test/yosupo/exp_of_formal_power_series.test.cpp

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• Last update: 2023-06-25 16:24:15+09:00
• Problem: https://judge.yosupo.jp/problem/exp_of_formal_power_series

Depends on

• basic/template.hpp
• basic/type_traits.hpp
• math/FormalPowerSeries.hpp
• NumberTheoreticTransform (math/NumberTheoreticTransform.hpp)
• StaticModInt (math/StaticModInt.hpp)

Code

#define PROBLEM "https://judge.yosupo.jp/problem/exp_of_formal_power_series"
#include "../../basic/template.hpp"
#include "../../math/StaticModInt.hpp"
#include "../../math/FormalPowerSeries.hpp"

using ModInt = StaticModInt<998244353>;
using FPS = FormalPowerSeries<ModInt>;
int main() {
	int N;
	FPS vec;
	std::cin >> N >> vec;
	std::cout << vec.exp() << std::endl;
}

#line 1 "test/yosupo/exp_of_formal_power_series.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/exp_of_formal_power_series"
#line 2 "basic/template.hpp"
#define _CRT_SECURE_NO_WARNINGS
#ifndef __clang__
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#endif
#include <string.h>
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cfloat>
#include <chrono>
#include <climits>
#include <cmath>
#include <complex>
#include <ctime>
#include <deque>
#include <fstream>
#include <functional>
#include <iomanip>
#include <iostream>
#include <iterator>
#include <list>
#include <map>
#include <memory>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

#define rep(i, n) for (int i = 0; i < int(n); i++)
#define REP(i, n) for (int i = 1; i <= int(n); i++)
#define all(V) V.begin(), V.end()

using i128 = __int128_t;
using u128 = __uint128_t;
using uint = unsigned int;
using lint = long long;
using ulint = unsigned long long;
using IP = std::pair<int, int>;
using LP = std::pair<lint, lint>;

constexpr int INF = INT_MAX / 2;
constexpr lint LINF = LLONG_MAX / 2;
constexpr double eps = DBL_EPSILON * 10;
constexpr double PI = 3.141592653589793238462643383279;

