proconlib
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tests/divisor_zeta.test.cpp
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- Last update: 2025-01-25 08:45:50+09:00
Depends on
- Assertion macro (tools/assert_that.hpp)
- Divisor Zeta transform (tools/divisor_zeta.hpp)
- Sieve of Eratosthenes (tools/eratosthenes_sieve.hpp)
Code
// competitive-verifier: STANDALONE
#include <iostream>
#include <random>
#include <vector>
#include <iterator>
#include "atcoder/modint.hpp"
#include "tools/assert_that.hpp"
#include "tools/divisor_zeta.hpp"
using mint = atcoder::modint998244353;
int main() {
std::cin.tie(nullptr);
std::ios_base::sync_with_stdio(false);
std::random_device seed_gen;
std::mt19937 engine(seed_gen());
std::uniform_int_distribution<int> dist(0, 998244352);
for (int N = 0; N <= 20; ++N) {
std::vector<mint> a(N);
for (auto&& a_i : a) a_i = mint::raw(dist(engine));
std::vector<mint> b(N, mint::raw(0));
if (N > 0) b[0] = a[0];
for (int i = 1; i < N; ++i) {
for (int j = 1; j < N; ++j) {
if (i % j == 0) b[i] += a[j];
}
}
std::vector<mint> actual_b;
tools::divisor_zeta(a.begin(), a.end(), std::back_inserter(actual_b));
assert_that(actual_b == b);
tools::divisor_zeta(a.begin(), a.end());
assert_that(a == b);
}
return 0;
}
#line 1 "tests/divisor_zeta.test.cpp"
// competitive-verifier: STANDALONE
#include <iostream>
#include <random>
#include <vector>
#include <iterator>
#line 1 "lib/ac-library/atcoder/modint.hpp"
#include <cassert>
#include <numeric>
#include <type_traits>
#ifdef _MSC_VER
#include <intrin.h>
#endif
#line 1 "lib/ac-library/atcoder/internal_math.hpp"
#include <utility>
#ifdef _MSC_VER
#include <intrin.h>
#endif
namespace atcoder {
namespace internal {
// @param m `1 <= m`
// @return x mod m
constexpr long long safe_mod(long long x, long long m) {
x %= m;
if (x < 0) x += m;
return x;
}
// Fast modular multiplication by barrett reduction
// Reference: https://en.wikipedia.org/wiki/Barrett_reduction
// NOTE: reconsider after Ice Lake
struct barrett {
unsigned int _m;
unsigned long long im;
// @param m `1 <= m`
explicit barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}
// @return m
unsigned int umod() const { return _m; }
// @param a `0 <= a < m`
// @param b `0 <= b < m`
// @return `a * b % m`
unsigned int mul(unsigned int a, unsigned int b) const {
// [1] m = 1
// a = b = im = 0, so okay
// [2] m >= 2
// im = ceil(2^64 / m)
// -> im * m = 2^64 + r (0 <= r < m)
// let z = a*b = c*m + d (0 <= c, d < m)
// a*b * im = (c*m + d) * im = c*(im*m) + d*im = c*2^64 + c*r + d*im
// c*r + d*im < m * m + m * im < m * m + 2^64 + m <= 2^64 + m * (m + 1) < 2^64 * 2
// ((ab * im) >> 64) == c or c + 1
unsigned long long z = a;
z *= b;
#ifdef _MSC_VER
unsigned long long x;
_umul128(z, im, &x);
#else
unsigned long long x =
(unsigned long long)(((unsigned __int128)(z)*im) >> 64);
#endif
unsigned long long y = x * _m;
return (unsigned int)(z - y + (z < y ? _m : 0));
}
};
// @param n `0 <= n`
// @param m `1 <= m`
// @return `(x ** n) % m`
constexpr long long pow_mod_constexpr(long long x, long long n, int m) {
if (m == 1) return 0;
unsigned int _m = (unsigned int)(m);
unsigned long long r = 1;
unsigned long long y = safe_mod(x, m);
while (n) {
if (n & 1) r = (r * y) % _m;
y = (y * y) % _m;
n >>= 1;
}
return r;
}
// Reference:
// M. Forisek and J. Jancina,
