test/comb_light.test.cpp

test/comb_light.test.cpp · GitHub で見る

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#define PROBLEM "https://yukicoder.me/problems/no/3172"
#define COMB_MAX 200000
#include "../math/comb_light.hpp"
#include <iostream>

int main() {
	std::cin.tie(nullptr)->sync_with_stdio(false);
	int n;
	std::cin >> n;
	for (int k = 0; k <= n; ++k)
		std::cout << ((n - k) % 2 ? mint(0) : light_combinatorics::comb(n, (n - k) / 2) * (k ? 2 : 1)) << (k == n ? '\n' : ' ');
}

#line 1 "test/comb_light.test.cpp"
#define PROBLEM "https://yukicoder.me/problems/no/3172"
#define COMB_MAX 200000
#line 1 "math/comb_light.hpp"



#line 1 "components/factorial_table_light.hpp"



#line 1 "math/mint.hpp"


#include <cassert>
#include <istream>
#include <ostream>
#include <type_traits>

#if defined(__GNUC__) && !defined(__clang__) && (defined(__x86_64__) || defined(__i386__))
#pragma GCC push_options
#pragma GCC optimize("O3")
#endif

namespace mint_detail {
template <class I>
constexpr bool mint_integral = std::is_integral_v<I>
#if defined(__SIZEOF_INT128__)
							   || std::is_same_v<I, __int128> || std::is_same_v<I, unsigned __int128>
#endif
	;
struct [[gnu::warn_unused]] Mint {
	using mint = Mint;
	unsigned v = 0;
	[[nodiscard]] static constexpr unsigned mod() { return 998244353; }
	[[nodiscard, gnu::always_inline]] static unsigned reduce(unsigned long long x) {
		return (x + (unsigned long long)(unsigned(x) * 998244351u) * mod()) >> 32;
	}
	[[gnu::always_inline]] Mint() = default;
	template <class I, std::enable_if_t<mint_integral<I>, int> = 0>
	Mint(I x) {
		long long r = x % (long long)mod();
		if (r < 0) r += mod();
		v = reduce((unsigned long long)r * 932051910);
	}
	[[nodiscard, gnu::always_inline]] static Mint raw(unsigned x) {
		Mint a;
		a.v = reduce((unsigned long long)x * 932051910);
		return a;
	}
	[[nodiscard, gnu::always_inline]] static Mint word(unsigned x) {
		Mint a;
		a.v = x;
		return a;
	}
	[[nodiscard, gnu::always_inline]] unsigned val() const {
		unsigned r = reduce(v);
		return r < mod() ? r : r - mod();
	}
	friend std::istream &operator>>(std::istream &is, Mint &x) {
		long long value;
		if (is >> value) x = Mint(value);
		return is;
	}
	friend std::ostream &operator<<(std::ostream &os, const Mint &x) {
		return os << x.val();
	}
	[[gnu::always_inline]] Mint &operator+=(Mint b) {
		v += b.v;
		if (v >= 2 * mod()) v -= 2 * mod();
		return *this;
	}
	[[gnu::always_inline]] Mint &operator-=(Mint b) {
		v -= b.v;
		if (v >> 31) v += 2 * mod();
		return *this;
	}
	[[gnu::always_inline]] Mint &operator*=(Mint b) {
		v = reduce((unsigned long long)v * b.v);
		return *this;
	}
	Mint &operator/=(Mint b) { return *this *= b.inv(); }
	Mint &operator++() { return *this += Mint(1); }
	Mint &operator--() { return *this -= Mint(1); }
	Mint operator++(int) {
		Mint a = *this;
		++*this;
		return a;
	}
	Mint operator--(int) {
		Mint a = *this;
		--*this;
		return a;
	}
	[[nodiscard, gnu::always_inline]] Mint operator+() const { return *this; }
	[[nodiscard, gnu::always_inline]] Mint operator-() const { return word(v ? 2 * mod() - v : 0); }
	[[nodiscard, gnu::always_inline]] Mint operator+(Mint b) const { return Mint(*this) += b; }
	[[nodiscard, gnu::always_inline]] Mint operator-(Mint b) const { return Mint(*this) -= b; }
	[[nodiscard, gnu::always_inline]] Mint operator*(Mint b) const { return Mint(*this) *= b; }
	[[nodiscard]] Mint operator/(Mint b) const { return Mint(*this) /= b; }
	[[nodiscard, gnu::always_inline]] bool operator==(Mint b) const { return (v < mod() ? v : v - mod()) == (b.v < mod() ? b.v : b.v - mod()); }
	[[nodiscard, gnu::always_inline]] bool operator!=(Mint b) const { return !(*this == b); }
	template <class I, std::enable_if_t<mint_integral<I>, int> = 0>
	[[nodiscard]] friend Mint operator+(I a, Mint b) { return Mint(a) + b; }
	template <class I, std::enable_if_t<mint_integral<I>, int> = 0>
	[[nodiscard]] friend Mint operator-(I a, Mint b) { return Mint(a) - b; }
	template <class I, std::enable_if_t<mint_integral<I>, int> = 0>
	[[nodiscard]] friend Mint operator*(I a, Mint b) { return Mint(a) * b; }
	template <class I, std::enable_if_t<mint_integral<I>, int> = 0>
	[[nodiscard]] friend Mint operator/(I a, Mint b) { return Mint(a) / b; }
	template <class I, std::enable_if_t<mint_integral<I>, int> = 0>
	[[nodiscard]] friend bool operator==(I a, Mint b) { return Mint(a) == b; }
	template <class I, std::enable_if_t<mint_integral<I>, int> = 0>
	[[nodiscard]] friend bool operator!=(I a, Mint b) { return Mint(a) != b; }
	[[nodiscard]] Mint pow(long long n) const {
		assert(n >= 0);
		if (!n) return Mint(1);
		Mint r(1), a = *this;
		for (; n > 1; n >>= 1, a *= a)
			if (n & 1) r *= a;
		return r * a;
	}
	[[nodiscard, gnu::noinline]] Mint inv() const {
		assert(*this != Mint(0));
		Mint a2 = *this * *this, a3 = a2 * *this;
		Mint a7 = a3 * a3 * *this;
		Mint a31 = a7;
		for (int i = 0; i < 2; ++i) a31 *= a31;
		a31 *= a3;
		Mint r = a7;
		for (int i = 0; i < 3; ++i) r *= r;
		r *= a3;
		r *= r;
		for (int j = 0; j < 4; ++j) {
			for (int i = 0; i < 5; ++i) r *= r;
			r *= a31;
		}
		for (int i = 0; i < 3; ++i) r *= r;
		return r * a7;
	}
};
} // namespace mint_detail

