結果

問題 No.194 フィボナッチ数列の理解(1)
コンテスト
ユーザー Haar
提出日時 2019-09-10 06:40:55
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 15 ms / 5,000 ms
コード長 8,951 bytes
コンパイル時間 2,466 ms
コンパイル使用メモリ 217,144 KB
最終ジャッジ日時 2025-01-07 17:33:54
ジャッジサーバーID
（参考情報） 		judge5 / judge4
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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 # 

#include <bits/stdc++.h>
#define LLI long long int
#define FOR(v, a, b) for(LLI v = (a); v < (b); ++v)
#define FORE(v, a, b) for(LLI v = (a); v <= (b); ++v)
#define REP(v, n) FOR(v, 0, n)
#define REPE(v, n) FORE(v, 0, n)
#define REV(v, a, b) for(LLI v = (a); v >= (b); --v)
#define ALL(x) (x).begin(), (x).end()
#define RALL(x) (x).rbegin(), (x).rend()
#define ITR(it, c) for(auto it = (c).begin(); it != (c).end(); ++it)
#define RITR(it, c) for(auto it = (c).rbegin(); it != (c).rend(); ++it)
#define EXIST(c,x) ((c).find(x) != (c).end())
#define fst first
#define snd second
#define popcount __builtin_popcount
#define UNIQ(v) (v).erase(unique(ALL(v)), (v).end())
#define bit(i) (1LL<<(i))

#ifdef DEBUG
#include <misc/C++/Debug.cpp>
#else
#define dump(...) ((void)0)
#endif

#define gcd __gcd

using namespace std;
template <class T> constexpr T lcm(T m, T n){return m/gcd(m,n)*n;}

template <typename I> void join(ostream &ost, I s, I t, string d=" "){for(auto i=s; i!=t; ++i){if(i!=s)ost<<d; ost<<*i;}ost<<endl;}
template <typename T> istream& operator>>(istream &is, vector<T> &v){for(auto &a : v) is >> a; return is;}

template <typename T, typename U> bool chmin(T &a, const U &b){return (a>b ? a=b, true : false);}
template <typename T, typename U> bool chmax(T &a, const U &b){return (a<b ? a=b, true : false);}
template <typename T, size_t N, typename U> void fill_array(T (&a)[N], const U &v){fill((U*)a, (U*)(a+N), v);}

struct Init{
  Init(){
    cin.tie(0);
    ios::sync_with_stdio(false);
  }
}init;

template <uint32_t M> class ModInt{
public:
  uint64_t val;
  ModInt(): val(0){}
  ModInt(int64_t n){
    if(n >= M) val = n % M;
    else if(n < 0) val = n % M + M;
    else val = n;
  }
  
  inline constexpr ModInt operator+(const ModInt &a) const {return ModInt((val+a.val)%M);}
  inline constexpr ModInt operator-(const ModInt &a) const {return ModInt((val-a.val+M)%M);}
  inline constexpr ModInt operator*(const ModInt &a) const {return ModInt((val*a.val)%M);}
  inline constexpr ModInt operator/(const ModInt &a) const {return ModInt((val*a.inv().val)%M);}
  
  inline constexpr ModInt& operator=(const ModInt &a){val = a.val; return *this;}
  inline constexpr ModInt& operator+=(const ModInt &a){if((val += a.val) >= M) val -= M; return *this;}
  inline constexpr ModInt& operator-=(const ModInt &a){if(val < a.val) val += M; val -= a.val; return *this;}
  inline constexpr ModInt& operator*=(const ModInt &a){(val *= a.val) %= M; return *this;}
  inline constexpr ModInt& operator/=(const ModInt &a){(val *= a.inv().val) %= M; return *this;}

  inline constexpr bool operator==(const ModInt &a) const {return val==a.val;}
  inline constexpr bool operator!=(const ModInt &a) const {return val!=a.val;}
  
  inline constexpr static ModInt power(LLI n, LLI p){
    ModInt ret = 1, e = n;
    for(; p; e *= e, p >>= 1) if(p&1) ret *= e;

