cp-library-cpp
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test/src/math/factorial_large/dummy.test.cpp
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- Last update: 2026-06-28 22:26:07+09:00
- Problem: https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=ITP1_1_A
Depends on
- 任意 $\mathrm{mod}$ 畳み込み
(library/convolution/arbitrary_mod_convolution.hpp)
- Naive Convolution
(library/convolution/convolution_naive.hpp)
- 階乗テーブル
(library/math/factorial.hpp)
- Factorial Large
(library/math/factorial_large.hpp)
- 逆元テーブル
(library/math/inv_mods.hpp)
- Modint Extension
(library/math/modint_extension.hpp)
- 形式的冪級数
(library/polynomial/fps.hpp)
- FFT-free な形式的べき級数
(library/polynomial/fps_naive.hpp)
- Shift of Sampling Points of Polynomial
(library/polynomial/shift_of_sampling_points.hpp)
- Type Traits
(library/type_traits/type_traits.hpp)
Code
#define PROBLEM "https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=ITP1_1_A"
#include <iostream>
#include <random>
#include <atcoder/modint>
#include "library/polynomial/fps.hpp"
#include "library/math/factorial_large.hpp"
template <int MOD>
void test() {
using mint = atcoder::static_modint<MOD>;
std::mt19937 rng{};
constexpr int MAX_N = 10000000;
std::uniform_int_distribution<int> dist(0, MAX_N);
const int q = 10000;
std::vector<int> ns(q);
for (int& e : ns) e = dist(rng);
// power of 2
for (int i = 0; 1 << i < MAX_N; ++i) ns[i] = 1 << i;
std::vector<mint> res1, res2;
{
suisen::factorial_large<mint> fac{};
fac.threshold = -1;
res1.resize(q);
for (int i = 0; i < q; ++i) res1[i] = fac.fac(ns[i]);
}
{
suisen::factorial<mint> fac{};
res2.resize(q);
for (int i = 0; i < q; ++i) res2[i] = fac.fac(ns[i]);
}
assert(res1 == res2);
}
int main() {
test<998244353>();
test<1000000007>();
test<1000000009>();
std::cout << "Hello World" << std::endl;
return 0;
}#line 1 "test/src/math/factorial_large/dummy.test.cpp"
#define PROBLEM "https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=ITP1_1_A"
#include <iostream>
#include <random>
#include <atcoder/modint>
#line 1 "library/polynomial/fps.hpp"
#include <algorithm>
#include <cassert>
#line 7 "library/polynomial/fps.hpp"
#include <queue>
#line 1 "library/polynomial/fps_naive.hpp"
#line 5 "library/polynomial/fps_naive.hpp"
#include <cmath>
#include <limits>
#include <type_traits>
#include <vector>
#line 1 "library/type_traits/type_traits.hpp"
#line 7 "library/type_traits/type_traits.hpp"
namespace suisen {
template <typename ...Constraints> using constraints_t = std::enable_if_t<std::conjunction_v<Constraints...>, std::nullptr_t>;
template <typename T, typename = std::nullptr_t> struct bitnum { static constexpr int value = 0; };
template <typename T> struct bitnum<T, constraints_t<std::is_integral<T>>> { static constexpr int value = std::numeric_limits<std::make_unsigned_t<T>>::digits; };
template <typename T> static constexpr int bitnum_v = bitnum<T>::value;
template <typename T, size_t n> struct is_nbit { static constexpr bool value = bitnum_v<T> == n; };
template <typename T, size_t n> static constexpr bool is_nbit_v = is_nbit<T, n>::value;
template <typename T, typename = std::nullptr_t> struct safely_multipliable { using type = T; };
template <typename T> struct safely_multipliable<T, constraints_t<std::is_signed<T>, is_nbit<T, 32>>> { using type = long long; };
template <typename T> struct safely_multipliable<T, constraints_t<std::is_signed<T>, is_nbit<T, 64>>> { using type = __int128_t; };
template <typename T> struct safely_multipliable<T, constraints_t<std::is_unsigned<T>, is_nbit<T, 32>>> { using type = unsigned long long; };
template <typename T> struct safely_multipliable<T, constraints_t<std::is_unsigned<T>, is_nbit<T, 64>>> { using type = __uint128_t; };
template <typename T> using safely_multipliable_t = typename safely_multipliable<T>::type;
template <typename T, typename = void> struct rec_value_type { using type = T; };
template <typename T> struct rec_value_type<T, std::void_t<typename T::value_type>> {
using type = typename rec_value_type<typename T::value_type>::type;
};
template <typename T> using rec_value_type_t = typename rec_value_type<T>::type;
template <typename T> class is_iterable {
template <typename T_> static auto test(T_ e) -> decltype(e.begin(), e.end(), std::true_type{});
static std::false_type test(...);
public:
static constexpr bool value = decltype(test(std::declval<T>()))::value;
};
template <typename T> static constexpr bool is_iterable_v = is_iterable<T>::value;
template <typename T> class is_writable {
template <typename T_> static auto test(T_ e) -> decltype(std::declval<std::ostream&>() << e, std::true_type{});
static std::false_type test(...);
public:
static constexpr bool value = decltype(test(std::declval<T>()))::value;
};
template <typename T> static constexpr bool is_writable_v = is_writable<T>::value;
template <typename T> class is_readable {
template <typename T_> static auto test(T_ e) -> decltype(std::declval<std::istream&>() >> e, std::true_type{});
static std::false_type test(...);
public:
static constexpr bool value = decltype(test(std::declval<T>()))::value;
};
template <typename T> static constexpr bool is_readable_v = is_readable<T>::value;
} // namespace suisen
#line 11 "library/polynomial/fps_naive.hpp"
#line 1 "library/math/modint_extension.hpp"
#line 5 "library/math/modint_extension.hpp"
#include <optional>
/**
* reference: https://37zigen.com/tonelli-shanks-algorithm/
* calculates x s.t. x^2 = a mod p in O((log p)^2).
*/
template <typename mint>
std::optional<mint> safe_sqrt(mint a) {
static int p = mint::mod();
if (a == 0) return std::make_optional(0);
if (p == 2) return std::make_optional(a);
if (a.pow((p - 1) / 2) != 1) return std::nullopt;
mint b = 1;
while (b.pow((p - 1) / 2) == 1) ++b;
static int tlz = __builtin_ctz(p - 1), q = (p - 1) >> tlz;
mint x = a.pow((q + 1) / 2);
b = b.pow(q);
for (int shift = 2; x * x != a; ++shift) {
mint e = a.inv() * x * x;
if (e.pow(1 << (tlz - shift)) != 1) x *= b;
b *= b;
}
return std::make_optional(x);
}
/**
* calculates x s.t. x^2 = a mod p in O((log p)^2).
* if not exists, raises runtime error.