// Fast Primality Testing for Integers That Fit into a Machine Word
// @param n `0 <= n`
constexpr bool is_prime_constexpr(int n) {
if (n <= 1) return false;
if (n == 2 || n == 7 || n == 61) return true;
if (n % 2 == 0) return false;
long long d = n - 1;
while (d % 2 == 0) d /= 2;
constexpr long long bases[3] = {2, 7, 61};
for (long long a : bases) {
long long t = d;
long long y = pow_mod_constexpr(a, t, n);
while (t != n - 1 && y != 1 && y != n - 1) {
y = y * y % n;
t <<= 1;
}
if (y != n - 1 && t % 2 == 0) {
return false;
}
}
return true;
}
template <int n> constexpr bool is_prime = is_prime_constexpr(n);
// @param b `1 <= b`
// @return pair(g, x) s.t. g = gcd(a, b), xa = g (mod b), 0 <= x < b/g
constexpr std::pair<long long, long long> inv_gcd(long long a, long long b) {
a = safe_mod(a, b);
if (a == 0) return {b, 0};
// Contracts:
// [1] s - m0 * a = 0 (mod b)
// [2] t - m1 * a = 0 (mod b)
// [3] s * |m1| + t * |m0| <= b
long long s = b, t = a;
long long m0 = 0, m1 = 1;
while (t) {
long long u = s / t;
s -= t * u;
m0 -= m1 * u; // |m1 * u| <= |m1| * s <= b
// [3]:
// (s - t * u) * |m1| + t * |m0 - m1 * u|
// <= s * |m1| - t * u * |m1| + t * (|m0| + |m1| * u)
// = s * |m1| + t * |m0| <= b
auto tmp = s;
s = t;
t = tmp;
tmp = m0;
m0 = m1;
m1 = tmp;
}
// by [3]: |m0| <= b/g
// by g != b: |m0| < b/g
if (m0 < 0) m0 += b / s;
return {s, m0};
}
// Compile time primitive root
// @param m must be prime
// @return primitive root (and minimum in now)
constexpr int primitive_root_constexpr(int m) {
if (m == 2) return 1;
if (m == 167772161) return 3;
if (m == 469762049) return 3;
if (m == 754974721) return 11;
if (m == 998244353) return 3;
int divs[20] = {};
divs[0] = 2;
int cnt = 1;
int x = (m - 1) / 2;
while (x % 2 == 0) x /= 2;
for (int i = 3; (long long)(i)*i <= x; i += 2) {
if (x % i == 0) {
divs[cnt++] = i;
while (x % i == 0) {
x /= i;
}
}
}
if (x > 1) {
divs[cnt++] = x;
}
for (int g = 2;; g++) {
bool ok = true;
for (int i = 0; i < cnt; i++) {
if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) {
ok = false;
break;
}
}
if (ok) return g;
}
}
template <int m> constexpr int primitive_root = primitive_root_constexpr(m);
// @param n `n < 2^32`
// @param m `1 <= m < 2^32`
// @return sum_{i=0}^{n-1} floor((ai + b) / m) (mod 2^64)
unsigned long long floor_sum_unsigned(unsigned long long n,
unsigned long long m,
unsigned long long a,
unsigned long long b) {
unsigned long long ans = 0;
while (true) {
if (a >= m) {
ans += n * (n - 1) / 2 * (a / m);
a %= m;
}
if (b >= m) {
ans += n * (b / m);
b %= m;
}
unsigned long long y_max = a * n + b;
if (y_max < m) break;
// y_max < m * (n + 1)
// floor(y_max / m) <= n
n = (unsigned long long)(y_max / m);
b = (unsigned long long)(y_max % m);
std::swap(m, a);
}
return ans;
}
} // namespace internal
} // namespace atcoder
#line 1 "lib/ac-library/atcoder/internal_type_traits.hpp"
#line 7 "lib/ac-library/atcoder/internal_type_traits.hpp"
namespace atcoder {
namespace internal {
#ifndef _MSC_VER
template <class T>
using is_signed_int128 =
typename std::conditional<std::is_same<T, __int128_t>::value ||
std::is_same<T, __int128>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int128 =
typename std::conditional<std::is_same<T, __uint128_t>::value ||
std::is_same<T, unsigned __int128>::value,
std::true_type,
std::false_type>::type;
template <class T>