    return ret;
  }

  inline constexpr ModInt power(LLI p) const{return power(val,p);}
  
  inline constexpr ModInt inv() const{
    int64_t a = val, b = M, u = 1, v = 0;

    while(b){
      int64_t t = a/b;
      a -= t*b; swap(a,b);
      u -= t*v; swap(u,v);
    }
    u %= M;
    if(u < 0) u += M;
    
    return u;
  }
};

template <uint32_t M> ModInt<M> operator-(const ModInt<M> &a){return M-a.val;}

template <uint32_t M> ModInt<M> operator+(int64_t a, const ModInt<M> &b){return ModInt<M>(ModInt<M>(a)+b.val);}
template <uint32_t M> ModInt<M> operator-(int64_t a, const ModInt<M> &b){return ModInt<M>(ModInt<M>(a)-b.val);}
template <uint32_t M> ModInt<M> operator*(int64_t a, const ModInt<M> &b){return ModInt<M>(ModInt<M>(a)*b.val);}
template <uint32_t M> ModInt<M> operator/(int64_t a, const ModInt<M> &b){return ModInt<M>(ModInt<M>(a)/b.val);}

template <uint32_t M> istream& operator>>(istream &is, ModInt<M> &a){is >> a.val; return is;}
template <uint32_t M> ostream& operator<<(ostream &os, const ModInt<M> &a){ os << a.val; return os;}

template <typename T> struct SquareMatrix{
  int N;
  vector<vector<T>> matrix;

  SquareMatrix(): N(0){}
  SquareMatrix(int N): N(N), matrix(N, vector<T>(N)){}
  SquareMatrix(int N, const T &val): N(N), matrix(N, vector<T>(N, val)){}
  SquareMatrix(const vector<vector<T>> &matrix): N(matrix.size()), matrix(matrix){}
  SquareMatrix(const SquareMatrix<T> &) = default;
  SquareMatrix(SquareMatrix<T> &&) = default;
  SquareMatrix(initializer_list<initializer_list<T>> list): N(list.size()), matrix(N, vector<T>(N)){
    int i = 0;
    ITR(it1,list){
      int j = 0;
      ITR(it2,*it1){
        matrix[i][j] = *it2;
        ++j;
      }
      ++i;
    }
  }
  
  SquareMatrix& operator=(const SquareMatrix &val){
    N = val.N;
    matrix = val.matrix;
    return *this;
  }

  bool operator==(const SquareMatrix<T> &val) const {
    return matrix == val.matrix;
  }

  bool operator!=(const SquareMatrix<T> &val) const {
    return !(*this == val);
  }

  SquareMatrix& operator+=(const SquareMatrix &val){
    REP(i,N) REP(j,N) matrix[i][j] = matrix[i][j] + val[i][j];
    return *this;
  }

  SquareMatrix& operator-=(const SquareMatrix &val){
    REP(i,N) REP(j,N) matrix[i][j] = matrix[i][j] - val[i][j];
    return *this;
  }

  SquareMatrix& operator*=(const SquareMatrix &val){
    vector<vector<T>> temp(N, vector<T>(N));
    REP(i,N) REP(j,N) REP(k,N) temp[i][j] = temp[i][j] + matrix[i][k] * val[k][j];
    swap(matrix, temp);
    return *this;
  }

  inline const vector<T>& operator[](size_t i) const {return matrix[i];}
  inline vector<T>& operator[](size_t i){return matrix[i];}
  inline int size() const {return N;}
  
  static SquareMatrix<T> make_unit(int N){
    SquareMatrix<T> ret(N);
    REP(i,N) ret[i][i] = 1;
    return ret;
  }

