proconlib
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tests/segmented_sieve.test.cpp
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- Last update: 2025-02-10 01:30:13+09:00
- Problem: https://atcoder.jp/contests/abc227/tasks/abc227_g
Depends on
$\left\lceil \frac{x}{y} \right\rceil$ (tools/ceil.hpp)- chmin function (tools/chmin.hpp)
- $\left\lfloor \sqrt{x} \right\rfloor$ (tools/floor_sqrt.hpp)
- std::is_integral extended for tools::int128_t and tools::uint128_t (tools/is_integral.hpp)
- std::is_unsigned extended for tools::int128_t and tools::uint128_t (tools/is_unsigned.hpp)
- Segmented sieve (tools/segmented_sieve.hpp)
Code
// competitive-verifier: PROBLEM https://atcoder.jp/contests/abc227/tasks/abc227_g
// competitive-verifier: IGNORE
#include <iostream>
#include <unordered_map>
#include "atcoder/modint.hpp"
#include "tools/segmented_sieve.hpp"
using ll = long long;
using mint = atcoder::modint998244353;
int main() {
std::cin.tie(nullptr);
std::ios_base::sync_with_stdio(false);
ll N, K;
std::cin >> N >> K;
std::unordered_map<ll, ll> nCk;
if (K > 0) {
tools::segmented_sieve<ll> sieve(K, N - K + 1, N);
for (ll i = N - K + 1; i <= N; ++i) {
for (const ll& p : sieve.prime_factor_range(i)) {
++nCk[p];
}
}
for (ll i = 1; i <= K; ++i) {
for (const ll& p : sieve.prime_factor_range(i)) {
--nCk[p];
}
}
}
mint answer(1);
for (const auto& [p, q] : nCk) {
answer *= mint(q + 1);
}
std::cout << answer.val() << '\n';
return 0;
}
#line 1 "tests/segmented_sieve.test.cpp"
// competitive-verifier: PROBLEM https://atcoder.jp/contests/abc227/tasks/abc227_g
// competitive-verifier: IGNORE
#include <iostream>
#include <unordered_map>
#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/segmented_sieve.hpp"
#include <vector>
#line 6 "tools/segmented_sieve.hpp"
#include <algorithm>
#include <limits>
#line 9 "tools/segmented_sieve.hpp"
#include <cstddef>
#include <iterator>
#line 1 "tools/floor_sqrt.hpp"
#line 5 "tools/floor_sqrt.hpp"
namespace tools {
template <typename T>
T floor_sqrt(const T n) {
assert(n >= 0);
T ok = 0;
T ng;
for (ng = 1; ng <= n / ng; ng *= 2);
while (ng - ok > 1) {
const T mid = ok + (ng - ok) / 2;
if (mid <= n / mid) {
ok = mid;
} else {
ng = mid;
}
}
return ok;
}
}
#line 1 "tools/chmin.hpp"
#line 6 "tools/chmin.hpp"
namespace tools {
template <typename M, typename N>
bool chmin(M& lhs, const N& rhs) {
bool updated;
if constexpr (::std::is_integral_v<M> && ::std::is_integral_v<N>) {
updated = ::std::cmp_less(rhs, lhs);
} else {
updated = rhs < lhs;
}
if (updated) lhs = rhs;
return updated;
}
}
#line 1 "tools/ceil.hpp"
#line 1 "tools/is_integral.hpp"
#line 5 "tools/is_integral.hpp"
namespace tools {
template <typename T>
struct is_integral : ::std::is_integral<T> {};
template <typename T>
inline constexpr bool is_integral_v = ::tools::is_integral<T>::value;
}
#line 1 "tools/is_unsigned.hpp"
#line 5 "tools/is_unsigned.hpp"
namespace tools {
template <typename T>
struct is_unsigned : ::std::is_unsigned<T> {};
template <typename T>
inline constexpr bool is_unsigned_v = ::tools::is_unsigned<T>::value;
}
#line 8 "tools/ceil.hpp"
namespace tools {
template <typename M, typename N> requires (
::tools::is_integral_v<M> && !::std::is_same_v<::std::remove_cv_t<M>, bool> &&