template <class T>
class prique : public std::priority_queue<T, std::vector<T>, std::greater<T>> {};
int popcount(uint x) {
#if __cplusplus >= 202002L
	return std::popcount(x);
#else
#ifndef __clang__
	return __builtin_popcount(x);
#endif
#endif
	x = (x & 0x55555555) + (x >> 1 & 0x55555555);
	x = (x & 0x33333333) + (x >> 2 & 0x33333333);
	x = (x & 0x0f0f0f0f) + (x >> 4 & 0x0f0f0f0f);
	x = (x & 0x00ff00ff) + (x >> 8 & 0x00ff00ff);
	return (x & 0x0000ffff) + (x >> 16 & 0x0000ffff);
}
template <class F>
inline constexpr decltype(auto) lambda_fix(F&& f) {
	return [f = std::forward<F>(f)](auto&&... args) {
		return f(f, std::forward<decltype(args)>(args)...);
	};
}
template <class T>
constexpr std::vector<T> make_vec(size_t n) {
	return std::vector<T>(n);
}
template <class T, class... Args>
constexpr auto make_vec(size_t n, Args&&... args) {
	return std::vector<decltype(make_vec<T>(args...))>(n, make_vec<T>(std::forward<Args>(args)...));
}
template <class T, class U, class Stream>
Stream& operator>>(Stream& ist, std::pair<T, U>& x) {
	return ist >> x.first >> x.second;
}
template <class T, class U, class Stream>
Stream& operator<<(Stream& ost, const std::pair<T, U>& x) {
	return ost << x.first << " " << x.second;
}
template <class Container,
		  std::enable_if_t<!std::is_same<Container, std::string>::value, std::nullptr_t> = nullptr>
auto operator>>(std::istream& ist, Container& cont)
	-> decltype(typename Container::iterator(), std::cin)& {
	Container tmp;
	while (true) {
		typename Container::value_type t;
		ist >> t;
		tmp.emplace_back(t);
		if (getchar() == '\n') break;
	}
	cont = Container(std::move(tmp));
	return ist;
}
template <class Container, class Stream,
		  std::enable_if_t<!std::is_same<Container, std::string>::value, std::nullptr_t> = nullptr>
auto operator<<(Stream& ost, const Container& cont)
	-> decltype(typename Container::iterator(), ost)& {
	for (auto it = cont.begin(); it != cont.end(); it++) {
		if (it != cont.begin()) ost << ' ';
		ost << *it;
	}
	return ost;
}
template <class Container>
auto sum(const Container& cont) -> decltype(typename Container::iterator(), 0LL) {
	lint res = 0;
	for (auto it = cont.begin(); it != cont.end(); it++) res += *it;
	return res;
}
template <class T, class U>
constexpr inline bool chmax(T& lhs, const U& rhs) noexcept {
	if (lhs < rhs) {
		lhs = rhs;
		return true;
	}
	return false;
}
template <class T, class U>
constexpr inline bool chmin(T& lhs, const U& rhs) noexcept {
	if (lhs > rhs) {
		lhs = rhs;
		return true;
	}
	return false;
}
constexpr inline lint gcd(lint a, lint b) noexcept {
	while (b) {
		lint c = a;
		a = b;
		b = c % b;
	}
	return a;
}
inline lint lcm(lint a, lint b) noexcept { return a / gcd(a, b) * b; }
constexpr bool isprime(lint n) noexcept {
	if (n == 1) return false;
	for (int i = 2; i * i <= n; i++) {
		if (n % i == 0) return false;
	}
	return true;
}
template <class T>
constexpr T mypow(T a, lint b) noexcept {
	T res(1);
	while (true) {
		if (b & 1) res *= a;
		b >>= 1;
		if (!b) break;
		a *= a;
	}
	return res;
}
constexpr lint modpow(lint a, lint b, lint m) noexcept {
	a %= m;
	lint res(1);
	while (b) {
		if (b & 1) res *= a, res %= m;
		a *= a, a %= m, b >>= 1;
	}
	return res;
}
LP extGcd(lint a, lint b) noexcept {
	if (b == 0) return {1, 0};
	LP s = extGcd(b, a % b);
	std::swap(s.first, s.second);
	s.second -= a / b * s.first;
	return s;
}
LP ChineseRem(const lint& b1, const lint& m1, const lint& b2, const lint& m2) noexcept {
	auto p = extGcd(m1, m2);
	lint g = gcd(m1, m2), l = m1 / g * m2;
	lint tmp = (b2 - b1) / g * p.first % (m2 / g);
	lint r = (b1 + m1 * tmp + l) % l;
	return {r, l};
}
int LCS(const std::string& a, const std::string& b) {
	auto dp = make_vec<int>(a.size() + 1, b.size() + 1);
	rep(i, a.size()) {
		rep(j, b.size()) {
			chmax(dp[i + 1][j], dp[i][j]);
			chmax(dp[i][j + 1], dp[i][j]);
			if (a[i] == b[j]) chmax(dp[i + 1][j + 1], dp[i][j] + 1);
		}
		chmax(dp[i + 1][b.size()], dp[i][b.size()]);
	}
	rep(j, b.size()) chmax(dp[a.size()][j + 1], dp[a.size()][j]);
	return dp[a.size()][b.size()];
}
template <class T, std::enable_if_t<std::is_convertible<int, T>::value, std::nullptr_t> = nullptr>
void compress(std::vector<T>& vec) {
	auto tmp = vec;
	std::sort(all(tmp));
	tmp.erase(std::unique(all(tmp)), tmp.end());
	for (T& i : vec) i = std::lower_bound(all(tmp), i) - tmp.begin();
}
template <class T>
void compress(T* l, T* r) {
	std::vector<T> tmp(l, r);
	std::sort(all(tmp));
	tmp.erase(std::unique(all(tmp)), tmp.end());
	for (auto i = l; i < r; i++) {
		*i = std::lower_bound(all(tmp), *i) - tmp.begin();
	}
}
template <class InputIter>
void compress(InputIter l, InputIter r) {
	std::vector<typename InputIter::value_type> tmp(l, r);
	std::sort(all(tmp));
	tmp.erase(std::unique(all(tmp)), tmp.end());
	for (auto i = l; i < r; i++) {
		*i = std::lower_bound(all(tmp), *i) - tmp.begin();
	}
}
template <class InputIter,
		  std::enable_if_t<std::is_same<typename InputIter::value_type, std::pair<IP, int>>::value,
						   std::nullptr_t> = nullptr>
void mo_sort(InputIter l, InputIter r, int N) {
	const int M = std::max(1.0, std::sqrt(lint(N) * N / std::distance(l, r)));
	std::sort(l, r, [M](const auto& lhs, const auto& rhs) {
		if (lhs.first.first / M < rhs.first.first / M) return true;
		if (lhs.first.first / M == rhs.first.first / M) return lhs.first.second < rhs.first.second;
		return false;
	});
	int before = -1, cnt = 0;
	bool f = false;
	for (InputIter i = l; i != r; i++) {
		if (before != i->first.first / M) {
			if (f) std::reverse(i - cnt, i);
			f ^= true, before = i->first.first / M, cnt = 1;
		} else
			cnt++;
	}
	if (f) std::reverse(r - cnt, r);
}
template <class T>
std::vector<T> xor_bases(const std::vector<T>& vec) {
	std::vector<T> res;
	for (T i : vec) {
		for (T j : res) {
			chmin(i, i ^ j);
		}
		if (i) res.emplace_back(i);
	}
	return res;
}
#line 3 "basic/type_traits.hpp"

class ModInt__Base {};
class StaticModInt__Base : ModInt__Base {};
class DynamicModInt__Base : ModInt__Base {};

template <class T>
class is_ModInt : public std::is_base_of<ModInt__Base, T> {};
template <class T>
constexpr bool is_ModInt_v = is_ModInt<T>::value;