  SquareMatrix<T> transpose() const{
    SquareMatrix<T> ret(N);
    REP(i,N) REP(j,N) ret[i][j] = matrix[j][i];
    return ret;
  }

  void show(int w = 10) const {
#ifdef DEBUG
    REP(i,N){
      cerr << (i==0 ? "⎛" : (i==N-1 ? "⎝" : "⎜"));
      REP(j,N) cerr << setw(w) << matrix[i][j] << " ";
      cerr << (i==0 ? "⎞" : (i==N-1 ? "⎠" : "⎟"));
      cerr << endl;
    }
#endif
  }
};

template <typename T> SquareMatrix<T> operator+(const SquareMatrix<T> &a, const SquareMatrix<T> &b){auto ret = a; ret += b; return ret;}
template <typename T> SquareMatrix<T> operator-(const SquareMatrix<T> &a, const SquareMatrix<T> &b){auto ret = a; ret -= b; return ret;}
template <typename T> SquareMatrix<T> operator*(const SquareMatrix<T> &a, const SquareMatrix<T> &b){auto ret = a; ret *= b; return ret;}

template <typename T> SquareMatrix<T> power(SquareMatrix<T> a, uint64_t p){
  int N = a.size();

  if(p == 0) return SquareMatrix<T>::make_unit(N);
  if(p == 1) return a;
  
  SquareMatrix<T> temp = power(a, p/2);
  auto ret = temp * temp;

  if(p%2) ret *= a;
 
  return ret;
}

template <typename T> vector<T> operator*(const SquareMatrix<T> &a, const vector<T> &b){
  vector<T> ret(a.size());

  REP(i,a.size()){
    REP(j,a.size()){
      ret[i] += a[i][j] * b[j];
    }
  }

  return ret;
}

template <typename T> vector<T> operator*(const vector<T> &b, const SquareMatrix<T> &a){
  vector<T> ret(a.size());

  REP(i,a.size()){
    REP(j,a.size()){
      ret[j] += b[i] * a[i][j];
    }
  }

  return ret;
}


template <typename T>
bool inverse_matrix(SquareMatrix<T> m, SquareMatrix<T> &ret){
  int N = m.size();

  ret = SquareMatrix<T>::make_unit(N);

  REP(i,N){
    int p = i;
    FOR(j,i,N){
      if(m[i][j] != 0){
        p = j;
        break;
      }
    }

    swap(m[i], m[p]);
    swap(ret[i], ret[p]);
    
    {
      T d = m[i][i];

      if(d == 0) return false;
    
      REP(j,N){
        m[i][j] /= d;
        ret[i][j] /= d;
      }
    }
    
    REP(j,N){
      if(i==j) continue;
      T d = m[j][i] / m[i][i];
      REP(k,N){
        m[j][k] -= m[i][k] * d;
        ret[j][k] -= ret[i][k] * d;
      }
    }
  }

  return true;
}

const LLI mod = 1e9+7;
using mint = ModInt<mod>;
using M = SquareMatrix<mint>;

pair<mint,mint> solve1(int N, LLI K, vector<int> a){
  M m(N);

  REP(i,N) m[0][i] = 1;
  REP(i,N-1) m[i+1][i] = 1;

  auto m2 = power(m,K-N);

  reverse(ALL(a));
  vector<mint> A(N);
  REP(i,N) A[i] = a[i];

  auto b = m2 * A;

  mint f = b[0];
  mint s = accumulate(ALL(a), 0);

  M c;
  auto t = M::make_unit(N)-m;
  inverse_matrix(t,c);

  auto temp = (M::make_unit(N)-power(m,K-N+1)) * c;
  temp -= M::make_unit(N);
    
  auto B = temp * A;

  s += B[0];

  return {f,s};
}

pair<mint,mint> solve2(int N, LLI K, vector<int> a){
  vector<mint> v(K);

  mint temp = 0;
  REP(i,N){
    temp += a[i];
    v[i] = a[i];
  }

  FOR(i,N,K){
    v[i] = temp;
    temp += v[i];
    temp -= v[i-N];
  }

  mint f = v.back();
  mint s = 0;
  for(auto &x : v) s += x;

  return {f,s};
}


int main(){
  LLI N,K;
  while(cin >> N >> K){
    vector<int> a(N); cin >> a;
    pair<mint,mint> ans;
    if(K > 1000000) ans = solve1(N,K,a);
    else ans = solve2(N,K,a);
    cout << ans.fst << " " << ans.snd << endl;
  }
  return 0;
}
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