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 sune232002
提出日時 2015-04-26 22:27:58
言語 C++11（廃止可能性あり）
(gcc 13.3.0)
結果
AC  
実行時間 8 ms / 5,000 ms
コード長 5,632 bytes
コンパイル時間 1,400 ms
コンパイル使用メモリ 165,216 KB
実行使用メモリ 7,692 KB
最終ジャッジ日時 2024-07-05 03:00:06
合計ジャッジ時間 2,679 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge1
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 # 

#include <bits/stdc++.h>
using namespace std;
#define REP(i,n) for(int i=0;i<(int)(n);++i)
#define REPR(i,n) for (int i=(int)(n)-1;i>=0;--i)
#define FOR(i,c) for(__typeof((c).begin())i=(c).begin();i!=(c).end();++i)
#define ALL(c) (c).begin(), (c).end()
#define valid(y,x,h,w) (0<=y&&y<h&&0<=x&&x<w)
#define tpl(...) make_tuple(__VA_ARGS__)
const int INF = 0x3f3f3f3f;
const double EPS = 1e-8;
const double PI = acos(-1);
const int dy[] = {-1,0,1,0};
const int dx[] = {0,1,0,-1};
typedef long long ll;
typedef pair<int,int> pii;
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 (b<a) { a=b; return 1; } return 0; }
template<typename Ch,typename Tr,typename C,typename=decltype(begin(C()))>basic_ostream<Ch,Tr>& operator<<(basic_ostream<Ch,Tr>&os,
const C& c){os<<'[';for(auto i=begin(c);i!=end(c);++i)os<<(i==begin(c)?"":" ")<<*i;return os<<']';}
template<class S,class T>ostream&operator<<(ostream &o,const pair<S,T>&t){return o<<'('<<t.first<<','<<t.second<<')';}
template<int N,class Tp>void output(ostream&,const Tp&){}
template<int N,class Tp,class,class ...Ts>void output(ostream &o,const Tp&t){if(N)o<<',';o<<get<N>(t);output<N+1,Tp,Ts...>(o,t);}
template<class ...Ts>ostream&operator<<(ostream&o,const tuple<Ts...>&t){o<<'(';output<0,tuple<Ts...>,Ts...>(o,t);return o<<')';}
template<class T>void output(T t,char z=10){if(t<0)t=-t,putchar(45);int c[20];
int k=0;while(t)c[k++]=t%10,t/=10;for(k||(c[k++]=0);k;)putchar(c[--k]^48);putchar(z);}
template<class T>void outputs(T t){output(t);}
template<class S,class ...T>void outputs(S a,T...t){output(a,32);outputs(t...);}
template<class T>void output(T *a,int n){REP(i,n)cout<<a[i]<<(i!=n-1?',':'\n');}
template<class T>void output(T *a,int n,int m){REP(i,n)output(a[i],m);}
template<class T>bool input(T &t){int n=1,c;for(t=0;!isdigit(c=getchar())&&~c&&c-45;);
if(!~c)return 0;for(c-45&&(n=0,t=c^48);isdigit(c=getchar());)t=10*t+c-48;t=n?-t:t;return 1;}
template<class S,class ...T>bool input(S&a,T&...t){input(a);return input(t...);}
template<class T>bool inputs(T *a, int n) { REP(i,n) if(!input(a[i])) return 0; return 1;}