using mint = mint_detail::Mint;
using fps_mint = mint;

#if defined(__GNUC__) && !defined(__clang__) && (defined(__x86_64__) || defined(__i386__))
#pragma GCC pop_options
#endif


#line 1 "components/factorial_table_generic.hpp"



#line 1 "components/barrett32.hpp"



#line 5 "components/barrett32.hpp"
#include <cstdint>

struct Barrett32 {
	std::uint32_t mod;
	std::uint64_t reciprocal;
	explicit Barrett32(std::uint32_t m) : mod(m), reciprocal(m > 1 ? std::uint64_t((__uint128_t(1) << 64) / m) : 0) {
		assert(m > 0);
	}
	std::uint32_t reduce(std::uint64_t x) const {
		if (mod == 1) return 0;
		std::uint64_t q = (__uint128_t(x) * reciprocal) >> 64, r = x - q * mod;
		return r < mod ? r : r - mod;
	}
	std::uint32_t mul(std::uint32_t a, std::uint32_t b) const { return reduce(std::uint64_t(a) * b); }
	std::uint32_t pow(std::uint32_t a, std::uint64_t e) const {
		std::uint32_t r = mod == 1 ? 0 : 1;
		for (; e; e >>= 1, a = mul(a, a)) if (e & 1) r = mul(r, a);
		return r;
	}
};