*/
template <typename mint>
auto sqrt(mint a) -> decltype(mint::mod(), mint()) {
return *safe_sqrt(a);
}
template <typename mint>
auto log(mint a) -> decltype(mint::mod(), mint()) {
assert(a == 1);
return 0;
}
template <typename mint>
auto exp(mint a) -> decltype(mint::mod(), mint()) {
assert(a == 0);
return 1;
}
template <typename mint, typename T>
auto pow(mint a, T b) -> decltype(mint::mod(), mint()) {
return a.pow(b);
}
template <typename mint>
auto inv(mint a) -> decltype(mint::mod(), mint()) {
return a.inv();
}
#line 1 "library/math/inv_mods.hpp"
#line 5 "library/math/inv_mods.hpp"
namespace suisen {
template <typename mint>
class inv_mods {
public:
inv_mods() = default;
inv_mods(int n) { ensure(n); }
const mint& operator[](int i) const {
ensure(i);
return invs[i];
}
static void ensure(int n) {
int sz = invs.size();
if (sz < 2) invs = { 0, 1 }, sz = 2;
if (sz < n + 1) {
invs.resize(n + 1);
for (int i = sz; i <= n; ++i) invs[i] = mint(mod - mod / i) * invs[mod % i];
}
}
private:
static std::vector<mint> invs;
static constexpr int mod = mint::mod();
};
template <typename mint>
std::vector<mint> inv_mods<mint>::invs{};
template <typename mint>
std::vector<mint> get_invs(const std::vector<mint>& vs) {
const int n = vs.size();
mint p = 1;
for (auto& e : vs) {
p *= e;
assert(e != 0);
}
mint ip = p.inv();
std::vector<mint> rp(n + 1);
rp[n] = 1;
for (int i = n - 1; i >= 0; --i) {
rp[i] = rp[i + 1] * vs[i];
}
std::vector<mint> res(n);
for (int i = 0; i < n; ++i) {
res[i] = ip * rp[i + 1];
ip *= vs[i];
}
return res;
}
}
#line 14 "library/polynomial/fps_naive.hpp"
namespace suisen {
template <typename T>
struct FPSNaive : std::vector<T> {
static inline int MAX_SIZE = std::numeric_limits<int>::max() / 2;
using value_type = T;
using element_type = rec_value_type_t<T>;
using std::vector<value_type>::vector;
FPSNaive(const std::initializer_list<value_type> l) : std::vector<value_type>::vector(l) {}
FPSNaive(const std::vector<value_type>& v) : std::vector<value_type>::vector(v) {}
static void set_max_size(int n) {
FPSNaive<T>::MAX_SIZE = n;
}
const value_type operator[](int n) const {
return n <= deg() ? unsafe_get(n) : value_type{ 0 };
}
value_type& operator[](int n) {
return ensure_deg(n), unsafe_get(n);
}
int size() const {
return std::vector<value_type>::size();
}
int deg() const {
return size() - 1;
}
int normalize() {
while (size() and this->back() == value_type{ 0 }) this->pop_back();
return deg();
}
FPSNaive& cut_inplace(int n) {
if (size() > n) this->resize(std::max(0, n));
return *this;
}
FPSNaive cut(int n) const {
FPSNaive f = FPSNaive(*this).cut_inplace(n);
return f;
}
FPSNaive operator+() const {
return FPSNaive(*this);
}
FPSNaive operator-() const {
FPSNaive f(*this);
for (auto& e : f) e = -e;
return f;
}
FPSNaive& operator++() { return ++(*this)[0], * this; }
FPSNaive& operator--() { return --(*this)[0], * this; }
FPSNaive& operator+=(const value_type x) { return (*this)[0] += x, *this; }
FPSNaive& operator-=(const value_type x) { return (*this)[0] -= x, *this; }
FPSNaive& operator+=(const FPSNaive& g) {
ensure_deg(g.deg());
for (int i = 0; i <= g.deg(); ++i) unsafe_get(i) += g.unsafe_get(i);
return *this;
}
FPSNaive& operator-=(const FPSNaive& g) {
ensure_deg(g.deg());
for (int i = 0; i <= g.deg(); ++i) unsafe_get(i) -= g.unsafe_get(i);
return *this;
}
FPSNaive& operator*=(const FPSNaive& g) { return *this = *this * g; }
FPSNaive& operator*=(const value_type x) {
for (auto& e : *this) e *= x;
return *this;
}
FPSNaive& operator/=(const FPSNaive& g) { return *this = *this / g; }
FPSNaive& operator%=(const FPSNaive& g) { return *this = *this % g; }
FPSNaive& operator<<=(const int shamt) {
this->insert(this->begin(), shamt, value_type{ 0 });
return *this;
}
FPSNaive& operator>>=(const int shamt) {
if (shamt > size()) this->clear();
else this->erase(this->begin(), this->begin() + shamt);
return *this;
}
friend FPSNaive operator+(FPSNaive f, const FPSNaive& g) { f += g; return f; }
friend FPSNaive operator+(FPSNaive f, const value_type& x) { f += x; return f; }
friend FPSNaive operator-(FPSNaive f, const FPSNaive& g) { f -= g; return f; }
friend FPSNaive operator-(FPSNaive f, const value_type& x) { f -= x; return f; }
friend FPSNaive operator*(const FPSNaive& f, const FPSNaive& g) {
if (f.empty() or g.empty()) return FPSNaive{};
const int n = f.size(), m = g.size();
FPSNaive h(std::min(MAX_SIZE, n + m - 1));
for (int i = 0; i < n; ++i) for (int j = 0; j < m; ++j) {
if (i + j >= MAX_SIZE) break;
h.unsafe_get(i + j) += f.unsafe_get(i) * g.unsafe_get(j);
}
return h;
}
friend FPSNaive operator*(FPSNaive f, const value_type& x) { f *= x; return f; }
friend FPSNaive operator/(FPSNaive f, const FPSNaive& g) { return std::move(f.div_mod(g).first); }
friend FPSNaive operator%(FPSNaive f, const FPSNaive& g) { return std::move(f.div_mod(g).second); }
friend FPSNaive operator*(const value_type x, FPSNaive f) { f *= x; return f; }
friend FPSNaive operator<<(FPSNaive f, const int shamt) { f <<= shamt; return f; }
friend FPSNaive operator>>(FPSNaive f, const int shamt) { f >>= shamt; return f; }
std::pair<FPSNaive, FPSNaive> div_mod(FPSNaive g) const {
FPSNaive f = *this;
const int fd = f.normalize(), gd = g.normalize();
assert(gd >= 0);
if (fd < gd) return { FPSNaive{}, f };
