18)+7;
constexpr ld EPS=1e-10;

vi iota(int n){vi a(n);iota(ALL(a),0);return a;}
TYPE(T) void fin(T a){cout<<a<<endl;exit(0);}
TYPE(T) bool chmax(T &a,T b){return (a<b&&(a=b,true));}
TYPE(T) bool chmin(T &a,T b){return (a>b&&(a=b,true));}
TYPES(T,Ns)
auto make_vector(T x,int n,Ns ...ns){
  if constexpr(sizeof...(ns)==0)return vector<T>(n,x);
  else return vector(n,make_vector<T>(x,ns...));
}
bool in(const ll S,const int a){return (S>>a)&1;}
int popcount(const ll S){return __builtin_popcountll(S);}
#pragma endregion template

#include <atcoder/modint>
#include <atcoder/segtree>
using namespace atcoder;
using mint=modint1000000007;
ostream& operator<<(ostream &os,mint a){os<<a.val();return os;}
istream& operator>>(istream &is,mint &a){
  long long b;is>>b;a=b;
  return is;
}

mint op(mint a,mint b){return a+b;}
mint e(){return 0;}

#define REP_(i,n) for(int i=0;i<(n);i++)
#define REP2_(i,s,n) for(int i=(s);i<(n);i++)
template<typename K>
struct Matrix{
  typedef vector<K> vec;
  typedef vector<vec> mat;
  size_t r,c;
  mat M;

  Matrix(size_t r,size_t c):r(r),c(c),M(r,vec(c,K())){}
  Matrix(mat A):M(A),r(A.size()),c(A[0].size()){}

  vec& operator[](size_t k){return M[k];}
  const vec& operator[](size_t k)const{return M[k];}

  friend Matrix operator+(const Matrix &A,const Matrix &B){
    assert(A.r==B.r&&A.c==B.c);
    Matrix res(A);
    REP_(i,A.r)REP_(j,A.c)res[i][j]+=B[i][j];
    return res;
  }

  Matrix& operator+=(const Matrix &B){
    assert(r==B.r&&c==B.c);
    REP_(i,r)REP_(j,c)M[i][j]+=B[i][j];
    return *this;
  }

  friend Matrix operator*(const Matrix &A,const Matrix &B){
    assert(A.c==B.r);
    Matrix res(A.r,B.c);
    REP_(i,A.r)REP_(k,A.c)REP_(j,B.c)res[i][j]+=A[i][k]*B[k][j];
    return res;
  }

  Matrix& operator*=(const Matrix &B){
    M=((*this)*B).M;
    return *this;
  }

  static Matrix I(size_t n){
    Matrix res(n,n);
    REP_(i,n)res[i][i]=K(1);
    return res;
  }

  Matrix pow(long long n)const{
    assert(n>=0&&r==c);
    Matrix A(M),res=I(r);
    while(n){
      if(n&1)res*=A;
      A*=A;
      n>>=1;
    }
    return res;
  }

  int rank() const{
    Matrix A(M);
    int res=0;
    REP_(k,c){
      for(int i=res+1;i<r&&A[res][k]==0;i++)
        if(A[i][k]!=0)swap(A[i],A[res]);
      if(A[res][k]==0)continue;
      REP2_(l,k+1,c)A[res][l]/=A[res][k];
      REP2_(j,res+1,r)REP2_(l,k+1,c)A[j][l]-=A[j][k]*A[res][l];
      res++;
    }
    return res;
  }

  K det() const{
    assert(r==c);
    Matrix A=M;
    K res(1);
    REP_(i,r){
      for(int j=i+1;j<c&&A[i][i]==0;j++)
        if(A[j][i]!=0)swap(A[i],A[j]),res=-res;
      if(A[i][i]==0)return 0;
      res*=A[i][i];
      REP2_(k,i+1,c)A[i][k]/=A[i][i];
      REP2_(j,i+1,r)REP2_(k,i+1,c)A[j][k]-=A[j][i]*A[i][k];
    }
    return res;
  }
};
#undef REP_
#undef REP2_

/**
* @docs //docs/matrix.md
*/

int main(){
  ios::sync_with_stdio(false);
  cin.tie(nullptr);
  
  LL(n,k);
  VLL(n,v);

  if(n>30){
    segtree<mint,op,e> seg(k);
    REP(i,n)seg.set(i,v[i]);
    REP(i,n,k)seg.set(i,seg.prod(i-n,i));
    cout<<seg.get(k-1)<<" "<<seg.all_prod()<<endl;
  }
  else{
    Matrix<mint> A(n+1,n+1);
    REP(i,n)A[0][i]=1;
    REP(i,1,n)A[i][i-1]=1;
    A[n][0]=A[n][n]=1;
    A=A.pow(k-n);
    Matrix<mint> B(n+1,1);
    REP(i,n)B[i][0]=v[n-1-i];
    auto C=A*B;
    mint ans1=C[0][0];
    mint ans2=C[n][0];
    REP(i,n-1)ans2+=v[i];
    ans2+=ans1;
    cout<<ans1<<" "<<ans2<<endl;
  }
}
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