結果

問題 No.194 フィボナッチ数列の理解(1)
ユーザー 👑 CleyL
提出日時 2024-01-21 22:42:21
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 9 ms / 5,000 ms
コード長 7,794 bytes
コンパイル時間 1,449 ms
コンパイル使用メモリ 133,996 KB
最終ジャッジ日時 2025-02-18 22:02:08
ジャッジサーバーID
（参考情報） 		judge2 / judge2
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 #
プレゼンテーションモードにする

//yukicoder@cpp17
#include <iostream>
#include <iomanip>
#include <algorithm>
#include <cmath>
#include <cctype>
#include <climits>
#include <cassert>
#include <string>
#include <vector>
#include <set>
#include <stack>
#include <queue>
#include <map>
#include <random>
#include <bitset>
#include <complex>
#include <utility>
#include <numeric>
#include <functional>
using namespace std;
using ll = long long;
using P = pair<ll,ll>;
const ll MOD = 998244353;
const ll MODx = 1000000007;
const int INF = (1<<30)-1;
const ll LINF = (1LL<<62LL)-1;
const double EPS = (1e-10);
P ar4[4] = {{0,1},{0,-1},{1,0},{-1,0}};
P ar8[8] = {{-1,-1},{-1,0},{-1,1},{0,-1},{0,1},{1,-1},{1,0},{1,1}};
template <typename T> vector<T> make_vector(size_t a, T b) { return vector<T>(a, b); }
template <typename... Ts> auto make_vector(size_t a, Ts... ts) { return vector<decltype(make_vector(ts...))>(a, make_vector(ts...)); }
 