if (gd == 0) return { f *= g.unsafe_get(0).inv(), FPSNaive{} };
const int k = f.deg() - gd;
value_type head_inv = g.unsafe_get(gd).inv();
FPSNaive q(k + 1);
for (int i = k; i >= 0; --i) {
value_type div = f.unsafe_get(i + gd) * head_inv;
q.unsafe_get(i) = div;
for (int j = 0; j <= gd; ++j) f.unsafe_get(i + j) -= div * g.unsafe_get(j);
}
f.cut_inplace(gd);
f.normalize();
return { q, f };
}
friend bool operator==(const FPSNaive& f, const FPSNaive& g) {
const int n = f.size(), m = g.size();
if (n < m) return g == f;
for (int i = 0; i < m; ++i) if (f.unsafe_get(i) != g.unsafe_get(i)) return false;
for (int i = m; i < n; ++i) if (f.unsafe_get(i) != 0) return false;
return true;
}
friend bool operator!=(const FPSNaive& f, const FPSNaive& g) {
return not (f == g);
}
FPSNaive mul(const FPSNaive& g, int n = -1) const {
if (n < 0) n = size();
if (this->empty() or g.empty()) return FPSNaive{};
const int m = size(), k = g.size();
FPSNaive h(std::min(n, m + k - 1));
for (int i = 0; i < m; ++i) {
for (int j = 0, jr = std::min(k, n - i); j < jr; ++j) {
h.unsafe_get(i + j) += unsafe_get(i) * g.unsafe_get(j);
}
}
return h;
}
FPSNaive diff() const {
if (this->empty()) return {};
FPSNaive g(size() - 1);
for (int i = 1; i <= deg(); ++i) g.unsafe_get(i - 1) = unsafe_get(i) * i;
return g;
}
FPSNaive intg() const {
const int n = size();
FPSNaive g(n + 1);
for (int i = 0; i < n; ++i) g.unsafe_get(i + 1) = unsafe_get(i) * invs[i + 1];
if (g.deg() > MAX_SIZE) g.cut_inplace(MAX_SIZE);
return g;
}
FPSNaive inv(int n = -1) const {
if (n < 0) n = size();
FPSNaive g(n);
const value_type inv_f0 = ::inv(unsafe_get(0));
g.unsafe_get(0) = inv_f0;
for (int i = 1; i < n; ++i) {
for (int j = 1; j <= i; ++j) g.unsafe_get(i) -= g.unsafe_get(i - j) * (*this)[j];
g.unsafe_get(i) *= inv_f0;
}
return g;
}
FPSNaive exp(int n = -1) const {
if (n < 0) n = size();
assert(unsafe_get(0) == value_type{ 0 });
FPSNaive g(n);
g.unsafe_get(0) = value_type{ 1 };
for (int i = 1; i < n; ++i) {
for (int j = 1; j <= i; ++j) g.unsafe_get(i) += j * g.unsafe_get(i - j) * (*this)[j];
g.unsafe_get(i) *= invs[i];
}
return g;
}
FPSNaive log(int n = -1) const {
if (n < 0) n = size();
assert(unsafe_get(0) == value_type{ 1 });
FPSNaive g(n);
g.unsafe_get(0) = value_type{ 0 };
for (int i = 1; i < n; ++i) {
g.unsafe_get(i) = i * (*this)[i];
for (int j = 1; j < i; ++j) g.unsafe_get(i) -= (i - j) * g.unsafe_get(i - j) * (*this)[j];
g.unsafe_get(i) *= invs[i];
}
return g;
}
FPSNaive pow(const long long k, int n = -1) const {
if (n < 0) n = size();
if (k == 0) {
FPSNaive res(n);
res[0] = 1;
return res;
}
int z = 0;
while (z < size() and unsafe_get(z) == value_type{ 0 }) ++z;
if (z == size() or z > (n - 1) / k) return FPSNaive(n, 0);
const int m = n - z * k;
FPSNaive g(m);
const value_type inv_f0 = ::inv(unsafe_get(z));
g.unsafe_get(0) = unsafe_get(z).pow(k);
for (int i = 1; i < m; ++i) {
for (int j = 1; j <= i; ++j) g.unsafe_get(i) += (element_type{ k } *j - (i - j)) * g.unsafe_get(i - j) * (*this)[z + j];
g.unsafe_get(i) *= inv_f0 * invs[i];
}
g <<= z * k;
return g;
}
std::optional<FPSNaive> safe_sqrt(int n = -1) const {
if (n < 0) n = size();
int dl = 0;
while (dl < size() and unsafe_get(dl) == value_type{ 0 }) ++dl;
if (dl == size()) return FPSNaive(n, 0);
if (dl & 1) return std::nullopt;
const int m = n - dl / 2;
FPSNaive g(m);
auto opt_g0 = ::safe_sqrt((*this)[dl]);
if (not opt_g0.has_value()) return std::nullopt;
g.unsafe_get(0) = *opt_g0;
value_type inv_2g0 = ::inv(2 * g.unsafe_get(0));
for (int i = 1; i < m; ++i) {
g.unsafe_get(i) = (*this)[dl + i];
for (int j = 1; j < i; ++j) g.unsafe_get(i) -= g.unsafe_get(j) * g.unsafe_get(i - j);
g.unsafe_get(i) *= inv_2g0;
}
g <<= dl / 2;
return g;
}
FPSNaive sqrt(int n = -1) const {
if (n < 0) n = size();
return *safe_sqrt(n);
}
value_type eval(value_type x) const {
value_type y = 0;
for (int i = size() - 1; i >= 0; --i) y = y * x + unsafe_get(i);
return y;
}
private:
static inline inv_mods<element_type> invs;
void ensure_deg(int d) {
if (deg() < d) this->resize(d + 1, value_type{ 0 });
}
const value_type& unsafe_get(int i) const {
return std::vector<value_type>::operator[](i);
}
value_type& unsafe_get(int i) {
return std::vector<value_type>::operator[](i);
}
};
} // namespace suisen
template <typename mint>
suisen::FPSNaive<mint> sqrt(suisen::FPSNaive<mint> a) {
return a.sqrt();
}
template <typename mint>
suisen::FPSNaive<mint> log(suisen::FPSNaive<mint> a) {
return a.log();
}
template <typename mint>
suisen::FPSNaive<mint> exp(suisen::FPSNaive<mint> a) {
return a.exp();
}
template <typename mint, typename T>
suisen::FPSNaive<mint> pow(suisen::FPSNaive<mint> a, T b) {
return a.pow(b);
}
template <typename mint>
suisen::FPSNaive<mint> inv(suisen::FPSNaive<mint> a) {
return a.inv();
}
#line 12 "library/polynomial/fps.hpp"
namespace suisen {
template <typename mint>
using convolution_t = std::vector<mint>(*)(const std::vector<mint>&, const std::vector<mint>&);
template <typename mint>
struct FPS : public std::vector<mint> {
using base_type = std::vector<mint>;
using value_type = typename base_type::value_type;
using base_type::vector;
FPS(const std::initializer_list<mint> l) : std::vector<mint>::vector(l) {}
FPS(const std::vector<mint>& v) : std::vector<mint>::vector(v) {}
