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 fumiphys
提出日時 2019-09-27 20:11:17
言語 C++14
(gcc 13.3.0 + boost 1.89.0)
結果
AC  
実行時間 15 ms / 5,000 ms
コード長 7,117 bytes
記録
記録タグの例:
初AC ショートコード 純ショートコード 純主流ショートコード 最速実行時間
コンパイル時間 1,963 ms
コンパイル使用メモリ 181,132 KB
実行使用メモリ 11,088 KB
最終ジャッジ日時 2024-09-24 20:19:56
合計ジャッジ時間 3,288 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge1
このコードへのチャレンジ
（要ログイン）
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 #
raw source code 

// includes
#include <bits/stdc++.h>
using namespace std;

// macros
#define pb emplace_back
#define mk make_pair
#define FOR(i, a, b) for(int i=(a);i<(b);++i)
#define rep(i, n) FOR(i, 0, n)
#define rrep(i, n) for(int i=((int)(n)-1);i>=0;i--)
#define irep(itr, st) for(auto itr = (st).begin(); itr != (st).end(); ++itr)
#define irrep(itr, st) for(auto itr = (st).rbegin(); itr != (st).rend(); ++itr)
#define all(x) (x).begin(),(x).end()
#define sz(x) ((int)(x).size())
#define UNIQUE(v) v.erase(unique(v.begin(), v.end()), v.end())
#define bit(n) (1LL<<(n))
// functions
template <class T>bool chmax(T &a, const T &b){if(a < b){a = b; return 1;} return 0;}
template <class T>bool chmin(T &a, const T &b){if(a > b){a = b; return 1;} return 0;}
template <typename T> istream &operator>>(istream &is, vector<T> &vec){for(auto &v: vec)is >> v; return is;}
template <typename T> ostream &operator<<(ostream &os, const vector<T>& vec){for(int i = 0; i < vec.size(); i++){ os << vec[i]; if(i + 1 != vec.size())os << " ";} return os;}
template <typename T> ostream &operator<<(ostream &os, const set<T>& st){for(auto itr = st.begin(); itr != st.end(); ++itr){ os << *itr; auto titr = itr; if(++titr != st.end())os << " ";} return os;}
template <typename T> ostream &operator<<(ostream &os, const unordered_set<T>& st){for(auto itr = st.begin(); itr != st.end(); ++itr){ os << *itr; auto titr = itr; if(++titr != st.end())os << " ";} return os;}
template <typename T> ostream &operator<<(ostream &os, const multiset<T>& st){for(auto itr = st.begin(); itr != st.end(); ++itr){ os << *itr; auto titr = itr; if(++titr != st.end())os << " ";} return os;}
template <typename T> ostream &operator<<(ostream &os, const unordered_multiset<T>& st){for(auto itr = st.begin(); itr != st.end(); ++itr){ os << *itr; auto titr = itr; if(++titr != st.end())os << " ";} return os;}
template <typename T1, typename T2> ostream &operator<<(ostream &os, const pair<T1, T2> &p){os << p.first << " " << p.second; return os;}
template <typename T1, typename T2> ostream &operator<<(ostream &os, const map<T1, T2> &mp){for(auto itr = mp.begin(); itr != mp.end(); ++itr){ os << itr->first << ":" << itr->second; auto titr = itr; if(++titr != mp.end())os << " "; } return os;}
template <typename T1, typename T2> ostream &operator<<(ostream &os, const unordered_map<T1, T2> &mp){for(auto itr = mp.begin(); itr != mp.end(); ++itr){ os << itr->first << ":" << itr->second; auto titr = itr; if(++titr != mp.end())os << " "; } return os;}
//  types
using ll = long long int;
using P = pair<int, int>;
// constants
const int inf = 1e9;
const ll linf = 1LL << 50;
const double EPS = 1e-10;
const int mod = 1000000007;
const int dx[4] = {-1, 0, 1, 0};
const int dy[4] = {0, -1, 0, 1};
// io
struct fast_io{
  fast_io(){ios_base::sync_with_stdio(false); cin.tie(0); cout << fixed << setprecision(20);}
} fast_io_;

template<typename T>
T extgcd(T a, T b, T &x, T &y){ 
  T d = a;
  if(b != 0){
    d = extgcd(b, a % b, y, x);
    y -= (a / b) * x;
  }else{
    x = 1, y = 0;
  }
  return d;
}

template <typename T>
T modinv(T a, T m){
  long long x = 0, y = 0;
  extgcd<long long>(a, m, x, y);
  x %= m;
  if(x < 0)x += m;
  return x;
}


