#769951 (C++17) No.1973 Divisor Sequence

提出ソース
結果

問題	No.1973 Divisor Sequence
ユーザー	mai
提出日時	2022-06-10 23:06:41
言語	C++17 (gcc 13.2.0 + boost 1.83.0)
結果	AC
実行時間	19 ms / 2,000 ms
コード長	14,343 bytes
コンパイル時間	3,816 ms
コンパイル使用メモリ	301,168 KB
実行使用メモリ	7,968 KB
最終ジャッジ日時	2023-10-21 06:22:34
合計ジャッジ時間	5,092 ms
ジャッジサーバーID （参考情報）	judge10 / judge12
このコードへのチャレンジ（β）
テストケース

テストケース表示
入力	結果	実行時間実行使用メモリ
testcase_00	AC	10 ms 7,924 KB
testcase_01	AC	9 ms 7,920 KB
testcase_02	AC	11 ms 7,924 KB
testcase_03	AC	11 ms 7,924 KB
testcase_04	AC	10 ms 7,924 KB
testcase_05	AC	11 ms 7,920 KB
testcase_06	AC	10 ms 7,924 KB
testcase_07	AC	11 ms 7,924 KB
testcase_08	AC	10 ms 7,924 KB
testcase_09	AC	10 ms 7,924 KB
testcase_10	AC	10 ms 7,924 KB
testcase_11	AC	10 ms 7,924 KB
testcase_12	AC	10 ms 7,924 KB
testcase_13	AC	11 ms 7,924 KB
testcase_14	AC	9 ms 7,924 KB
testcase_15	AC	10 ms 7,924 KB
testcase_16	AC	10 ms 7,924 KB
testcase_17	AC	10 ms 7,924 KB
testcase_18	AC	11 ms 7,924 KB
testcase_19	AC	10 ms 7,924 KB
testcase_20	AC	11 ms 7,924 KB
testcase_21	AC	11 ms 7,924 KB
testcase_22	AC	11 ms 7,924 KB
testcase_23	AC	19 ms 7,968 KB
testcase_24	AC	10 ms 7,924 KB
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

raw source code
#pragma GCC optimize("O3")
#include <bits/stdc++.h>

// clang-format off
using namespace std;
using ll = long long int;

#define all(v) (v).begin(),(v).end()
#define repeat(cnt,l) for(typename remove_const<typename remove_reference<decltype(l)>::type>::type cnt={};(cnt)<(l);++(cnt))
#define rrepeat(cnt,l) for(auto cnt=(l)-1;0<=(cnt);--(cnt))
#define iterate(cnt,b,e) for(auto cnt=(b);(cnt)!=(e);++(cnt))
#define upto(cnt,b,e,step) for(auto cnt=(b);(cnt)<=(e);(cnt)+=(step))
#define downto(cnt,b,e,step) for(auto cnt=(b);(e)<=(cnt);(cnt)-=(step))
const long long MD = 1000000007; const long double PI = 3.1415926535897932384626433832795L;
template<typename T1, typename T2> inline ostream& operator <<(ostream &o, const pair<T1, T2> p) { o << '(' << p.first << ':' << p.second << ')'; return o; }
template<typename T> inline T& chmax(T& to, const T& val) { return to = max(to, val); }
template<typename T> inline T& chmin(T& to, const T& val) { return to = min(to, val); }
void bye(string s, int code = 0) { cout << s << endl; exit(code); }
mt19937_64 randdev(8901016);
template<typename T, typename Random = decltype(randdev), typename enable_if<is_integral<T>::value>::type* = nullptr>
inline T rand(T l, T h, Random& rand = randdev) { return uniform_int_distribution<T>(l, h)(rand); }
template<typename T, typename Random = decltype(randdev), typename enable_if<is_floating_point<T>::value>::type* = nullptr>
inline T rand(T l, T h, Random& rand = randdev) { return uniform_real_distribution<T>(l, h)(rand); }template<typename T>
static ostream& operator<<(ostream& o, const std::vector<T>& v) {
  o << "[ "; for(const auto& e : v) o<<e<<' '; return o << ']';
}