FPS(std::vector<mint>&& v) : std::vector<mint>::vector(std::move(v)) {}
static void set_multiplication(convolution_t<mint> multiplication) {
FPS<mint>::mult = multiplication;
}
int size() const noexcept {
return base_type::size();
}
int deg() const noexcept {
return size() - 1;
}
void ensure(int n) {
if (size() < n) this->resize(n);
}
value_type safe_get(int d) const {
return d <= deg() ? (*this)[d] : 0;
}
value_type& safe_get(int d) {
ensure(d + 1);
return (*this)[d];
}
FPS& cut_trailing_zeros() {
while (this->size() and this->back() == 0) this->pop_back();
return *this;
}
FPS& cut(int n) {
if (size() > n) this->resize(std::max(0, n));
return *this;
}
FPS cut_copy(int n) const {
FPS res(this->begin(), this->begin() + std::min(size(), n));
res.ensure(n);
return res;
}
FPS cut_copy(int l, int r) const {
if (l >= size()) return FPS(r - l, 0);
FPS res(this->begin() + l, this->begin() + std::min(size(), r));
res.ensure(r - l);
return res;
}
/* Unary Operations */
FPS operator+() const { return *this; }
FPS operator-() const {
FPS res = *this;
for (auto& e : res) e = -e;
return res;
}
FPS& operator++() { return ++safe_get(0), * this; }
FPS& operator--() { return --safe_get(0), * this; }
FPS operator++(int) {
FPS res = *this;
++(*this);
return res;
}
FPS operator--(int) {
FPS res = *this;
--(*this);
return res;
}
/* Binary Operations With Constant */
FPS& operator+=(const value_type& x) { return safe_get(0) += x, *this; }
FPS& operator-=(const value_type& x) { return safe_get(0) -= x, *this; }
FPS& operator*=(const value_type& x) {
for (auto& e : *this) e *= x;
return *this;
}
FPS& operator/=(const value_type& x) { return *this *= x.inv(); }
friend FPS operator+(FPS f, const value_type& x) { f += x; return f; }
friend FPS operator+(const value_type& x, FPS f) { f += x; return f; }
friend FPS operator-(FPS f, const value_type& x) { f -= x; return f; }
friend FPS operator-(const value_type& x, FPS f) { f -= x; return -f; }
friend FPS operator*(FPS f, const value_type& x) { f *= x; return f; }
friend FPS operator*(const value_type& x, FPS f) { f *= x; return f; }
friend FPS operator/(FPS f, const value_type& x) { f /= x; return f; }
/* Binary Operations With Formal Power Series */
FPS& operator+=(const FPS& g) {
const int n = g.size();
ensure(n);
for (int i = 0; i < n; ++i) (*this)[i] += g[i];
return *this;
}
FPS& operator-=(const FPS& g) {
const int n = g.size();
ensure(n);
for (int i = 0; i < n; ++i) (*this)[i] -= g[i];
return *this;
}
FPS& operator*=(const FPS& g) { return *this = *this * g; }
FPS& operator/=(const FPS& g) { return *this = *this / g; }
FPS& operator%=(const FPS& g) { return *this = *this % g; }
friend FPS operator+(FPS f, const FPS& g) { f += g; return f; }
friend FPS operator-(FPS f, const FPS& g) { f -= g; return f; }
friend FPS operator*(const FPS& f, const FPS& g) { return mult(f, g); }
friend FPS operator/(FPS f, FPS g) {
if (f.size() < 60) return FPSNaive<mint>(f).div_mod(g).first;
f.cut_trailing_zeros(), g.cut_trailing_zeros();
const int fd = f.deg(), gd = g.deg();
assert(gd >= 0);
if (fd < gd) return {};
if (gd == 0) {
f /= g[0];
return f;
}
std::reverse(f.begin(), f.end()), std::reverse(g.begin(), g.end());
const int qd = fd - gd;
FPS q = f * g.inv(qd + 1);
q.cut(qd + 1);
std::reverse(q.begin(), q.end());
return q;
}
friend FPS operator%(const FPS& f, const FPS& g) { return f.div_mod(g).second; }
std::pair<FPS, FPS> div_mod(const FPS& g) const {
if (size() < 60) {
auto [q, r] = FPSNaive<mint>(*this).div_mod(g);
return { q, r };
}
FPS q = *this / g, r = *this - g * q;
r.cut_trailing_zeros();
return { q, r };
}
/* Shift Operations */
FPS& operator<<=(const int shamt) {
return this->insert(this->begin(), shamt, 0), * this;
}
FPS& operator>>=(const int shamt) {
return this->erase(this->begin(), this->begin() + std::min(shamt, size())), * this;
}
friend FPS operator<<(FPS f, const int shamt) { f <<= shamt; return f; }
friend FPS operator>>(FPS f, const int shamt) { f >>= shamt; return f; }
/* Compare */
friend bool operator==(const FPS& f, const FPS& g) {
const int n = f.size(), m = g.size();
if (n < m) return g == f;
for (int i = 0; i < m; ++i) if (f[i] != g[i]) return false;
for (int i = m; i < n; ++i) if (f[i] != 0) return false;
return true;
}
friend bool operator!=(const FPS& f, const FPS& g) { return not (f == g); }
/* Other Operations */
FPS& diff_inplace() {
const int n = size();
for (int i = 1; i < n; ++i) (*this)[i - 1] = (*this)[i] * i;
return (*this)[n - 1] = 0, *this;
}
FPS diff() const {
FPS res = *this;
res.diff_inplace();
return res;
}
FPS& intg_inplace() {
const int n = size();
inv_mods<value_type> invs(n);
this->resize(n + 1);
for (int i = n; i > 0; --i) (*this)[i] = (*this)[i - 1] * invs[i];
return (*this)[0] = 0, *this;
}
FPS intg() const {
FPS res = *this;
res.intg_inplace();
return res;
}
FPS& inv_inplace(const int n = -1) { return *this = inv(n); }
FPS inv(int n = -1) const {
if (n < 0) n = size();
if (n < 60) return FPSNaive<mint>(*this).inv(n);
if (auto sp_f = sparse_fps_format(15); sp_f.has_value()) return inv_sparse(std::move(*sp_f), n);
FPS g{ (*this)[0].inv() };
for (int k = 1; k < n; k *= 2) {
FPS f_lo = cut_copy(k), f_hi = cut_copy(k, 2 * k);
FPS h = (f_hi * g).cut(k) + ((f_lo * g) >>= k);
FPS g_hi = g * h;