using make_unsigned_int128 =
typename std::conditional<std::is_same<T, __int128_t>::value,
__uint128_t,
unsigned __int128>;
template <class T>
using is_integral = typename std::conditional<std::is_integral<T>::value ||
is_signed_int128<T>::value ||
is_unsigned_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_signed_int = typename std::conditional<(is_integral<T>::value &&
std::is_signed<T>::value) ||
is_signed_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int =
typename std::conditional<(is_integral<T>::value &&
std::is_unsigned<T>::value) ||
is_unsigned_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using to_unsigned = typename std::conditional<
is_signed_int128<T>::value,
make_unsigned_int128<T>,
typename std::conditional<std::is_signed<T>::value,
std::make_unsigned<T>,
std::common_type<T>>::type>::type;
#else
template <class T> using is_integral = typename std::is_integral<T>;
template <class T>
using is_signed_int =
typename std::conditional<is_integral<T>::value && std::is_signed<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int =
typename std::conditional<is_integral<T>::value &&
std::is_unsigned<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using to_unsigned = typename std::conditional<is_signed_int<T>::value,
std::make_unsigned<T>,
std::common_type<T>>::type;
#endif
template <class T>
using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;
template <class T>
using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;
template <class T> using to_unsigned_t = typename to_unsigned<T>::type;
} // namespace internal
} // namespace atcoder
#line 14 "lib/ac-library/atcoder/modint.hpp"
namespace atcoder {
namespace internal {
struct modint_base {};
struct static_modint_base : modint_base {};
template <class T> using is_modint = std::is_base_of<modint_base, T>;
template <class T> using is_modint_t = std::enable_if_t<is_modint<T>::value>;
} // namespace internal
template <int m, std::enable_if_t<(1 <= m)>* = nullptr>
struct static_modint : internal::static_modint_base {
using mint = static_modint;
public:
static constexpr int mod() { return m; }
static mint raw(int v) {
mint x;
x._v = v;
return x;
}
static_modint() : _v(0) {}
template <class T, internal::is_signed_int_t<T>* = nullptr>
static_modint(T v) {
long long x = (long long)(v % (long long)(umod()));
if (x < 0) x += umod();
_v = (unsigned int)(x);
}
template <class T, internal::is_unsigned_int_t<T>* = nullptr>
static_modint(T v) {
_v = (unsigned int)(v % umod());
}
unsigned int val() const { return _v; }
mint& operator++() {
_v++;
if (_v == umod()) _v = 0;
return *this;
}
mint& operator--() {
if (_v == 0) _v = umod();
_v--;
return *this;
}
mint operator++(int) {
mint result = *this;
++*this;
return result;
}
mint operator--(int) {
mint result = *this;
--*this;
return result;
}
mint& operator+=(const mint& rhs) {
_v += rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
mint& operator-=(const mint& rhs) {
_v -= rhs._v;
if (_v >= umod()) _v += umod();
return *this;
}
mint& operator*=(const mint& rhs) {
unsigned long long z = _v;
z *= rhs._v;
_v = (unsigned int)(z % umod());
return *this;
}
mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }
mint operator+() const { return *this; }
mint operator-() const { return mint() - *this; }
mint pow(long long n) const {
assert(0 <= n);