template <typename I> struct MyRangeFormat{ I b,e; MyRangeFormat(I _b, I _e):b(_b),e(_e){} };
template<typename I> static ostream& operator<<(ostream& o, const MyRangeFormat<I>& f) {
  o << "[ "; iterate(i,f.b,f.e) o<<*i<<' '; return o << ']';
}
template <typename I> struct MyMatrixFormat{
  const I& p; long long n, m;
  MyMatrixFormat(const I& _p, long long _n, long long _m):p(_p),n(_n),m(_m){}
};
template<typename I> static ostream& operator<<(ostream& o, const MyMatrixFormat<I>& f) {
  o<<'\n'; repeat(i,(f.n)) { repeat(j,f.m) o<<f.p[i][j]<<' '; o<<'\n'; }
  return o;
}
struct LOG_t { ~LOG_t() { cout << endl; } };
#define LOG (LOG_t(),cout<<'L'<<__LINE__<<": ")
#define FMTA(m,w) (MyRangeFormat<decltype(m+0)>(m,m+w))
#define FMTR(b,e) (MyRangeFormat<decltype(e)>(b,e))
#define FMTV(v) FMTR(v.begin(),v.end())
#define FMTM(m,h,w) (MyMatrixFormat<decltype(m+0)>(m,h,w))

#if defined(_WIN32) || defined(_WIN64)
#define getc_x _getc_nolock
#define putc_x _putc_nolock
#elif defined(__GNUC__)
#define getc_x getc_unlocked
#define putc_x putc_unlocked
#else
#define getc_x getc
#define putc_x putc
#endif
class MaiScanner {
  FILE* fp_;
  constexpr bool isvisiblechar(char c) noexcept { return (0x21<=(c)&&(c)<=0x7E); }
public:
  inline MaiScanner(FILE* fp):fp_(fp){}
  template<typename T> void input_integer(T& var) noexcept {
    var = 0; T sign = 1;
    int cc = getc_x(fp_);
    for (; cc < '0' || '9' < cc; cc = getc_x(fp_))
      if (cc == '-') sign = -1;
    for (; '0' <= cc && cc <= '9'; cc = getc_x(fp_))
      var = (var << 3) + (var << 1) + cc - '0';
    var = var * sign;
  }
  inline int c() noexcept { return getc_x(fp_); }
  template<typename T, typename enable_if<is_integral<T>::value, nullptr_t>::type = nullptr>
  inline MaiScanner& operator>>(T& var) noexcept { input_integer<T>(var); return *this; }
  inline MaiScanner& operator>>(string& var) {
    int cc = getc_x(fp_);
    for (; !isvisiblechar(cc); cc = getc_x(fp_));
    for (; isvisiblechar(cc); cc = getc_x(fp_))
      var.push_back(cc);
    return *this;
  }
  template<typename IT> inline void in(IT begin, IT end) { for (auto it = begin; it != end; ++it) *this >> *it; }
};
class MaiPrinter {
  FILE* fp_;
public:
  inline MaiPrinter(FILE* fp):fp_(fp){}
  template<typename T>
  void output_integer(T var) noexcept {
    if (var == 0) { putc_x('0', fp_); return; }
    if (var < 0)
      putc_x('-', fp_),
      var = -var;
    char stack[32]; int stack_p = 0;
    while (var)
      stack[stack_p++] = '0' + (var % 10),
      var /= 10;
    while (stack_p)
      putc_x(stack[--stack_p], fp_);
  }
  inline MaiPrinter& operator<<(char c) noexcept { putc_x(c, fp_); return *this; }
  template<typename T, typename enable_if<is_integral<T>::value, nullptr_t>::type = nullptr>
  inline MaiPrinter& operator<<(T var) noexcept { output_integer<T>(var); return *this; }
  inline MaiPrinter& operator<<(const char* str_p) noexcept { while (*str_p) putc_x(*(str_p++), fp_); return *this; }
  inline MaiPrinter& operator<<(const string& str) {
    const char* p = str.c_str();
    const char* l = p + str.size();
    while (p < l) putc_x(*p++, fp_);
    return *this;
  }
  template<typename IT> void join(IT begin, IT end, char sep = ' ') { for (bool b = 0; begin != end; ++begin, b = 1) b ? *this << sep << *begin : *this << *begin; }
};
MaiScanner scanner(stdin);
MaiPrinter printer(stdout);
// clang-format on