template<int MOD>
struct ModInt {
  int x;
  ModInt() : x(0) {}
  ModInt(ll s) { if ((x = s % MOD) < 0) x += MOD; }
  ModInt operator+=(ModInt rhs) { if ((x+=rhs.x) >= MOD) x -= MOD; return *this; }
  ModInt operator-=(ModInt rhs) { if ((x-=rhs.x) < 0) x += MOD; return *this; }
  ModInt operator*=(ModInt rhs) { x = (ll)x*rhs.x % MOD; return *this; }
  ModInt operator+(ModInt rhs) const { return ModInt(*this) += rhs; }
  ModInt operator-(ModInt rhs) const { return ModInt(*this) -= rhs; }
  ModInt operator*(ModInt rhs) const { return ModInt(*this) *= rhs; }
  ModInt operator/=(ModInt rhs) {
    static const ll inv2 = ModInt(2).inv().x; // 2で割るのは特別に保存してみる
    ll i = (rhs.x == 2 ? inv2 : rhs.inv().x);
    x = x*i%MOD; return *this;
  }
  ModInt operator/(ModInt rhs) const { return ModInt(*this) /= rhs; }
  ModInt inv() { return pow(MOD-2); }
  ModInt pow(ll n) const {
    ModInt r = 1, t = x;
    for (;n;n>>=1,t*=t) if (n&1) r *= t;
    return r;
  }
  static ModInt strnum(const string &n) {ModInt a = 0; for (char c:n) a = a*10+c-'0'; return a;}
  friend ostream& operator<<(ostream &os, const ModInt rhs){ return os << rhs.x; }
};
typedef ModInt<int(1e9+7)> mint;

template<class T, int H, int W>
struct Matrix {
  T v[H][W];
  int h,w;
  T* operator[](int i) { return v[i]; }
  const T* operator[](int i) const { return v[i]; }

  Matrix() : h(0),w(0) {}
  Matrix(int h, int w) : h(h),w(w) { REP(i,h)REP(j,w)v[i][j] = 0; }
  Matrix(const vector<vector<T> > &u) : h(u.size()),w(u[0].size()) {
    REP(i,h)REP(j,w)v[i][j]=u[i][j];
  }
  static Matrix identity(int n) {
    Matrix A(n,n);
    REP(i,n) A[i][i] = 1;
    return A;
  }
  Matrix operator*(const Matrix &B) const {
    Matrix res(h,B.w);
    REP(i,h)REP(j,B.w) REP(k,w) res[i][j] += v[i][k] * B[k][j];
    return res;
  }
  Matrix& operator*=(const Matrix &B) { return *this = *this * B; }
  Matrix& operator+=(const Matrix &B) { REP(i,h)REP(j,w)v[i][j]+=B[i][j]; return *this; }
  Matrix& operator-=(const Matrix &B) { REP(i,h)REP(j,w)v[i][j]-=B[i][j]; return *this; }
  Matrix operator+(const Matrix &B) const { return Matrix(*this)+=B; }
  Matrix operator-(const Matrix &B) const { return Matrix(*this)-=B; }
  Matrix pow(ll n) {
    Matrix A(*this);
    Matrix B = identity(h);
    for (;n;n>>=1) {
      if (n&1) B *= A;
      A *= A;
    }
    return B;
  }
  // vector
  vector<T> operator*(const vector<T> &b) const {
    vector<T> res(w);
    REP(i,h) REP(j,w) res[i] += v[i][j] * b[j];
    return res;
  }
  friend ostream &operator<<(ostream &os, const Matrix &rhs) {
    REP(i,rhs.h) REP(j,rhs.w) os << rhs[i][j] << (j!=rhs.w-1?' ':'\n');
    return os;
  }
};

typedef Matrix<mint,50,50> mat;

int A[100000];
mint F[1000001];

void solve1(int n, int K) {
  mint sum = 0;
  REP(i,n) {
    F[i] = A[i];
    sum += F[i];
  }
  mint S = sum;
  for (int i=n; i<K; ++i) {
    F[i] = sum;
    sum += F[i] - F[i-n];
    S += F[i];
  }
  cout << F[K-1] << " " << S << endl;
}

void solve2(int n, ll K) {
  mat M(n+1,n+1);
  vector<mint> v(n+1);
  REP(i,n) v[i] = A[n-1-i];
  v[n] = A[0];
  REP(i,n) M[0][i] = 1;
  REP(i,n-1) M[1+i][i] = 1;
  M[n][n] = 1;
  M[n][n-2] = 1;
  // cout << M << endl;
  vector<mint> t = M.pow(K-1) * v;
  // cout << t << endl;
  cout << t[n-1] << " " << t[n] << endl;
}

int main() {
  ll n,k;
  while(input(n,k)) {
    REP(i,n) input(A[i]);
    if (k<=1000000) {
      solve1(n,k);
    } else {
      solve2(n,k);
    }
  }
}
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