mint x = *this, r = 1;
while (n) {
if (n & 1) r *= x;
x *= x;
n >>= 1;
}
return r;
}
mint inv() const {
if (prime) {
assert(_v);
return pow(umod() - 2);
} else {
auto eg = internal::inv_gcd(_v, m);
assert(eg.first == 1);
return eg.second;
}
}
friend mint operator+(const mint& lhs, const mint& rhs) {
return mint(lhs) += rhs;
}
friend mint operator-(const mint& lhs, const mint& rhs) {
return mint(lhs) -= rhs;
}
friend mint operator*(const mint& lhs, const mint& rhs) {
return mint(lhs) *= rhs;
}
friend mint operator/(const mint& lhs, const mint& rhs) {
return mint(lhs) /= rhs;
}
friend bool operator==(const mint& lhs, const mint& rhs) {
return lhs._v == rhs._v;
}
friend bool operator!=(const mint& lhs, const mint& rhs) {
return lhs._v != rhs._v;
}
private:
unsigned int _v;
static constexpr unsigned int umod() { return m; }
static constexpr bool prime = internal::is_prime<m>;
};
template <int id> struct dynamic_modint : internal::modint_base {
using mint = dynamic_modint;
public:
static int mod() { return (int)(bt.umod()); }
static void set_mod(int m) {
assert(1 <= m);
bt = internal::barrett(m);
}
static mint raw(int v) {
mint x;
x._v = v;
return x;
}
dynamic_modint() : _v(0) {}
template <class T, internal::is_signed_int_t<T>* = nullptr>
dynamic_modint(T v) {
long long x = (long long)(v % (long long)(mod()));
if (x < 0) x += mod();
_v = (unsigned int)(x);
}
template <class T, internal::is_unsigned_int_t<T>* = nullptr>
dynamic_modint(T v) {
_v = (unsigned int)(v % mod());
}
unsigned int val() const { return _v; }
mint& operator++() {
_v++;
if (_v == umod()) _v = 0;
return *this;
}
mint& operator--() {
if (_v == 0) _v = umod();
_v--;
return *this;
}
mint operator++(int) {
mint result = *this;
++*this;
return result;
}
mint operator--(int) {
mint result = *this;
--*this;
return result;
}
mint& operator+=(const mint& rhs) {
_v += rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
mint& operator-=(const mint& rhs) {
_v += mod() - rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
mint& operator*=(const mint& rhs) {
_v = bt.mul(_v, rhs._v);
return *this;
}
mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }
mint operator+() const { return *this; }
mint operator-() const { return mint() - *this; }
mint pow(long long n) const {
assert(0 <= n);
mint x = *this, r = 1;
while (n) {
if (n & 1) r *= x;
x *= x;
n >>= 1;
}
return r;
}
mint inv() const {
auto eg = internal::inv_gcd(_v, mod());
assert(eg.first == 1);
return eg.second;
}
friend mint operator+(const mint& lhs, const mint& rhs) {
return mint(lhs) += rhs;
}
friend mint operator-(const mint& lhs, const mint& rhs) {
return mint(lhs) -= rhs;
}
friend mint operator*(const mint& lhs, const mint& rhs) {
return mint(lhs) *= rhs;
}
friend mint operator/(const mint& lhs, const mint& rhs) {
return mint(lhs) /= rhs;
}
friend bool operator==(const mint& lhs, const mint& rhs) {
return lhs._v == rhs._v;
}
friend bool operator!=(const mint& lhs, const mint& rhs) {
return lhs._v != rhs._v;
}
private:
unsigned int _v;
static internal::barrett bt;
static unsigned int umod() { return bt.umod(); }
};
template <int id> internal::barrett dynamic_modint<id>::bt(998244353);
using modint998244353 = static_modint<998244353>;
using modint1000000007 = static_modint<1000000007>;
using modint = dynamic_modint<-1>;
namespace internal {
template <class T>