template <int MOD = int(1e9+7)>
struct LMatrix{
  vector<vector<long long>> v;
  int n, m;
  LMatrix(int n_, int m_ = -1): n(n_), m(m_){
    if(m < 0)m = n;
    v.resize(n);
    for(int i = 0; i < n; i++)v[i].resize(m);
  }
  void identity(){
    assert(n == m);
    for(int i = 0; i < n; i++){
      for(int j = 0; j < n; j++){
        v[i][j] = (i == j ? 1: 0);
      }
    }
  }
  vector<long long> &operator[](size_t i){
    return v[i];
  }
  const vector<long long> &operator[](size_t i) const{
    return v[i];
  }
  LMatrix operator*(const LMatrix &r) const{
    assert(m == r.n);
    int l = r.m;
    LMatrix res(n, l);
    for(int i = 0; i < n; i++){
      for(int j = 0; j < l; j++){
        res.v[i][j] = 0;
        for(int k = 0; k < m; k++){
          res.v[i][j] = (res.v[i][j] + v[i][k] * r.v[k][j] % MOD) % MOD;
        }
      }
    }
    return res;
  }
  LMatrix operator+(const LMatrix &r) const{
    assert(n == r.n);
    assert(m == r.m);
    LMatrix res(n, m);
    for(int i = 0; i < n; i++){
      for(int j = 0; j < m; j++){
        res[i][j] = (v[i][j] + r[i][j]) % MOD;
      }
    }
    return res;
  }
  LMatrix operator-(const LMatrix &r) const{
    assert(n == r.n);
    assert(m == r.m);
    LMatrix res(n, m);
    for(int i = 0; i < n; i++){
      for(int j = 0; j < m; j++){
        res[i][j] = (v[i][j] - r[i][j]) % MOD;
        if(res[i][j] < 0)res[i][j] += MOD;
      }
    }
    return res;
  }
  template <typename T>
  LMatrix operator*(T a) const{
    LMatrix res = *this;
    for(int i = 0; i < n; i++){
      for(int j = 0; j < n; j++){
        res[i][j] = a * res[i][j] % MOD;
      }
    }
    return res;
  }
  LMatrix inv2() const{
    assert(n == 2 && m == 2);
    long long det = v[0][0] * v[1][1] % MOD - v[0][1] * v[1][0] % MOD;
    if(det < 0)det += MOD;
    assert(det != 0);
    LMatrix res(2, 2);
    long long inv = modinv(det, (long long)MOD);
    res[0][0] = v[1][1];
    res[1][1] = v[0][0];
    res[1][0] = - v[1][0];
    res[0][1] = - v[0][1];
    for(int i = 0; i < n; i++){
      for(int j = 0; j < m; j++){
        res[i][j] %= MOD;
        res[i][j] = res[i][j] * inv % MOD;
        if(res[i][j] < 0)res[i][j] += MOD;
      }
    }
    return res;
  }
};

template <typename T, int MOD = int(1e9+7)>
LMatrix<MOD> operator*(T a, const LMatrix<MOD> b){
  return b * a;
}

template <int MOD = int(1e9+7)>
LMatrix<MOD> powerm(LMatrix<MOD> &a, long long n){
  long long tmp = n;
  LMatrix<MOD> curr = a;
  LMatrix<MOD> res(a.n);
  res.identity();
  while(tmp){
    if(tmp % 2 == 1){
      res = res * curr;
    }
    curr = curr * curr;
    tmp /= 2;
  }
  return res;
}

int main(int argc, char const* argv[])
{
  int n; cin >> n;
  ll k; cin >> k;
  vector<ll> a(n); cin >> a;
  --k;
  if(k <= 1000000){
    if(k < n){
      ll sum = 0;
      rep(i, k)sum = (sum + a[i]) % mod;
      cout << a[k] << " " << sum << endl;
      return 0;
    }
    vector<ll> b(k + 1);
    rep(i, n){
      b[i] = a[i];
      b[n] += b[i];
    }
    b[n] %= mod;
    for(int i = n + 1; i <= k; i++){
      b[i] = (b[i-1] + b[i-1] - b[i-n-1]) % mod;
    }
    if(b[k] < 0)b[k] += mod;
    ll sum = 0;
    rep(i, k + 1)sum = (sum + b[i]) % mod;
    if(sum < 0)sum += mod;
    cout << b[k] << " " << sum << endl;
  }else{
    if(k < n){
      ll sum = 0;
      rep(i, k)sum = (sum + a[i]) % mod;
      cout << a[k] << " " << sum << endl;
      return 0;
    }
    LMatrix<> lm(n + 1, n + 1);
    rep(i, n)lm[0][i] = 1;
    FOR(i, 1, n){
      lm[i][i-1] = 1;
    }
    rep(i, n + 1)lm[n][i] = 1;
    auto p = powerm(lm, k - n + 1);
    ll f = 0, s = 0;
    rep(i, n)f = (f + p[0][i] * a[n-1-i] % mod) % mod;
    rep(i, n)s = (s + p[n][i] * a[n-1-i] % mod) % mod;
    ll S = 0;
    rep(i, n)S += a[i];
    f = (f + p[0][n] * S % mod) % mod;
    s = (s + p[n][n] * S % mod) % mod;
    if(f < 0)f += mod;
    if(s < 0)s += mod;
    cout << f << " " << s << endl;
  }
  return 0;
}
0