結果

問題 No.980 Fibonacci Convolution Hard
ユーザー Haar
提出日時 2020-01-31 22:50:34
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 595 ms / 2,000 ms
コード長 5,648 bytes
コンパイル時間 2,081 ms
コンパイル使用メモリ 200,344 KB
最終ジャッジ日時 2025-01-08 21:22:47
ジャッジサーバーID
（参考情報） 		judge4 / judge4
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ファイルパターン 結果
other AC * 17
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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 <Mylib/Debug/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> void puts_all(const T &value){std::cout << value << "\n";}
template <typename T, typename ...Args> void puts_all(const T &value, const Args&... args){std::cout << value << " ";puts_all(args...);}

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);}
template <typename T> auto make_vector(int n, int m, const T &value){return vector<vector<T>>(n, vector<T>(m, value));}


struct Init{
  Init(){
    cin.tie(0);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(12);
    cerr << fixed << setprecision(12);
  }
}init;


template <std::uint32_t M> class ModInt{
public:
  std::uint64_t val;
  ModInt(): val(0){}
  ModInt(std::int64_t n){
    if(n >= M) val = n % M;
    else if(n < 0) val = n % M + M;
    else val = n;
  }
  
  inline constexpr auto operator+(const ModInt &a) const {return ModInt(val + a.val);}
  inline constexpr auto operator-(const ModInt &a) const {return ModInt(val - a.val);}
  inline constexpr auto operator*(const ModInt &a) const {return ModInt(val * a.val);}
  inline constexpr auto operator/(const ModInt &a) const {return ModInt(val * a.inv().val);}
  
  inline constexpr auto& operator=(const ModInt &a){val = a.val; return *this;}
  inline constexpr auto& operator+=(const ModInt &a){if((val += a.val) >= M) val -= M; return *this;}
  inline constexpr auto& operator-=(const ModInt &a){if(val < a.val) val += M; val -= a.val; return *this;}
  inline constexpr auto& operator*=(const ModInt &a){(val *= a.val) %= M; return *this;}
  inline constexpr auto& 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 auto& operator++(){*this += 1; return *this;}
  inline constexpr auto& operator--(){*this -= 1; return *this;}

  inline constexpr auto operator++(int){auto t = *this; *this += 1; return t;}
  inline constexpr auto operator--(int){auto t = *this; *this -= 1; return t;}

  inline constexpr static auto frac(std::int64_t a, std::int64_t b){
    return ModInt(a) / ModInt(b);
  }
  
  inline constexpr static ModInt power(std::int64_t n, std::int64_t p){
    if(p < 0) return power(n, -p).inv();
    
    ModInt ret = 1, e = n;
    for(; p; e *= e, p >>= 1) if(p & 1) ret *= e;
    return ret;
  }

  inline constexpr auto power(std::int64_t p) const {return power(val, p);}
  
  inline constexpr ModInt inv() const {
    std::int64_t a = val, b = M, u = 1, v = 0;
    
    while(b){
      std::int64_t t = a/b;
      a -= t*b; std::swap(a,b);
      u -= t*v; std::swap(u,v);
    }
    u %= M;
    if(u < 0) u += M;
    
    return u;
  }
};

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

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

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

using mint = ModInt<1000000007>;

const int MAX = 2000000;


int main(){
  int p, Q;
  while(cin >> p >> Q){

    vector<mint> a(MAX+1);
    a[1] = 0;
    a[2] = 1;
    FORE(i,3,MAX) a[i] = a[i-1] * p + a[i-2];


    vector<mint> sum(MAX+1);

    FORE(i,2,MAX){
      if(i % 2 == 0){
        sum[i] = (sum[i-1] * p / 2 + (sum[i-2] + a[i/2-1] * a[i/2-1]) / 2) * 2 + a[i/2] * a[i/2];
      }else{
        sum[i] = ((sum[i-1] + a[i/2] * a[i/2]) / 2 * p + sum[i-2] / 2 + a[(i-2)/2] * a[i-2-(i-2)/2]) * 2;
      }
    }

    /*
    FORE(i,1,10){
      dump(a[i]);
    }

    FORE(s,2,10){
      mint t = 0;

      FORE(i,1,s-1){
        if(i < s-i)
          t += a[i] * a[s-i];
      }

      dump(t);
    }
    */
    

    REP(i,Q){
      int q; cin >> q;

      cout << sum[q] << endl;
    }

    
  }

  return 0;
}
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