g.resize(2 * k);
for (int i = 0; i < k; ++i) g[k + i] = -g_hi[i];
}
g.resize(n);
return g;
}
FPS& log_inplace(int n = -1) { return *this = log(n); }
FPS log(int n = -1) const {
assert(safe_get(0) == 1);
if (n < 0) n = size();
if (n < 60) return FPSNaive<mint>(cut_copy(n)).log(n);
if (auto sp_f = sparse_fps_format(15); sp_f.has_value()) return log_sparse(std::move(*sp_f), n);
FPS res = inv(n) * diff();
res.resize(n - 1);
return res.intg();
}
FPS& exp_inplace(int n = -1) { return *this = exp(n); }
FPS exp(int n = -1) {
assert(safe_get(0) == 0);
if (n < 0) n = size();
if (n < 60) return FPSNaive<mint>(cut_copy(n)).exp(n);
if (auto sp_f = sparse_fps_format(15); sp_f.has_value()) return exp_sparse(std::move(*sp_f), n);
FPS res{ 1 };
for (int k = 1; k < n; k *= 2) res *= ++(cut_copy(k * 2) - res.log(k * 2)), res.cut(k * 2);
res.resize(n);
return res;
}
FPS& pow_inplace(long long k, int n = -1) { return *this = pow(k, n); }
FPS pow(const long long k, int n = -1) const {
if (n < 0) n = size();
if (n < 60) return FPSNaive<mint>(cut_copy(n)).pow(k, n);
if (auto sp_f = sparse_fps_format(15); sp_f.has_value()) return pow_sparse(std::move(*sp_f), k, n);
if (k == 0) {
FPS f{ 1 };
f.resize(n);
return f;
}
int tlz = 0;
while (tlz < size() and (*this)[tlz] == 0) ++tlz;
if (tlz == size() or tlz > (n - 1) / k) return FPS(n, 0);
const int m = n - tlz * k;
FPS f = *this >> tlz;
value_type base = f[0];
return ((((f /= base).log(m) *= k).exp(m) *= base.pow(k)) <<= (tlz * k));
}
std::optional<FPS> safe_sqrt(int n = -1) const {
if (n < 0) n = size();
if (n < 60) return FPSNaive<mint>(cut_copy(n)).safe_sqrt(n);
if (auto sp_f = sparse_fps_format(15); sp_f.has_value()) return safe_sqrt_sparse(std::move(*sp_f), n);
int tlz = 0;
while (tlz < size() and (*this)[tlz] == 0) ++tlz;
if (tlz == size()) return FPS(n, 0);
if (tlz & 1) return std::nullopt;
const int m = n - tlz / 2;
FPS h(this->begin() + tlz, this->end());
auto q0 = ::safe_sqrt(h[0]);
if (not q0.has_value()) return std::nullopt;
FPS f{ *q0 }, g{ q0->inv() };
mint inv_2 = mint(2).inv();
for (int k = 1; k < m; k *= 2) {
FPS tmp = h.cut_copy(2 * k) * f.inv(2 * k);
tmp.cut(2 * k);
f += tmp, f *= inv_2;
}
f.resize(m);
f <<= tlz / 2;
return f;
}
FPS& sqrt_inplace(int n = -1) { return *this = sqrt(n); }
FPS sqrt(int n = -1) const {
return *safe_sqrt(n);
}
mint eval(mint x) const {
mint y = 0;
for (int i = size() - 1; i >= 0; --i) y = y * x + (*this)[i];
return y;
}
static FPS prod(const std::vector<FPS>& fs) {
auto comp = [](const FPS& f, const FPS& g) { return f.size() > g.size(); };
std::priority_queue<FPS, std::vector<FPS>, decltype(comp)> pq{ comp };
for (const auto& f : fs) pq.push(f);
while (pq.size() > 1) {
auto f = pq.top();
pq.pop();
auto g = pq.top();
pq.pop();
pq.push(f * g);
}
return pq.top();
}
std::optional<std::vector<std::pair<int, value_type>>> sparse_fps_format(int max_size) const {
std::vector<std::pair<int, value_type>> res;
for (int i = 0; i <= deg() and int(res.size()) <= max_size; ++i) if (value_type v = (*this)[i]; v != 0) res.emplace_back(i, v);
if (int(res.size()) > max_size) return std::nullopt;
return res;
}
protected:
static convolution_t<mint> mult;
static FPS div_fps_sparse(const FPS& f, const std::vector<std::pair<int, value_type>>& g, int n) {
const int size = g.size();
assert(size and g[0].first == 0);
const value_type inv_g0 = g[0].second.inv();
FPS h(n);
for (int i = 0; i < n; ++i) {
value_type v = f.safe_get(i);
for (int idx = 1; idx < size; ++idx) {
const auto& [j, gj] = g[idx];
if (j > i) break;
v -= gj * h[i - j];
}
h[i] = v * inv_g0;
}
return h;
}
static FPS inv_sparse(const std::vector<std::pair<int, value_type>>& g, const int n) {
return div_fps_sparse(FPS{ 1 }, g, n);
}
static FPS exp_sparse(const std::vector<std::pair<int, value_type>>& f, const int n) {
const int size = f.size();
assert(not size or f[0].first != 0);
FPS g(n);
g[0] = 1;
inv_mods<value_type> invs(n);
for (int i = 1; i < n; ++i) {
value_type v = 0;
for (const auto& [j, fj] : f) {
if (j > i) break;
v += j * fj * g[i - j];
}
v *= invs[i];
g[i] = v;
}
return g;
}
static FPS log_sparse(const std::vector<std::pair<int, value_type>>& f, const int n) {
const int size = f.size();
assert(size and f[0].first == 0 and f[0].second == 1);
FPS g(n);
for (int idx = 1; idx < size; ++idx) {
const auto& [j, fj] = f[idx];
if (j >= n) break;
g[j] = j * fj;
}
inv_mods<value_type> invs(n);
for (int i = 1; i < n; ++i) {
value_type v = g[i];
for (int idx = 1; idx < size; ++idx) {
const auto& [j, fj] = f[idx];
if (j > i) break;
v -= fj * g[i - j] * (i - j);
}
v *= invs[i];
g[i] = v;
}
return g;
}
static FPS pow_sparse(const std::vector<std::pair<int, value_type>>& f, const long long k, const int n) {
if (k == 0) {
FPS res(n, 0);
res[0] = 1;
return res;
}
const int size = f.size();
if (not size) return FPS(n, 0);
const int p = f[0].first;
if (p > (n - 1) / k) return FPS(n, 0);
const value_type inv_f0 = f[0].second.inv();
const int lz = p * k;
FPS g(n);
g[lz] = f[0].second.pow(k);
inv_mods<value_type> invs(n);
for (int i = 1; lz + i < n; ++i) {
value_type v = 0;
for (int idx = 1; idx < size; ++idx) {
auto [j, fj] = f[idx];
j -= p;
if (j > i) break;
v += fj * g[lz + i - j] * (value_type(k) * j - (i - j));
}
v *= invs[i] * inv_f0;
g[lz + i] = v;