using is_static_modint = std::is_base_of<internal::static_modint_base, T>;
template <class T>
using is_static_modint_t = std::enable_if_t<is_static_modint<T>::value>;
template <class> struct is_dynamic_modint : public std::false_type {};
template <int id>
struct is_dynamic_modint<dynamic_modint<id>> : public std::true_type {};
template <class T>
using is_dynamic_modint_t = std::enable_if_t<is_dynamic_modint<T>::value>;
} // namespace internal
} // namespace atcoder
#line 1 "tools/assert_that.hpp"
#line 5 "tools/assert_that.hpp"
#include <cstdlib>
#define assert_that_impl(cond, file, line, func) do {\
if (!cond) {\
::std::cerr << file << ':' << line << ": " << func << ": Assertion `" << #cond << "' failed." << '\n';\
::std::exit(EXIT_FAILURE);\
}\
} while (false)
#define assert_that(...) assert_that_impl((__VA_ARGS__), __FILE__, __LINE__, __func__)
#line 1 "tools/divisor_zeta.hpp"
#line 6 "tools/divisor_zeta.hpp"
#include <algorithm>
#line 1 "tools/eratosthenes_sieve.hpp"
#include <array>
#include <cstdint>
#line 7 "tools/eratosthenes_sieve.hpp"
#include <cstddef>
#line 11 "tools/eratosthenes_sieve.hpp"
namespace tools {
template <typename T>
class eratosthenes_sieve {
constexpr static ::std::array<::std::uint64_t, 15> init = {
UINT64_C(0b0010100000100010100010100010000010100000100010100010100010000010),
UINT64_C(0b1000001010000010001010001010001000001010000010001010001010001000),
UINT64_C(0b1000100000101000001000101000101000100000101000001000101000101000),
UINT64_C(0b0010100010000010100000100010100010100010000010100000100010100010),
UINT64_C(0b1010001010001000001010000010001010001010001000001010000010001010),
UINT64_C(0b1000101000101000100000101000001000101000101000100000101000001000),
UINT64_C(0b0000100010100010100010000010100000100010100010100010000010100000),
UINT64_C(0b1010000010001010001010001000001010000010001010001010001000001010),
UINT64_C(0b0000101000001000101000101000100000101000001000101000101000100000),
UINT64_C(0b0010000010100000100010100010100010000010100000100010100010100010),
UINT64_C(0b1010001000001010000010001010001010001000001010000010001010001010),
UINT64_C(0b1000101000100000101000001000101000101000100000101000001000101000),
UINT64_C(0b0010100010100010000010100000100010100010100010000010100000100010),
UINT64_C(0b0010001010001010001000001010000010001010001010001000001010000010),
UINT64_C(0b1000001000101000101000100000101000001000101000101000100000101000),
};
::std::vector<::std::uint64_t> m_is_prime;
int m_n;
public:
class prime_iterable {
private:
::tools::eratosthenes_sieve<T> const *m_parent;
int m_l;
int m_r;
public:
class iterator {
private:
::tools::eratosthenes_sieve<T> const *m_parent;
int m_p;
public:
using difference_type = ::std::ptrdiff_t;
using value_type = T;
using reference = const T&;
using pointer = const T*;
using iterator_category = ::std::input_iterator_tag;
iterator() = default;
iterator(::tools::eratosthenes_sieve<T> const * const parent, const int p) : m_parent(parent), m_p(p) {
for (; this->m_p <= parent->m_n && !parent->is_prime(this->m_p); ++this->m_p);
}
value_type operator*() const {
return this->m_p;
}
iterator& operator++() {
for (++this->m_p; this->m_p <= this->m_parent->m_n && !this->m_parent->is_prime(this->m_p); ++this->m_p);
return *this;
}
iterator operator++(int) {
const auto self = *this;
++*this;
return self;
}
