結果

問題 No.1973 Divisor Sequence
ユーザー maimai
提出日時 2022-06-10 23:06:41
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 16 ms / 2,000 ms
コード長 14,343 bytes
コンパイル時間 3,490 ms
コンパイル使用メモリ 301,868 KB
最終ジャッジ日時 2025-01-29 20:15:24
ジャッジサーバーID
(参考情報)
judge3 / judge3
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ファイルパターン 結果
sample AC * 3
other AC * 22
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ソースコード

diff #
プレゼンテーションモードにする

#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 : ...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;
}
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