// template <int Max = 2000>
template <int Max>
class Prime {
  int d_[Max + 1];
  int n_;
  int li_[std::max(10000, Max / 10)];

 public:
  constexpr Prime() : d_(), n_(), li_() {
    d_[0] = d_[1] = 0;
    for (int i = 2; i <= Max; i += 2) {
      d_[i] = 2;
    }
    n_ = 1;
    li_[0] = 2;
    int p = 3;
    for (p = 3; p * p <= Max; p += 2) {
      if (d_[p] != 0)
        continue;
      d_[p] = p;
      li_[n_++] = p;
      for (int j = p * p; j <= Max; j += p) {  // i*i
        d_[j] = p;
      }
    }
    for (; p <= Max; p += 2) {
      if (d_[p] != 0)
        continue;
      d_[p] = p;
      li_[n_++] = p;
    }
  }
  constexpr inline bool isPrime(int x) const { return (x >= 2) && (x == 2 || d_[x] == x); }
  constexpr inline int operator[](int i) const { return li_[i]; }

  class iterator {
    const Prime& pl;
    int ptr = 0;

   public:
    constexpr iterator(const decltype(pl)& _pl, int _ptr = 0) : pl(_pl), ptr(_ptr) {}
    constexpr int operator*() const { return pl[ptr]; }
    constexpr iterator& operator++() {
      ptr++;
      return *this;
    }  // prefix
    constexpr inline bool operator!=(const iterator& it) const {
      return ptr != it.ptr ? !(pl.n_ <= ptr && pl.n_ <= it.ptr) : false;
    }
    constexpr inline bool operator==(const iterator& it) const {
      return ptr != it.ptr ? (pl.n_ <= ptr && pl.n_ <= it.ptr) : true;
    }
  };
  constexpr Prime::iterator begin() const { return Prime::iterator(*this, 0); }
  constexpr Prime::iterator end() const { return Prime::iterator(*this, n_); }

  std::map<int, int> division(long long number) const {
    std::map<int, int> div;
    // for large number
    for (int i = 0; (long long)Max <= number && i < n_; ++i) {
      long long p = li_[i];
      int c = 0;
      while (number / p * p == number)
        ++c, number /= p;
      if (c > 0)
        div[(int)p] = c;
    }
    if ((long long)Max <= number) {
      // guess it's prime number.
      div[number] += 1;
      return div;
    }
    while (number >= 2) {
      long long p = d_[number];
      int c = 0;
      while (number / p * p == number)
        ++c, number /= p;
      if (c > 0)
        div[(int)p] = c;
    }
    return div;
  }
};

template <typename T, typename Container = valarray<T>>
// using T = double;
class Matrix {
 public:
  size_t height_, width_;
  Container data_;
  Matrix(size_t height = 1, size_t width = 1)
      : height_(height), width_(width), data_(height * width) {}
  template <typename V>
  Matrix(size_t height, size_t width, const V& data)
      : height_(height), width_(width), data_(data) {}
  Matrix(size_t height, size_t width, initializer_list<T> init)
      : height_(height), width_(width), data_(init) {}

  static Matrix<T> makeDiag(size_t n, T val) {
    Matrix<T> mat(n, n);
    for (size_t i = 0; i < n; ++i)
      mat(i, i) = val;
    return mat;
  }