friend bool operator==(const iterator lhs, const iterator rhs) {
assert(lhs.m_parent == rhs.m_parent);
return lhs.m_p == rhs.m_p;
}
friend bool operator!=(const iterator lhs, const iterator rhs) {
return !(lhs == rhs);
}
};
prime_iterable() = default;
prime_iterable(::tools::eratosthenes_sieve<T> const * const parent, const int l, const int r) : m_parent(parent), m_l(l), m_r(r) {
}
iterator begin() const {
return iterator(this->m_parent, this->m_l);
};
iterator end() const {
return iterator(this->m_parent, this->m_r + 1);
}
};
eratosthenes_sieve() = default;
explicit eratosthenes_sieve(const int n) : m_n(n) {
assert(n >= 1);
this->m_is_prime.reserve((n >> 6) + 1);
for (int i = 0; i <= n; i += 960) {
::std::copy(init.begin(), n < i + 959 ? ::std::next(init.begin(), (n >> 6) % 15 + 1) : init.end(), ::std::back_inserter(this->m_is_prime));
}
this->m_is_prime[0] ^= UINT64_C(0b101110);
int i = 7;
while (true) {
if (n < i * i) break;
if (this->is_prime(i)) { // 7
int j = i * i;
while (true) {
this->m_is_prime[j >> 6] &= ~(UINT64_C(1) << (j & 0b111111)); // 7 * 7
j += i * 4;
if (n < j) break;
this->m_is_prime[j >> 6] &= ~(UINT64_C(1) << (j & 0b111111)); // 7 * 11
j += i + i;
if (n < j) break;
this->m_is_prime[j >> 6] &= ~(UINT64_C(1) << (j & 0b111111)); // 7 * 13
j += i * 4;
if (n < j) break;
this->m_is_prime[j >> 6] &= ~(UINT64_C(1) << (j & 0b111111)); // 7 * 17
j += i + i;
if (n < j) break;
this->m_is_prime[j >> 6] &= ~(UINT64_C(1) << (j & 0b111111)); // 7 * 19
j += i * 4;
if (n < j) break;
this->m_is_prime[j >> 6] &= ~(UINT64_C(1) << (j & 0b111111)); // 7 * 23
j += i * 6;
if (n < j) break;
this->m_is_prime[j >> 6] &= ~(UINT64_C(1) << (j & 0b111111)); // 7 * 29
j += i + i;
if (n < j) break;
this->m_is_prime[j >> 6] &= ~(UINT64_C(1) << (j & 0b111111)); // 7 * 1
j += i * 6;
if (n < j) break;
}
}
i += 4;
if (n < i * i) break;
if (this->is_prime(i)) { // 11
int j = i * i;
while (true) {
this->m_is_prime[j >> 6] &= ~(UINT64_C(1) << (j & 0b111111)); // 11 * 11
j += i + i;
if (n < j) break;
this->m_is_prime[j >> 6] &= ~(UINT64_C(1) << (j & 0b111111)); // 11 * 13
j += i * 4;
if (n < j) break;
this->m_is_prime[j >> 6] &= ~(UINT64_C(1) << (j & 0b111111)); // 11 * 17
j += i + i;
if (n < j) break;
this->m_is_prime[j >> 6] &= ~(UINT64_C(1) << (j & 0b111111)); // 11 * 19
j += i * 4;
if (n < j) break;
this->m_is_prime[j >> 6] &= ~(UINT64_C(1) << (j & 0b111111)); // 11 * 23
j += i * 6;
if (n < j) break;
this->m_is_prime[j >> 6] &= ~(UINT64_C(1) << (j & 0b111111)); // 11 * 29
j += i + i;
if (n < j) break;
this->m_is_prime[j >> 6] &= ~(UINT64_C(1) << (j & 0b111111)); // 11 * 1
j += i * 6;
if (n < j) break;
this->m_is_prime[j >> 6] &= ~(UINT64_C(1) << (j & 0b111111)); // 11 * 7
j += i * 4;
if (n < j) break;
}
}
i += 2;
if (n < i * i) break;
if (this->is_prime(i)) { // 13
int j = i * i;
while (true) {
this->m_is_prime[j >> 6] &= ~(UINT64_C(1) << (j & 0b111111)); // 13 * 13
j += i * 4;
if (n < j) break;
this->m_is_prime[j >> 6] &= ~(UINT64_C(1) << (j & 0b111111)); // 13 * 17
j += i + i;
if (n < j) break;
this->m_is_prime[j >> 6] &= ~(UINT64_C(1) << (j & 0b111111)); // 13 * 19
j += i * 4;
if (n < j) break;
this->m_is_prime[j >> 6] &= ~(UINT64_C(1) << (j & 0b111111)); // 13 * 23
j += i * 6;
if (n < j) break;
this->m_is_prime[j >> 6] &= ~(UINT64_C(1) << (j & 0b111111)); // 13 * 29
j += i + i;
if (n < j) break;