}
return g;
}
static std::optional<FPS> safe_sqrt_sparse(const std::vector<std::pair<int, value_type>>& f, const int n) {
const int size = f.size();
if (not size) return FPS(n, 0);
const int p = f[0].first;
if (p % 2 == 1) return std::nullopt;
if (p / 2 >= n) return FPS(n, 0);
const value_type inv_f0 = f[0].second.inv();
const int lz = p / 2;
FPS g(n);
auto opt_g0 = ::safe_sqrt(f[0].second);
if (not opt_g0.has_value()) return std::nullopt;
g[lz] = *opt_g0;
value_type k = mint(2).inv();
inv_mods<value_type> invs(n);
for (int i = 1; lz + i < n; ++i) {
value_type v = 0;
for (int idx = 1; idx < size; ++idx) {
auto [j, fj] = f[idx];
j -= p;
if (j > i) break;
v += fj * g[lz + i - j] * (k * j - (i - j));
}
v *= invs[i] * inv_f0;
g[lz + i] = v;
}
return g;
}
static FPS sqrt_sparse(const std::vector<std::pair<int, value_type>>& f, const int n) {
return *safe_sqrt(f, n);
}
};
template <typename mint>
convolution_t<mint> FPS<mint>::mult = [](const auto&, const auto&) {
std::cerr << "convolution function is not available." << std::endl;
assert(false);
return std::vector<mint>{};
};
} // namespace suisen
template <typename mint>
suisen::FPS<mint> sqrt(suisen::FPS<mint> a) {
return a.sqrt();
}
template <typename mint>
suisen::FPS<mint> log(suisen::FPS<mint> a) {
return a.log();
}
template <typename mint>
suisen::FPS<mint> exp(suisen::FPS<mint> a) {
return a.exp();
}
template <typename mint, typename T>
suisen::FPS<mint> pow(suisen::FPS<mint> a, T b) {
return a.pow(b);
}
template <typename mint>
suisen::FPS<mint> inv(suisen::FPS<mint> a) {
return a.inv();
}
#line 1 "library/math/factorial_large.hpp"
#include <utility>
#line 1 "library/polynomial/shift_of_sampling_points.hpp"
#line 5 "library/polynomial/shift_of_sampling_points.hpp"
#include <atcoder/convolution>
#line 1 "library/math/factorial.hpp"
#line 6 "library/math/factorial.hpp"
namespace suisen {
// 引数として与える値に対して、法が十分大きいことを仮定する
template <typename T, typename U = T>
struct factorial {
factorial() = default;
factorial(int n) { ensure(n); }
static void ensure(const int n) {
int sz = _fac.size();
if (n + 1 <= sz) return;
int new_size = std::max(n + 1, sz * 2);
_fac.resize(new_size), _fac_inv.resize(new_size);
for (int i = sz; i < new_size; ++i) _fac[i] = _fac[i - 1] * i;
_fac_inv[new_size - 1] = U(1) / _fac[new_size - 1];
for (int i = new_size - 1; i > sz; --i) _fac_inv[i - 1] = _fac_inv[i] * i;
}
T fac(const int i) {
ensure(i);
return _fac[i];
}
T operator()(int i) {
return fac(i);
}
U fac_inv(const int i) {
ensure(i);
return _fac_inv[i];
}
// i の逆数
// i = 0 の場合は assert 違反となる
U inv(const int i) {
assert(i > 0);
ensure(i);
return _fac_inv[i] * _fac[i - 1];
}
U binom(const int n, const int r) {
if (n < 0 or r < 0 or n < r) return 0;
ensure(n);
return _fac[n] * _fac_inv[r] * _fac_inv[n - r];
}
// binom(n, r) の逆数
// binom(n, r) = 0 の場合は assert 違反となる
U binom_inv(const int n, const int r) {
assert(r >= 0 and n >= r);
ensure(n);
return _fac_inv[n] * _fac[r] * _fac[n - r];
}
// n 種類から重複を許して r 個選ぶ場合の数
// x_1+x_2+...+x_n=r（x_i は非負整数）となる x の個数でもある
// multichoose(n, r) = binom(n + r - 1, r)
U multichoose(const int n, const int r) {
if (n < 0 or r < 0) return 0;
return r > 0 ? binom(n + r - 1, r) : U(1);
}
// n 種類から重複を許して r 個選ぶ場合の数 multichoose(n, r) の逆数
// x_1+x_2+...+x_n=r（x_i は非負整数）となる x の個数の逆数でもある
// multichoose(n, r) = binom(n + r - 1, r)
// multichoose(n, r) = 0 の場合は assert 違反となる
U multichoose_inv(const int n, const int r) {
assert(n >= 0 and r >= 0);
return r > 0 ? binom_inv(n + r - 1, r) : U(1);
}
template <typename ...Ds, std::enable_if_t<std::conjunction_v<std::is_integral<Ds>...>, std::nullptr_t> = nullptr>
U polynom(const int n, const Ds& ...ds) {
if (n < 0) return 0;
ensure(n);
int sumd = 0;
U res = _fac[n];
for (int d : { ds... }) {
if (d < 0 or d > n) return 0;
sumd += d;
res *= _fac_inv[d];
}
if (sumd > n) return 0;
res *= _fac_inv[n - sumd];
return res;
}
U perm(const int n, const int r) {
if (n < 0 or r < 0 or n < r) return 0;
ensure(n);
return _fac[n] * _fac_inv[n - r];
}
// perm(n, r) の逆数
// perm(n, r) = 0 の場合は assert 違反となる
U perm_inv(const int n, const int r) {
assert(r >= 0 and n >= r);
ensure(n);
return _fac_inv[n] * _fac[n - r];
}
private:
static std::vector<T> _fac;
static std::vector<U> _fac_inv;
};
template <typename T, typename U>
std::vector<T> factorial<T, U>::_fac{ 1 };
template <typename T, typename U>
std::vector<U> factorial<T, U>::_fac_inv{ 1 };
} // namespace suisen
#line 8 "library/polynomial/shift_of_sampling_points.hpp"
namespace suisen {
template <typename mint, typename Convolve,
std::enable_if_t<std::is_invocable_r_v<std::vector<mint>, Convolve, std::vector<mint>, std::vector<mint>>, std::nullptr_t> = nullptr>
std::vector<mint> shift_of_sampling_points(const std::vector<mint>& ys, mint t, int m, const Convolve &convolve) {
const int n = ys.size();
factorial<mint> fac(std::max(n, m));
std::vector<mint> b = [&] {
std::vector<mint> f(n), g(n);
for (int i = 0; i < n; ++i) {
f[i] = ys[i] * fac.fac_inv(i);
g[i] = (i & 1 ? -1 : 1) * fac.fac_inv(i);
}
std::vector<mint> b = convolve(f, g);
b.resize(n);
return b;
}();
std::vector<mint> e = [&] {
std::vector<mint> c(n);
mint prd = 1;
std::reverse(b.begin(), b.end());
for (int i = 0; i < n; ++i) {
b[i] *= fac.fac(n - i - 1);
c[i] = prd * fac.fac_inv(i);