  inline T& operator()(size_t y, size_t x) { return data_[y * width_ + x]; }
  inline T operator()(size_t y, size_t x) const { return data_[y * width_ + x]; }
  inline T& operator[](size_t i) { return data_[i]; }
  inline T operator[](size_t i) const { return data_[i]; }
  inline void resize(size_t h, size_t w) {
    height_ = h;
    width_ = w;
    data_.resize(h * w);
  }
  inline void resize(size_t h, size_t w, T val) {
    height_ = h;
    width_ = w;
    data_.resize(h * w, val);
  }
  inline void fill(T val) { data_ = val; }
  void transpose() {
    for (size_t y = 0; y < height_; ++y)
      for (size_t x = y + 1; x < width_; ++x)
        swap(operator()(y, x), operator()(x, y));
  }
  Matrix<T> transposed() const {
    auto m = *this;
    m.transpose();
    return m;
  }

  void print(ostream& os) {
    os << "- - -" << endl;  //  << setprecision(3)
    for (size_t y = 0; y < height_; ++y) {
      for (size_t x = 0; x < width_; ++x) {
        os << setw(7) << operator()(y, x) << ' ';
      }
      os << endl;
    }
  }
};
template <typename T>
inline ostream& operator<<(ostream& os, Matrix<T> mat) {
  mat.print(os);
  return os;
}

template <typename T>
Matrix<T> multiply(const Matrix<T>& mat1, const Matrix<T>& mat2) {
  assert(mat1.width_ == mat2.height_);
  Matrix<T> result(mat1.height_, mat2.width_);
  for (size_t i = 0; i < mat1.height_; ++i)
    for (size_t j = 0; j < mat2.width_; ++j)
      for (size_t k = 0; k < mat1.width_; ++k)
        result(i, j) += mat1(i, k) * mat2(k, j);
  return result;
}
template <typename T, typename V>
V multiply(const Matrix<T>& mat1, const V& vec2) {
  assert(mat1.width_ == vec2.size());
  V result(mat1.height_);
  for (size_t i = 0, j; i < mat1.height_; ++i)
    for (j = 0; j < mat1.width_; ++j)
      result[i] += mat1(i, j) * vec2[j];
  return result;
}

template <typename T>
inline Matrix<T>& operator+=(Matrix<T>& mat, T val) {
  mat.data_ += val;
  return mat;
}
template <typename T>
inline Matrix<T>& operator-=(Matrix<T>& mat, T val) {
  mat.data_ -= val;
  return mat;
}
template <typename T>
inline Matrix<T>& operator*=(Matrix<T>& mat, T val) {
  mat.data_ *= val;
  return mat;
}
template <typename T>
inline Matrix<T>& operator/=(Matrix<T>& mat, T val) {
  mat.data_ /= val;
  return mat;
}
template <typename T>
inline Matrix<T>& operator^=(Matrix<T>& mat, T val) {
  mat.data_ ^= val;
  return mat;
}
template <typename T>
inline Matrix<T>& operator+=(Matrix<T>& mat1, const Matrix<T>& mat2) {
  mat1.data_ += mat2.data_;
  return mat1;
}
template <typename T>
inline Matrix<T> operator+(Matrix<T>& mat1, const Matrix<T>& mat2) {
  return Matrix<T>(mat1.height_, mat1.width_, mat1.data_ + mat2.data_);
}
template <typename T>
inline Matrix<T>& operator-=(Matrix<T>& mat1, const Matrix<T>& mat2) {
  mat1.data_ -= mat2.data_;
  return mat1;
}
template <typename T>
inline Matrix<T> operator-(Matrix<T>& mat1, const Matrix<T>& mat2) {
  return Matrix<T>(mat1.height_, mat1.width_, mat1.data_ - mat2.data_);
}
template <typename T>
inline Matrix<T>& operator*=(Matrix<T>& mat1, const Matrix<T>& mat2) {
  mat1 = multiply(mat1, mat2);
  return mat1;
}
template <typename T>
inline Matrix<T> operator*(const Matrix<T>& mat1, const Matrix<T>& mat2) {
  return multiply(mat1, mat2);
}
template <typename T, typename V>
inline V operator*(const Matrix<T>& mat1, const V& vec2) {
  return multiply(mat1, vec2);
}