this->m_is_prime[j >> 6] &= ~(UINT64_C(1) << (j & 0b111111)); // 13 * 1
j += i * 6;
if (n < j) break;
this->m_is_prime[j >> 6] &= ~(UINT64_C(1) << (j & 0b111111)); // 13 * 7
j += i * 4;
if (n < j) break;
this->m_is_prime[j >> 6] &= ~(UINT64_C(1) << (j & 0b111111)); // 13 * 11
j += i + i;
if (n < j) break;
}
}
i += 4;
if (n < i * i) break;
if (this->is_prime(i)) { // 17
int j = i * i;
while (true) {
this->m_is_prime[j >> 6] &= ~(UINT64_C(1) << (j & 0b111111)); // 17 * 17
j += i + i;
if (n < j) break;
this->m_is_prime[j >> 6] &= ~(UINT64_C(1) << (j & 0b111111)); // 17 * 19
j += i * 4;
if (n < j) break;
this->m_is_prime[j >> 6] &= ~(UINT64_C(1) << (j & 0b111111)); // 17 * 23
j += i * 6;
if (n < j) break;
this->m_is_prime[j >> 6] &= ~(UINT64_C(1) << (j & 0b111111)); // 17 * 29
j += i + i;
if (n < j) break;
this->m_is_prime[j >> 6] &= ~(UINT64_C(1) << (j & 0b111111)); // 17 * 1
j += i * 6;
if (n < j) break;
this->m_is_prime[j >> 6] &= ~(UINT64_C(1) << (j & 0b111111)); // 17 * 7
j += i * 4;
if (n < j) break;
this->m_is_prime[j >> 6] &= ~(UINT64_C(1) << (j & 0b111111)); // 17 * 11
j += i + i;
if (n < j) break;
this->m_is_prime[j >> 6] &= ~(UINT64_C(1) << (j & 0b111111)); // 17 * 13
j += i * 4;
if (n < j) break;
}
}
i += 2;
if (n < i * i) break;
if (this->is_prime(i)) { // 19
int j = i * i;
while (true) {
this->m_is_prime[j >> 6] &= ~(UINT64_C(1) << (j & 0b111111)); // 19 * 19
j += i * 4;
if (n < j) break;
this->m_is_prime[j >> 6] &= ~(UINT64_C(1) << (j & 0b111111)); // 19 * 23
j += i * 6;
if (n < j) break;
this->m_is_prime[j >> 6] &= ~(UINT64_C(1) << (j & 0b111111)); // 19 * 29
j += i + i;
if (n < j) break;
this->m_is_prime[j >> 6] &= ~(UINT64_C(1) << (j & 0b111111)); // 19 * 1
j += i * 6;
if (n < j) break;
this->m_is_prime[j >> 6] &= ~(UINT64_C(1) << (j & 0b111111)); // 19 * 7
j += i * 4;
if (n < j) break;
this->m_is_prime[j >> 6] &= ~(UINT64_C(1) << (j & 0b111111)); // 19 * 11
j += i + i;
if (n < j) break;
this->m_is_prime[j >> 6] &= ~(UINT64_C(1) << (j & 0b111111)); // 19 * 13
j += i * 4;
if (n < j) break;
this->m_is_prime[j >> 6] &= ~(UINT64_C(1) << (j & 0b111111)); // 19 * 17
j += i + i;
if (n < j) break;
}
}
i += 4;
if (n < i * i) break;
if (this->is_prime(i)) { // 23
int j = i * i;
while (true) {
this->m_is_prime[j >> 6] &= ~(UINT64_C(1) << (j & 0b111111)); // 23 * 23
j += i * 6;
if (n < j) break;
this->m_is_prime[j >> 6] &= ~(UINT64_C(1) << (j & 0b111111)); // 23 * 29
j += i + i;
if (n < j) break;
this->m_is_prime[j >> 6] &= ~(UINT64_C(1) << (j & 0b111111)); // 23 * 1
j += i * 6;
if (n < j) break;
this->m_is_prime[j >> 6] &= ~(UINT64_C(1) << (j & 0b111111)); // 23 * 7
j += i * 4;
if (n < j) break;
this->m_is_prime[j >> 6] &= ~(UINT64_C(1) << (j & 0b111111)); // 23 * 11
j += i + i;
if (n < j) break;
this->m_is_prime[j >> 6] &= ~(UINT64_C(1) << (j & 0b111111)); // 23 * 13
j += i * 4;
if (n < j) break;
this->m_is_prime[j >> 6] &= ~(UINT64_C(1) << (j & 0b111111)); // 23 * 17
j += i + i;
if (n < j) break;
this->m_is_prime[j >> 6] &= ~(UINT64_C(1) << (j & 0b111111)); // 23 * 19
j += i * 4;
if (n < j) break;
}
}
i += 6;
if (n < i * i) break;
if (this->is_prime(i)) { // 29
int j = i * i;
while (true) {
this->m_is_prime[j >> 6] &= ~(UINT64_C(1) << (j & 0b111111)); // 29 * 29
j += i + i;
if (n < j) break;
this->m_is_prime[j >> 6] &= ~(UINT64_C(1) << (j & 0b111111)); // 29 * 1