#line 5 "components/factorial_table_generic.hpp"
#include <concepts>
#line 7 "components/factorial_table_generic.hpp"
#include <limits>
#line 9 "components/factorial_table_generic.hpp"

namespace factorial_table_detail {
template<class Mint, bool Canonical = true> void build(Mint *factorial, Mint *inverse_factorial, int n) {
	if constexpr (Canonical && requires(const Mint &x) { { x.val() } -> std::integral; }) {
		const auto modulus = Mint::mod();
		if (std::uint64_t(modulus) <= std::numeric_limits<std::uint32_t>::max()) {
			Barrett32 arithmetic(modulus);
			auto make = [](std::uint32_t value) { return Mint(value); };
			std::uint32_t value = 1;
			factorial[0] = make(value);
			for (int i = 1; i <= n; ++i) {
				value = arithmetic.mul(value, i);
				factorial[i] = make(value);
			}
			inverse_factorial[n] = factorial[n].inv();
			if constexpr (std::is_signed_v<decltype(inverse_factorial[n].val())>) {
				std::int64_t residue = inverse_factorial[n].val() % std::int64_t(modulus);
				value = residue < 0 ? residue + modulus : residue;
			} else value = arithmetic.reduce(inverse_factorial[n].val());
			for (int i = n; i > 0; --i) {
				value = arithmetic.mul(value, i);
				inverse_factorial[i - 1] = make(value);
			}
			return;
		}
	}
	factorial[0] = Mint(1);
	for (int i = 1; i <= n; ++i) factorial[i] = factorial[i - 1] * Mint(i);
	inverse_factorial[n] = factorial[n].inv();
	for (int i = n; i > 0; --i) inverse_factorial[i - 1] = inverse_factorial[i] * Mint(i);
}
}


#line 6 "components/factorial_table_light.hpp"
#include <algorithm>
#line 11 "components/factorial_table_light.hpp"
#include <vector>

namespace light_factorial_detail {
template<class Mint> struct Table {
	decltype(Mint::mod()) modulus;
	std::vector<Mint> factorial, inverse_factorial;

	explicit Table(int max_n) : modulus(Mint::mod()) {
		assert(0 <= max_n && max_n < std::numeric_limits<int>::max() && modulus > 1);
		int n = static_cast<int>(std::min(std::uint64_t(max_n), std::uint64_t(modulus) - 1));
		factorial.resize(n + 1), inverse_factorial.resize(n + 1);
		factorial_table_detail::build<Mint, !std::is_same_v<Mint, mint>>(factorial.data(), inverse_factorial.data(), n);
	}
};
}


#line 5 "math/comb_light.hpp"

#ifndef COMB_MAX
#define COMB_MAX 10000000
#endif

namespace light_combinatorics {
inline constexpr int COMB_INF = static_cast<int>(COMB_MAX);
static_assert(COMB_INF >= 0 && COMB_INF < mint::mod());
namespace detail {
template<class Mint>
const light_factorial_detail::Table<Mint>& table() {
	static light_factorial_detail::Table<Mint> value(COMB_INF);
	if (value.modulus != Mint::mod()) value = light_factorial_detail::Table<Mint>(COMB_INF);
	return value;
}
template<class Mint, bool Inverse> struct Factorial {
	Mint operator[](int i) const {
		if (i < 0) return Mint(0);
		assert(i <= COMB_INF);
		const auto& value = table<Mint>();
		assert(std::size_t(i) < value.factorial.size());
		if constexpr (Inverse) return value.inverse_factorial[i];
		else return value.factorial[i];
	}
};
}

template<class Mint = mint>
Mint comb(int n, int k) {
	if (n < 0 || k < 0 || k > n) return Mint(0);
	assert(n <= COMB_INF);
	const auto& value = detail::table<Mint>();
	assert(std::size_t(n) < value.factorial.size());
	return value.factorial[n] * value.inverse_factorial[k] * value.inverse_factorial[n - k];
}

template<class Mint = mint> struct Comb {
	inline static constexpr detail::Factorial<Mint, false> fact{};
	inline static constexpr detail::Factorial<Mint, true> finv{};
	static Mint comb(int n, int k) { return light_combinatorics::comb<Mint>(n, k); }
};
inline constexpr auto& fact = Comb<>::fact;
inline constexpr auto& finv = Comb<>::finv;
}


#line 4 "test/comb_light.test.cpp"
#include <iostream>

int main() {
	std::cin.tie(nullptr)->sync_with_stdio(false);
	int n;
	std::cin >> n;
	for (int k = 0; k <= n; ++k)
		std::cout << ((n - k) % 2 ? mint(0) : light_combinatorics::comb(n, (n - k) / 2) * (k ? 2 : 1)) << (k == n ? '\n' : ' ');
}