template <typename T>
Matrix<T> pow(Matrix<T> a, long long p) {
  assert(a.height_ == a.width_);
  auto b = Matrix<T>::makeDiag(a.height_, 1);
  while (0 < p) {
    if (p & 1)
      b *= a;
    a *= a;
    p >>= 1;
  }
  return b;
}

class llmod {
 private:
  using value_type = long long;
  value_type val_;
  // inline ll cut(ll v) const { return ((v%MOD) + MOD) % MOD; } // safe
 public:
  static const value_type MOD = 1000000007;  // <=

  llmod() : val_(0) {}
  llmod(value_type num) : val_(((num % MOD) + MOD) % MOD) {}

  inline operator value_type() const { return val_; }
  inline value_type operator*() const { return val_; }
  inline llmod& operator=(const llmod& lm) {
    val_ = lm.val_;
    return *this;
  }
  inline llmod& operator=(value_type v) {
    val_ = (v) % MOD;
    return *this;
  }

  inline llmod& operator+=(value_type v) {
    val_ = (val_ + v) % MOD;
    return *this;
  }
  inline llmod& operator+=(const llmod& l) {
    val_ = (val_ + l.val_) % MOD;
    return *this;
  }
  inline llmod& operator-=(value_type v) {
    val_ = (val_ - v + MOD) % MOD;
    return *this;
  }
  inline llmod& operator-=(const llmod& l) {
    val_ = (val_ - l.val_ + MOD) % MOD;
    return *this;
  }
  inline llmod& operator*=(value_type v) {
    val_ = (val_ * v) % MOD;
    return *this;
  }
  inline llmod& operator*=(const llmod& l) {
    val_ = (val_ * l.val_) % MOD;
    return *this;
  }
  inline llmod& operator++() {
    val_ = (val_ + 1) % MOD;
    return *this;
  }
  inline llmod operator++(int) {
    llmod t = *this;
    val_ = (val_ + 1) % MOD;
    return t;
  }
  inline llmod& justify() {
    val_ = ((val_ % MOD) + MOD) % MOD;
    return *this;
  }
  friend llmod pow(llmod, long long);
};
inline std::ostream& operator<<(std::ostream& os, const llmod& l) {
  os << *l;
  return os;
}

inline llmod operator+(llmod t, const llmod& r) {
  return t += r;
}
inline llmod operator-(llmod t, const llmod& r) {
  return t -= r;
}
inline llmod operator*(llmod t, const llmod& r) {
  return t *= r;
}

// MEMO : 逆元...pow(n,MD-2)
llmod pow(llmod x, long long p) {
  llmod::value_type y = 1;
  llmod::value_type xval = x.justify();
  while (0 < p) {
    if (p & 1)
      y = (xval * y) % llmod::MOD;
    xval = (xval * xval) % llmod::MOD;
    p >>= 1;
  }
  return llmod(y);
}

inline llmod& operator/=(llmod& l, const llmod& r) {
  return l *= pow(r, llmod::MOD - 2);
}

//

Prime<1001000> prime;

//


ll solve(ll N, ll n) {
  Matrix<llmod> mat(n, n);
  repeat(i, n) {
    upto(j, 0, n-i-1, 1) {
      mat(i, j) = 1;
    }
  }
  vector<llmod> vec(n);
  repeat(i, n) vec[i] =  1;
  auto vec2 = pow(mat, N-1)*vec;
  
  // LOG << vec2;
  
  llmod total = 0;
  repeat(i, n) total += vec2[i];
  return *total;
}

int main() {
ll N, M;
  
  scanner >> N >> M;
  
  ll total = 1;
  auto div = prime.division(M);
  for (auto p : div) {
    // LOG << p;
    ll n = p.second;
    ll s = solve(N, n+1);
    // LOG << s;
    total *= s;
    total %= MD;
  }
  
  cout << (total%MD) << endl;
  
  return 0;
}
yukicoder

結果

テストケース

ソースコード