::tools::is_integral_v<N> && !::std::is_same_v<::std::remove_cv_t<N>, bool>)
constexpr ::std::common_type_t<M, N> ceil(const M x, const N y) noexcept {
assert(y != 0);
if (y >= 0) {
if (x > 0) {
return (x - 1) / y + 1;
} else {
if constexpr (::tools::is_unsigned_v<::std::common_type_t<M, N>>) {
return 0;
} else {
return x / y;
}
}
} else {
if (x >= 0) {
if constexpr (::tools::is_unsigned_v<::std::common_type_t<M, N>>) {
return 0;
} else {
return x / y;
}
} else {
return (x + 1) / y + 1;
}
}
}
}
#line 15 "tools/segmented_sieve.hpp"
namespace tools {
template <typename T>
class segmented_sieve {
private:
::std::vector<T> m_lpf;
::std::vector<::std::vector<T>> m_pf;
::std::vector<T> m_aux;
T m_l;
public:
segmented_sieve() = default;
segmented_sieve(const ::tools::segmented_sieve<T>&) = default;
segmented_sieve(::tools::segmented_sieve<T>&&) = default;
~segmented_sieve() = default;
::tools::segmented_sieve<T>& operator=(const ::tools::segmented_sieve<T>&) = default;
::tools::segmented_sieve<T>& operator=(::tools::segmented_sieve<T>&&) = default;
segmented_sieve(const T& k, const T& l, const T& r) {
assert(l <= r);
const T lpf_max = ::std::max(::tools::floor_sqrt(r), k);
this->m_lpf.resize(lpf_max + 1);
::std::fill(this->m_lpf.begin(), this->m_lpf.end(), ::std::numeric_limits<T>::max());
this->m_pf.resize(r - l + 1);
this->m_aux.resize(r - l + 1);
::std::iota(this->m_aux.begin(), this->m_aux.end(), l);
this->m_l = l;
for (T p = 2; p <= lpf_max; ++p) {
if (::tools::chmin(this->m_lpf[p], p)) {
for (T np = p * p; np <= lpf_max; np += p) {
::tools::chmin(this->m_lpf[np], p);
}
for (T p_q = p, np_q; (np_q = ::tools::ceil(l, p_q) * p_q) <= r; p_q *= p) {
for (; np_q <= r; np_q += p_q) {
if (lpf_max < this->m_aux[np_q - l]) {
this->m_pf[np_q - l].push_back(p);
this->m_aux[np_q - l] /= p;
}
}
}
}
}
for (T i = l; i <= r; ++i) {
if (lpf_max < this->m_aux[i - l]) {
this->m_pf[i - l].push_back(this->m_aux[i - l]);
this->m_aux[i - l] = 1;
}
}
}
segmented_sieve(const T& l, const T& r) :
segmented_sieve(0, l, r) {
}
T lpf_max() const {
return this->m_lpf.size() - 1;
}
T l() const {
return this->m_l;
}
T r() const {
return this->m_l + this->m_pf.size() - 1;
}
class prime_factor_iterable {
private:
const ::tools::segmented_sieve<T> *m_parent;
T m_n;
public:
class iterator {
private:
const prime_factor_iterable *m_parent;
bool m_large;
T m_i;
T n() const {
return this->m_parent->m_n;
}
public:
using difference_type = ::std::ptrdiff_t;
using value_type = T;
using reference = T&;
using pointer = T*;
using iterator_category = ::std::input_iterator_tag;
iterator() = default;
iterator(const iterator&) = default;
iterator(iterator&&) = default;
~iterator() = default;
iterator& operator=(const iterator&) = default;
iterator& operator=(iterator&&) = default;
iterator(prime_factor_iterable const * const parent, const bool large, const T& i) :
m_parent(parent), m_large(large), m_i(i) {
}
T operator*() const {
if (this->m_large) {
return this->m_parent->m_parent->m_pf[this->n() - this->m_parent->m_parent->l()][this->m_i];
} else {
return this->m_parent->m_parent->m_lpf[this->m_i];
}
}
iterator& operator++() {
if (this->m_large) {
++this->m_i;