prd *= t - i;
}
std::vector<mint> e = convolve(b, c);
e.resize(n);
return e;
}();
std::reverse(e.begin(), e.end());
for (int i = 0; i < n; ++i) {
e[i] *= fac.fac_inv(i);
}
std::vector<mint> f(m);
for (int i = 0; i < m; ++i) f[i] = fac.fac_inv(i);
std::vector<mint> res = convolve(e, f);
res.resize(m);
for (int i = 0; i < m; ++i) res[i] *= fac.fac(i);
return res;
}
template <typename mint>
std::vector<mint> shift_of_sampling_points(const std::vector<mint>& ys, mint t, int m) {
auto convolve = [&](const std::vector<mint> &f, const std::vector<mint> &g) { return atcoder::convolution(f, g); };
return shift_of_sampling_points(ys, t, m, convolve);
}
} // namespace suisen
#line 1 "library/convolution/arbitrary_mod_convolution.hpp"
#line 6 "library/convolution/arbitrary_mod_convolution.hpp"
#line 1 "library/convolution/convolution_naive.hpp"
#line 5 "library/convolution/convolution_naive.hpp"
namespace suisen::internal {
template <typename T, typename R = T>
std::vector<R> convolution_naive(const std::vector<T>& a, const std::vector<T>& b) {
const int n = a.size(), m = b.size();
std::vector<R> c(n + m - 1);
if (n < m) {
for (int j = 0; j < m; j++) for (int i = 0; i < n; i++) c[i + j] += R(a[i]) * b[j];
} else {
for (int i = 0; i < n; i++) for (int j = 0; j < m; j++) c[i + j] += R(a[i]) * b[j];
}
return c;
}
} // namespace suisen
#line 8 "library/convolution/arbitrary_mod_convolution.hpp"
namespace suisen {
template <typename mint, atcoder::internal::is_modint_t<mint>* = nullptr>
std::vector<mint> arbitrary_mod_convolution(const std::vector<mint>& a, const std::vector<mint>& b) {
int n = int(a.size()), m = int(b.size());
if constexpr (atcoder::internal::is_static_modint<mint>::value) {
if constexpr (not (mint::mod() & 63)) {
int maxz = 1;
while (not ((mint::mod() - 1) & maxz)) maxz <<= 1;
int z = 1;
while (z < n + m - 1) z <<= 1;
if (z <= maxz) return atcoder::convolution<mint>(a, b);
}
}
if (n == 0 or m == 0) return {};
if (std::min(n, m) <= 120) return internal::convolution_naive(a, b);
static constexpr long long MOD1 = 754974721; // 2^24
static constexpr long long MOD2 = 167772161; // 2^25
static constexpr long long MOD3 = 469762049; // 2^26
static constexpr long long M1M2 = MOD1 * MOD2;
static constexpr long long INV_M1_MOD2 = atcoder::internal::inv_gcd(MOD1, MOD2).second;
static constexpr long long INV_M1M2_MOD3 = atcoder::internal::inv_gcd(M1M2, MOD3).second;
std::vector<int> a2(n), b2(m);
for (int i = 0; i < n; ++i) a2[i] = a[i].val();
for (int i = 0; i < m; ++i) b2[i] = b[i].val();
auto c1 = atcoder::convolution<MOD1>(a2, b2);
auto c2 = atcoder::convolution<MOD2>(a2, b2);
auto c3 = atcoder::convolution<MOD3>(a2, b2);
const long long m1m2 = mint(M1M2).val();
std::vector<mint> c(n + m - 1);
for (int i = 0; i < n + m - 1; ++i) {
// Garner's Algorithm
// X = x1 + x2 * m1 + x3 * m1 * m2
// x1 = c1[i], x2 = (c2[i] - x1) / m1 (mod m2), x3 = (c3[i] - x1 - x2 * m1) / m2 (mod m3)
long long x1 = c1[i];
long long x2 = (atcoder::static_modint<MOD2>(c2[i] - x1) * INV_M1_MOD2).val();
long long x3 = (atcoder::static_modint<MOD3>(c3[i] - x1 - x2 * MOD1) * INV_M1M2_MOD3).val();
c[i] = x1 + x2 * MOD1 + x3 * m1m2;
}
return c;
}
std::vector<__uint128_t> convolution_int(const std::vector<int> &a, const std::vector<int> &b) {
int n = int(a.size()), m = int(b.size());
auto check_nonnegative = [](int e) { return e >= 0; };
assert(std::all_of(a.begin(), a.end(), check_nonnegative));
assert(std::all_of(b.begin(), b.end(), check_nonnegative));
if (n == 0 or m == 0) return {};
if (std::min(n, m) <= 120) return internal::convolution_naive<int, __uint128_t>(a, b);
static constexpr long long MOD1 = 754974721; // 2^24
static constexpr long long MOD2 = 167772161; // 2^25
static constexpr long long MOD3 = 469762049; // 2^26
static constexpr long long M1M2 = MOD1 * MOD2;
static constexpr long long INV_M1_MOD2 = atcoder::internal::inv_gcd(MOD1, MOD2).second;
static constexpr long long INV_M1M2_MOD3 = atcoder::internal::inv_gcd(M1M2, MOD3).second;
auto c1 = atcoder::convolution<MOD1>(a, b);
auto c2 = atcoder::convolution<MOD2>(a, b);
auto c3 = atcoder::convolution<MOD3>(a, b);
std::vector<__uint128_t> c(n + m - 1);
for (int i = 0; i < n + m - 1; ++i) {
// Garner's Algorithm
// X = x1 + x2 * m1 + x3 * m1 * m2
// x1 = c1[i], x2 = (c2[i] - x1) / m1 (mod m2), x3 = (c3[i] - x1 - x2 * m1) / m2 (mod m3)
int x1 = c1[i];
int x2 = (atcoder::static_modint<MOD2>(c2[i] - x1) * INV_M1_MOD2).val();
int x3 = (atcoder::static_modint<MOD3>(c3[i] - x1 - x2 * MOD1) * INV_M1M2_MOD3).val();
c[i] = x1 + x2 * MOD1 + __uint128_t(x3) * M1M2;
}
return c;
}
} // namespace suisen
#line 9 "library/math/factorial_large.hpp"
namespace suisen {
// mod must be a prime number
template <typename mint,
std::enable_if_t<atcoder::internal::is_static_modint<mint>::value, std::nullptr_t> = nullptr>
struct factorial_large {
using value_type = mint;
static constexpr int LOG_BLOCK_SIZE = 9;
static constexpr int BLOCK_SIZE = 1 << LOG_BLOCK_SIZE;
static constexpr int BLOCK_NUM = value_type::mod() >> LOG_BLOCK_SIZE;
static inline int threshold = 2000000;
static_assert(atcoder::internal::is_prime_constexpr(mint::mod()));
static value_type fac(long long n) {
if (n >= mint::mod()) return 0;
return n <= threshold ? factorial<mint>{}.fac(n) : _large_fac(n);