j += i * 6;
if (n < j) break;
this->m_is_prime[j >> 6] &= ~(UINT64_C(1) << (j & 0b111111)); // 29 * 7
j += i * 4;
if (n < j) break;
this->m_is_prime[j >> 6] &= ~(UINT64_C(1) << (j & 0b111111)); // 29 * 11
j += i + i;
if (n < j) break;
this->m_is_prime[j >> 6] &= ~(UINT64_C(1) << (j & 0b111111)); // 29 * 13
j += i * 4;
if (n < j) break;
this->m_is_prime[j >> 6] &= ~(UINT64_C(1) << (j & 0b111111)); // 29 * 17
j += i + i;
if (n < j) break;
this->m_is_prime[j >> 6] &= ~(UINT64_C(1) << (j & 0b111111)); // 29 * 19
j += i * 4;
if (n < j) break;
this->m_is_prime[j >> 6] &= ~(UINT64_C(1) << (j & 0b111111)); // 29 * 23
j += i * 6;
if (n < j) break;
}
}
i += 2;
if (n < i * i) break;
if (this->is_prime(i)) { // 1
int j = i * i;
while (true) {
this->m_is_prime[j >> 6] &= ~(UINT64_C(1) << (j & 0b111111)); // 1 * 1
j += i * 6;
if (n < j) break;
this->m_is_prime[j >> 6] &= ~(UINT64_C(1) << (j & 0b111111)); // 1 * 7
j += i * 4;
if (n < j) break;
this->m_is_prime[j >> 6] &= ~(UINT64_C(1) << (j & 0b111111)); // 1 * 11
j += i + i;
if (n < j) break;
this->m_is_prime[j >> 6] &= ~(UINT64_C(1) << (j & 0b111111)); // 1 * 13
j += i * 4;
if (n < j) break;
this->m_is_prime[j >> 6] &= ~(UINT64_C(1) << (j & 0b111111)); // 1 * 17
j += i + i;
if (n < j) break;
this->m_is_prime[j >> 6] &= ~(UINT64_C(1) << (j & 0b111111)); // 1 * 19
j += i * 4;
if (n < j) break;
this->m_is_prime[j >> 6] &= ~(UINT64_C(1) << (j & 0b111111)); // 1 * 23
j += i * 6;
if (n < j) break;
this->m_is_prime[j >> 6] &= ~(UINT64_C(1) << (j & 0b111111)); // 1 * 29
j += i + i;
if (n < j) break;
}
}
i += 6;
}
}
inline bool is_prime(const int i) const {
assert(1 <= i && i <= this->m_n);
return (this->m_is_prime[i >> 6] >> (i & 0b111111)) & 1;
}
prime_iterable prime_range(const int l, const int r) const {
assert(1 <= l && l <= r && r <= this->m_n);
return prime_iterable(this, l, r);
}
};
}
#line 8 "tools/divisor_zeta.hpp"
namespace tools {
template <typename RandomAccessIterator>
void divisor_zeta(const RandomAccessIterator begin, const RandomAccessIterator end) {
const int N = end - begin;
if (N < 2) return;
::tools::eratosthenes_sieve<int> sieve(N - 1);
for (const auto p : sieve.prime_range(1, N - 1)) {
for (int i = 1; i * p < N; ++i) {
begin[i * p] += begin[i];
}
}
}
template <typename InputIterator, typename OutputIterator>
void divisor_zeta(const InputIterator begin, const InputIterator end, const OutputIterator result) {
using T = typename ::std::iterator_traits<InputIterator>::value_type;
::std::vector<T> a(begin, end);
::tools::divisor_zeta(a.begin(), a.end());
::std::move(a.begin(), a.end(), result);
}
}
#line 10 "tests/divisor_zeta.test.cpp"
using mint = atcoder::modint998244353;
int main() {
std::cin.tie(nullptr);
std::ios_base::sync_with_stdio(false);
std::random_device seed_gen;
std::mt19937 engine(seed_gen());
std::uniform_int_distribution<int> dist(0, 998244352);
for (int N = 0; N <= 20; ++N) {
std::vector<mint> a(N);
for (auto&& a_i : a) a_i = mint::raw(dist(engine));
std::vector<mint> b(N, mint::raw(0));
if (N > 0) b[0] = a[0];
for (int i = 1; i < N; ++i) {
for (int j = 1; j < N; ++j) {
if (i % j == 0) b[i] += a[j];
}
}
std::vector<mint> actual_b;
tools::divisor_zeta(a.begin(), a.end(), std::back_inserter(actual_b));
assert_that(actual_b == b);
tools::divisor_zeta(a.begin(), a.end());
assert_that(a == b);
}
return 0;
}