if (this->m_i == T(this->m_parent->m_parent->m_pf[this->n() - this->m_parent->m_parent->l()].size())) {
this->m_large = false;
this->m_i = this->m_parent->m_parent->m_aux[this->n() - this->m_parent->m_parent->l()];
}
} else {
this->m_i /= this->m_parent->m_parent->m_lpf[this->m_i];
}
return *this;
}
iterator operator++(int) {
const iterator self = *this;
++*this;
return self;
}
friend bool operator==(const iterator& lhs, const iterator& rhs) {
return lhs.m_large == rhs.m_large && (!lhs.m_large || lhs.n() == rhs.n()) && lhs.m_i == rhs.m_i;
}
friend bool operator!=(const iterator& lhs, const iterator& rhs) {
return !(lhs == rhs);
}
};
prime_factor_iterable(::tools::segmented_sieve<T> const * const parent, const T& n) :
m_parent(parent), m_n(n) {
}
iterator begin() const {
if (this->m_n <= this->m_parent->lpf_max()) {
return iterator(this, false, this->m_n);
} else {
return iterator(this, true, 0);
}
}
iterator end() const {
return iterator(this, false, 1);
}
};
class distinct_prime_factor_iterable {
private:
const ::tools::segmented_sieve<T> *m_parent;
T m_n;
public:
class iterator {
private:
const distinct_prime_factor_iterable *m_parent;
bool m_large;
T m_i;
::std::pair<T, T> m_value;
T n() const {
return this->m_parent->m_n;
}
void next() {
const ::std::vector<T>& lpf = this->m_parent->m_parent->m_lpf;
if (this->m_large) {
const ::std::vector<T>& pf = this->m_parent->m_parent->m_pf[this->m_parent->m_n - this->m_parent->m_parent->l()];
this->m_value.first = pf[this->m_i];
this->m_value.second = 0;
for (; this->m_i < T(pf.size()) && pf[this->m_i] == this->m_value.first; ++this->m_i) {
++this->m_value.second;
}
if (this->m_i == T(pf.size())) {
this->m_large = false;
this->m_i = this->m_parent->m_parent->m_aux[this->m_parent->m_n - this->m_parent->m_parent->l()];
for (; lpf[this->m_i] == this->m_value.first; this->m_i /= lpf[this->m_i]) {
++this->m_value.second;
}
}
} else {
if (this->m_i == 1) {
this->m_value.first = ::std::numeric_limits<T>::max();
this->m_value.second = 0;
} else {
this->m_value.first = lpf[this->m_i];
this->m_value.second = 0;
for (; lpf[this->m_i] == this->m_value.first; this->m_i /= lpf[this->m_i]) {
++this->m_value.second;
}
}
}
}
public:
using difference_type = ::std::ptrdiff_t;
using value_type = ::std::pair<T, T>;
using reference = ::std::pair<T, T>&;
using pointer = ::std::pair<T, T>*;
using iterator_category = ::std::input_iterator_tag;
iterator() = default;
iterator(const iterator&) = default;
iterator(iterator&&) = default;
~iterator() = default;
iterator& operator=(const iterator&) = default;
iterator& operator=(iterator&&) = default;
iterator(distinct_prime_factor_iterable const * const parent, const bool large, const T& i) :
m_parent(parent), m_large(large), m_i(i) {
this->next();
}
::std::pair<T, T> operator*() const {
return this->m_value;
}
iterator& operator++() {
this->next();
return *this;
}
iterator operator++(int) {
const iterator self = *this;
++*this;
return self;
}
friend bool operator==(const iterator& lhs, const iterator& rhs) {
return lhs.n() == rhs.n() && lhs.m_value.first == rhs.m_value.first;
}
friend bool operator!=(const iterator& lhs, const iterator& rhs) {
return !(lhs == rhs);
}
};
distinct_prime_factor_iterable(::tools::segmented_sieve<T> const * const parent, const T& n) :