}
static value_type fac_inv(long long n) {
assert(n < (long long) mint::mod());
return n <= threshold ? factorial<mint>{}.fac_inv(n) : _large_fac(n).inv();
}
static value_type binom(long long n, long long r) {
if (n < 0 or r < 0 or n < r) return 0;
return _binom_lucas(n, r);
}
// binom(n, r) の逆数
// binom(n, r) = 0 の場合は assert 違反となる
static value_type binom_inv(long long n, long long r) {
assert(r >= 0 and n >= r);
return _binom_inv_lucas(n, r);
}
// n 種類から重複を許して r 個選ぶ場合の数
// x_1+x_2+...+x_n=r（x_i は非負整数）となる x の個数でもある
// multichoose(n, r) = binom(n + r - 1, r)
static value_type multichoose(long long n, long long r) {
if (n < 0 or r < 0) return 0;
if (r == 0) return value_type(1);
if (n == 0) return value_type(0);
return binom(n + r - 1, r);
}
// n 種類から重複を許して r 個選ぶ場合の数 multichoose(n, r) の逆数
// x_1+x_2+...+x_n=r（x_i は非負整数）となる x の個数の逆数でもある
// multichoose(n, r) = binom(n + r - 1, r)
// multichoose(n, r) = 0 の場合は assert 違反となる
static value_type multichoose_inv(long long n, long long r) {
assert(n >= 0 and r >= 0);
if (r == 0) return value_type(1);
assert(n > 0);
return binom_inv(n + r - 1, r);
}
template <typename ...Ds, std::enable_if_t<std::conjunction_v<std::is_integral<Ds>...>, std::nullptr_t> = nullptr>
static value_type polynom(const int n, const Ds& ...ds) {
if (n < 0) return 0;
long long sumd = 0;
value_type res = fac(n);
for (int d : { ds... }) {
if (d < 0 or d > n) return 0;
sumd += d;
res *= fac_inv(d);
}
if (sumd > n) return 0;
res *= fac_inv(n - sumd);
return res;
}
static value_type perm(long long n, long long r) {
if (r < 0 or r > n or r >= mint::mod()) return 0;
n %= mint::mod();
if (r > n) return 0;
return fac(n) * fac_inv(n - r);
}
// perm(n, r) の逆数
// perm(n, r) = 0 の場合は assert 違反となる
static value_type perm_inv(long long n, long long r) {
assert(r >= 0 and n >= r and r < mint::mod());
n %= mint::mod();
assert(n >= r);
return fac_inv(n) * fac(n - r);
}
private:
static value_type _binom_under_mod(long long n, long long r) {
if (r < 0 or n < r) return 0;
return fac(n) * fac_inv(r) * fac_inv(n - r);
}
static value_type _binom_inv_under_mod(long long n, long long r) {
assert(r >= 0 and n >= r);
return fac_inv(n) * fac(r) * fac(n - r);
}
static value_type _binom_lucas(long long n, long long r) {
if (n < 0 or r < 0 or n < r) return 0;
value_type res = 1;
const int p = value_type::mod();
while (n or r) {
const int ni = n % p;
const int ri = r % p;
if (ri > ni) return 0;
res *= _binom_under_mod(ni, ri);
n /= p;
r /= p;
}
return res;
}
static value_type _binom_inv_lucas(long long n, long long r) {
assert(0 <= r and r <= n);
value_type res = 1;
const int p = value_type::mod();
while (n or r) {
const int ni = n % p;
const int ri = r % p;
assert(ri <= ni);
res *= _binom_inv_under_mod(ni, ri);
n /= p;
r /= p;
}
return res;
}
static inline std::vector<value_type> _block_fac{};
static void _build() {
if (_block_fac.size()) {
return;
}
std::vector<value_type> f{ 1 };
f.reserve(BLOCK_SIZE);
for (int i = 0; i < LOG_BLOCK_SIZE; ++i) {
std::vector<value_type> g = shift_of_sampling_points<value_type>(f, 1 << i, 3 << i, arbitrary_mod_convolution<value_type>);
const auto get = [&](int j) { return j < (1 << i) ? f[j] : g[j - (1 << i)]; };
f.resize(2 << i);
for (int j = 0; j < 2 << i; ++j) {
f[j] = get(2 * j) * get(2 * j + 1) * ((2 * j + 1) << i);
}
}
// f_B(x) = (x+1) * ... * (x+B-1)
if (BLOCK_NUM > BLOCK_SIZE) {
std::vector<value_type> g = shift_of_sampling_points<value_type>(f, BLOCK_SIZE, BLOCK_NUM - BLOCK_SIZE, arbitrary_mod_convolution<value_type>);
std::move(g.begin(), g.end(), std::back_inserter(f));
} else {
f.resize(BLOCK_NUM);
}
for (int i = 0; i < BLOCK_NUM; ++i) {
f[i] *= value_type(i + 1) * BLOCK_SIZE;
}
// f[i] = (i*B + 1) * ... * (i*B + B)
f.insert(f.begin(), 1);
for (int i = 1; i <= BLOCK_NUM; ++i) {
f[i] *= f[i - 1];
}
_block_fac = std::move(f);
}
static value_type _large_fac(int n) {
_build();
value_type res;
int q = n / BLOCK_SIZE, r = n % BLOCK_SIZE;
if (2 * r <= BLOCK_SIZE) {
res = _block_fac[q];
for (int i = 0; i < r; ++i) {
res *= value_type::raw(n - i);
}
} else if (q != factorial_large::BLOCK_NUM) {
res = _block_fac[q + 1];
value_type den = 1;
for (int i = 1; i <= BLOCK_SIZE - r; ++i) {
den *= value_type::raw(n + i);
}
res /= den;
} else {
// Wilson's theorem
res = value_type::mod() - 1;
value_type den = 1;
for (int i = value_type::mod() - 1; i > n; --i) {
den *= value_type::raw(i);
}
res /= den;
}
return res;
}
};
} // namespace suisen
#line 10 "test/src/math/factorial_large/dummy.test.cpp"
template <int MOD>
void test() {
using mint = atcoder::static_modint<MOD>;
std::mt19937 rng{};
constexpr int MAX_N = 10000000;
std::uniform_int_distribution<int> dist(0, MAX_N);
const int q = 10000;
std::vector<int> ns(q);
for (int& e : ns) e = dist(rng);
// power of 2
for (int i = 0; 1 << i < MAX_N; ++i) ns[i] = 1 << i;
std::vector<mint> res1, res2;
{
suisen::factorial_large<mint> fac{};
fac.threshold = -1;
res1.resize(q);
for (int i = 0; i < q; ++i) res1[i] = fac.fac(ns[i]);
}
{
suisen::factorial<mint> fac{};
res2.resize(q);
for (int i = 0; i < q; ++i) res2[i] = fac.fac(ns[i]);
}
assert(res1 == res2);
}
int main() {
test<998244353>();
test<1000000007>();
test<1000000009>();
std::cout << "Hello World" << std::endl;
return 0;
}