 /*
確認ポイント
cout << fixed << setprecision(n) << 小数計算//n桁の小数表記になる
計算量は変わらないが楽できるシリーズ
min(max)_element(iter,iter)で一番小さい(大きい)値のポインタが帰ってくる
count(iter,iter,int)でintがiterからiterの間にいくつあったかを取得できる
*/
/*
function corner below
*/
/*
Function corner above
*/
/* comment outed because can cause bugs
__attribute__((constructor))
void initial() {
 cin.tie(0);
 ios::sync_with_stdio(false);
}
*/
template <int mod>
struct ModInt{
  int n;
  ModInt():n(0){}
  ModInt(long long n_):n(n_ >= 0 ? n_%mod : mod - ((-n_)%mod) ){}
  ModInt(int n_):n(n_ >= 0 ? n_%mod : mod - ((-n_)%mod) ){}
  ModInt &operator+=(const ModInt &p){
    if((n+=p.n) >= mod)n-=mod;
    return *this;
  }
  ModInt &operator-=(const ModInt &p){
    n+=mod-p.n;
    if(n >= mod)n-=mod;
    return *this;
  }
  ModInt &operator*=(const ModInt &p){
    n = (int) ((1LL*n*p.n)%mod);
    return *this;
  }
  ModInt &operator/=(const ModInt &p){
    *this *= p.inverse();
    return *this;
  }
  ModInt operator-() const {return ModInt(-n);}
  ModInt operator+(const ModInt &p) const {return ModInt(*this) += p;}
  ModInt operator-(const ModInt &p) const {return ModInt(*this) -= p;}
  ModInt operator*(const ModInt &p) const {return ModInt(*this) *= p;}
  ModInt operator/(const ModInt &p) const {return ModInt(*this) /= p;}
  bool operator==(const ModInt &p) const {return n==p.n;}
    bool operator<(const ModInt &p) const {return n<p.n;}
    bool operator>(const ModInt &p) const {return n>p.n;}
    bool operator>=(const ModInt &p) const {return n>=p.n;}
    bool operator<=(const ModInt &p) const {return n<=p.n;}
  bool operator!=(const ModInt &p) const {return n!=p.n;}
  ModInt inverse() const {
    int a = n,b = mod,u = 1,v = 0;
    while(b){
      int t = a/b;
      a -= t*b; swap(a,b);
      u -= t*v; swap(u,v);
    }
    return ModInt(u);
  }
  ModInt pow(int64_t z) const {
    ModInt ret(1),mul(n);
    while(z > 0){
      if(z & 1) ret *= mul;
      mul *= mul;
      z >>= 1;
    }
    return ret;
  }
  friend ostream &operator<<(ostream &os, const ModInt &p){
    return os << p.n;
  }
  friend istream &operator>>(istream &is, ModInt &a){
    int64_t t;
    is >> t;
    a = ModInt<mod> ((long long)t);
    return (is);
  }
};
using mint = ModInt<MODx>;
template <typename T>
struct mat{
  vector<vector<T>> x;
  int h,w;
  mat():x(vector<vector<T>>()){}
  mat(int h,int w):x(vector<vector<T>>(h,vector<T>(w))),h(h),w(w){}
  mat(int h,int w, T c):x(vector<vector<T>>(h,vector<T>(w,c))),h(h),w(w){}
  mat(vector<vector<T>> A):x(A),h(A.size()),w(A[0].size()){}
  vector<T>& operator[](int i){return x[i];}
  void resize(int h, int w){
    x.assign(h, vector<T>(w, 0));
  }
  mat base(){
    return mat(h,w,0);
  }
  mat& operator*=(mat& y){
    mat<T> ret(h,y.w,0);
    if(w != y.h){
      for(int i = 0; h > i; i++){
        for(int j = 0; y.w > j; j++){
          ret[i][j] = -1;
        }
      }
    }else{
      for(int i = 0; h > i; i++){
        for(int j = 0; y.w > j; j++){
          for(int k = 0; w > k; k++){
            ret[i][j] = ret[i][j] + x[i][k]*y[k][j];
          }
        }
      }
    }
    for(int i = 0; h > i; i++){
      x[i].resize(y.w);
    }
    w = y.w;
    for(int i = 0; h > i; i++){
      for(int j = 0; y.w > j; j++){
        x[i][j] = ret[i][j];
      }
    }
    return *this;
  }
  mat operator*(mat& y){return mat(*this) *= y;}
  mat pow(long long n){//正方行列のみ
    mat<T> res(h,w);
    mat<T> ret(h,w,0);
    mat<T> a(h,w);
    for(int i = 0; h > i; i++){
      ret[i][i] = 1;
    }
    for(int i = 0; h > i; i++){
      for(int j = 0; w > j; j++){
        a[i][j] = (*this)[i][j];
      }
    }
    while(n > 0){
      if(n & 1){
        ret *= a;
      }
      a *= a;
      n/=2;
    }
    for(int i = 0; h > i; i++){
      for(int j = 0; w > j; j++){
        res[i][j] = ret[i][j];
      }
    }
    return res;
  }
  // Requirement: h==w
  pair<bool, mat> inv(){
    if(h != w)return {false, base()};
    mat<T> gaussianMat(h, 2*w, 0);
    for(int i = 0; h > i; i++){
      for(int j = 0; w > j; j++){
        gaussianMat[i][j] = (*this)[i][j];
      }
    }
    for(int i = 0; h > i; i++){
      gaussianMat[i][w+i] = 1;
    }
    for(int i = 0; h > i; i++){
      for(int j = i; h > j; j++){
        if(gaussianMat[j][i] != 0){
          swap(gaussianMat[i], gaussianMat[j]);
        }
      }
      T initCoeffient = gaussianMat[i][i];
      if(initCoeffient == 0){
        return {false, base()};
      }
      for(int j = 0; 2*w > j; j++){
        gaussianMat[i][j] /= initCoeffient;
      }
      for(int j = i+1; h > j; j++){
        T deleteCoeffient = gaussianMat[j][i] * -1;
        for(int k = i; 2*w > k; k++){
          gaussianMat[j][k] += deleteCoeffient * gaussianMat[i][k];
        }
      }
    }
    for(int i = 0; h > i; i++){
      if(gaussianMat[i][i] != 1){
        T normarizeCoeffient = gaussianMat[i][i];
        if(normarizeCoeffient == 0)continue;
        for(int j = i; 2*w > j; j++){
          gaussianMat[i][j] /= normarizeCoeffient;
        }
      }
    }
    for(int i = h-1; 0 <= i; i--){
      for(int j = 0; i > j; j++){
        T deleteCoeffient = gaussianMat[j][i] * -1;
        for(int k = i; 2*w > k; k++){
          gaussianMat[j][k] += deleteCoeffient * gaussianMat[i][k];
        }
      }
    }
    mat v(h, w);
    for(int i = 0; h > i; i++){
      for(int j = 0; w > j; j++){
        v[i][j] = gaussianMat[i][j+w];
      }
    }
    return {true, v};
  }
  friend istream &operator>>(istream &is, mat &m){
    for(int i = 0; m.h > i; i++){
      for(int j = 0; m.w > j; j++){
        is>>m.x[i][j];
      }
    }
    return is;
  }
  friend ostream &operator<<(ostream &os, const mat &m){
    for(int i = 0; m.h > i; i++){
      for(int j = 0; m.w > j; j++){
        os << m.x[i][j];
        if(j+1 != m.w)cout << " ";
      }
      if(i+1 != m.h)cout << "\n";
    }
    return os;
  }
};
void solve1(int n, long long k){
  mat<mint> A(n+1,n+1,0);
  for(int i = 0; n > i; i++){
    A[0][i] = 1;
  }
  for(int i = 0; n-1 > i; i++){
    A[i+1][i] = 1;
  }
  A[n][0] = A[n][n] = 1;
  mat<mint> B(n+1,1);
  mint sm = 0;
  for(int i = 0; n > i; i++){
    cin>>B[n-i-1][0];
    if(i+1 != n)sm += B[n-i-1][0];
  }
  B[n][0] = sm;
  mat<mint> C = (A.pow(k-n)*B);
  cout << C[0][0] << " " << (A*C)[n][0] << endl;
}
void solve2(int n, int k){
  vector<mint> A(k+1);
  mint sm = 0;
  mint rsm = 0;
  for(int i = 0; n > i; i++){
    cin>>A[i];
    sm += A[i];
    rsm += A[i];
  }
  for(int i = n; k > i; i++){
    A[i] = sm;
    sm -= A[i-n];
    sm += A[i];
    rsm += A[i];
  }
  cout << A[k-1] << " " << rsm << endl;
}
int main(){
  long long n,k;cin>>n>>k;
  if(n <= 30){
    solve1(n,k);
  }else{
    solve2(n,k);
  }
  return 0;
}
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