m_parent(parent), m_n(n) {
}
iterator begin() const {
if (this->m_n <= this->m_parent->lpf_max()) {
return iterator(this, false, this->m_n);
} else {
return iterator(this, true, 0);
}
}
iterator end() const {
return iterator(this, false, 1);
}
};
class prime_iterable {
private:
const ::tools::segmented_sieve<T> *m_parent;
T m_lb;
T m_ub;
public:
class iterator {
private:
const prime_iterable *m_parent;
T m_i;
void next() {
++this->m_i;
for (; this->m_i <= this->m_parent->m_ub && (
(this->m_i <= this->m_parent->m_parent->lpf_max() && this->m_parent->m_parent->m_lpf[this->m_i] != this->m_i)
|| (this->m_parent->m_parent->lpf_max() < this->m_i && this->m_parent->m_parent->m_pf[this->m_i - this->m_parent->m_parent->l()][0] != this->m_i)
); ++this->m_i);
}
public:
using difference_type = ::std::ptrdiff_t;
using value_type = T;
using reference = T&;
using pointer = T*;
using iterator_category = ::std::input_iterator_tag;
iterator() = default;
iterator(const iterator&) = default;
iterator(iterator&&) = default;
~iterator() = default;
iterator& operator=(const iterator&) = default;
iterator& operator=(iterator&&) = default;
iterator(prime_iterable const * const parent, const T& i) :
m_parent(parent), m_i(i) {
this->next();
}
T operator*() const {
return this->m_i;
}
iterator& operator++() {
this->next();
return *this;
}
iterator operator++(int) {
const iterator self = *this;
++*this;
return self;
}
friend bool operator==(const iterator& lhs, const iterator& rhs) {
return lhs.m_i == rhs.m_i;
}
friend bool operator!=(const iterator& lhs, const iterator& rhs) {
return !(lhs == rhs);
}
};
prime_iterable(::tools::segmented_sieve<T> const * const parent, const T& lb, const T& ub) :
m_parent(parent), m_lb(lb), m_ub(ub) {
}
iterator begin() const {
return iterator(this, this->m_lb - 1);
}
iterator end() const {
return iterator(this, this->m_ub);
}
};
prime_factor_iterable prime_factor_range(const T& n) const {
assert((1 <= n && n <= this->lpf_max()) || (this->l() <= n && n <= this->r()));
return prime_factor_iterable(this, n);
}
distinct_prime_factor_iterable distinct_prime_factor_range(const T& n) const {
assert((1 <= n && n <= this->lpf_max()) || (this->l() <= n && n <= this->r()));
return distinct_prime_factor_iterable(this, n);
}
prime_iterable prime_range(const T& lb, const T& ub) const {
assert(lb <= ub);
const bool is_in_small_sieve = 1 <= lb && ub <= this->lpf_max();
const bool is_in_large_sieve = this->l() <= lb && ub <= this->r();
assert(is_in_small_sieve || is_in_large_sieve);
return prime_iterable(this, lb, ub);
}
};
}
#line 8 "tests/segmented_sieve.test.cpp"
using ll = long long;
using mint = atcoder::modint998244353;
int main() {
std::cin.tie(nullptr);
std::ios_base::sync_with_stdio(false);
ll N, K;
std::cin >> N >> K;
std::unordered_map<ll, ll> nCk;
if (K > 0) {
tools::segmented_sieve<ll> sieve(K, N - K + 1, N);
for (ll i = N - K + 1; i <= N; ++i) {
for (const ll& p : sieve.prime_factor_range(i)) {
++nCk[p];
}
}
for (ll i = 1; i <= K; ++i) {
for (const ll& p : sieve.prime_factor_range(i)) {
--nCk[p];
}
}
}
mint answer(1);
for (const auto& [p, q] : nCk) {
answer *= mint(q + 1);
}
std::cout << answer.val() << '\n';
return 0;
}