template <class T>
class is_StaticModInt : public std::is_base_of<StaticModInt__Base, T> {};
template <class T>
constexpr bool is_StaticModInt_v = is_StaticModInt<T>::value;

template <class T>
class is_DynamicModInt : public std::is_base_of<DynamicModInt__Base, T> {};
template <class T>
constexpr bool is_DynamicModInt_v = is_DynamicModInt<T>::value;
#line 4 "math/StaticModInt.hpp"
template <int modulo>
class StaticModInt : StaticModInt__Base {
	uint value;
	static constexpr int inv1000000007[] = {0,		   1,		  500000004, 333333336,
											250000002, 400000003, 166666668, 142857144,
											125000001, 111111112, 700000005},
						 inv998244353[] = {0,		  1,		 499122177, 332748118,
										   748683265, 598946612, 166374059, 855638017,
										   873463809, 443664157, 299473306};

  public:
	static constexpr int mod_value = modulo;

	constexpr StaticModInt() : value(0) {}
	template <class T, std::enable_if_t<!std::is_convertible<T, StaticModInt>::value,
										std::nullptr_t> = nullptr>
	constexpr StaticModInt(T value = 0) : value(value % modulo) {
		if (this->value < 0) this->value += modulo;
	}
	inline constexpr StaticModInt inv() const {
		if constexpr (modulo == 1000000007) {
			if (*this <= 10) return inv1000000007[*this];
		} else if constexpr (modulo == 998244353) {
			if (*this <= 10) return inv998244353[*this];
		}
		return mypow(*this, modulo - 2);
	}
	inline constexpr StaticModInt pow(lint k) const { return mypow(*this, k); }
	inline constexpr operator int() const { return value; }
	inline constexpr StaticModInt& operator+=(const StaticModInt& x) {
		value = value + x.value;
		if (value >= modulo) value -= modulo;
		return *this;
	}
	inline constexpr StaticModInt& operator++() {
		if (value == modulo - 1)
			value = 0;
		else
			value++;
		return *this;
	}
	inline constexpr StaticModInt operator++(int) {
		StaticModInt res = *this;
		++*this;
		return res;
	}
	inline constexpr StaticModInt operator-() const { return StaticModInt(0) -= *this; }
	inline constexpr StaticModInt& operator-=(const StaticModInt& x) {
		if (value < x.value) value += modulo;
		value -= x.value;
		return *this;
	}
	inline constexpr StaticModInt& operator--() {
		if (value == 0)
			value = modulo - 1;
		else
			value--;
		return *this;
	}
	inline constexpr StaticModInt operator--(int) {
		StaticModInt res = *this;
		--*this;
		return res;
	}
	inline constexpr StaticModInt& operator*=(const StaticModInt& x) {
		value = (ulint)value * x.value % modulo;
		return *this;
	}
	inline constexpr StaticModInt& operator/=(const StaticModInt& rhs) {
		return *this *= rhs.inv();
	}
	template <class T>
	constexpr StaticModInt operator+(const T& rhs) const {
		return StaticModInt(*this) += rhs;
	}
	template <class T>
	constexpr StaticModInt& operator+=(const T& rhs) {
		return operator+=(StaticModInt(rhs));
	}
	template <class T>
	constexpr StaticModInt operator-(const T& rhs) const {
		return StaticModInt(*this) -= rhs;
	}
	template <class T>
	constexpr StaticModInt& operator-=(const T& rhs) {
		return operator-=(StaticModInt(rhs));
	}
	template <class T>
	constexpr StaticModInt operator*(const T& rhs) const {
		return StaticModInt(*this) *= rhs;
	}
	template <class T>
	constexpr StaticModInt& operator*=(const T& rhs) {
		return operator*=(StaticModInt(rhs));
	}
	template <class T>
	constexpr StaticModInt operator/(const T& rhs) const {
		return StaticModInt(*this) /= rhs;
	}
	template <class T>
	constexpr StaticModInt& operator/=(const T& rhs) {
		return operator/=(StaticModInt(rhs));
	}
	static StaticModInt primitive_root() {
		if constexpr (modulo == 1012924417) return 5;
		if constexpr (modulo == 924844033) return 5;
		if constexpr (modulo == 998244353) return 3;
		if constexpr (modulo == 1224736769) return 3;
		if constexpr (modulo == 167772161) return 3;
		if constexpr (modulo == 469762049) return 3;
		if constexpr (modulo == 1107296257) return 10;

		int p = 0;
		std::mt19937 mt(0);
		std::uniform_int_distribution<> uid(1, modulo - 1);
		if (p) return p;

		// use naive factorize due to file size limit
		std::vector<int> vec;
		int tmp = modulo - 1;
		for (int i = 2; i * i <= tmp; i++) {
			if (tmp % i == 0) {
				vec.emplace_back(i);
				do {
					tmp /= i;
				} while (tmp % i == 0);
			}
		}
		if (tmp != 1) vec.emplace_back(tmp);

		while (true) {
			p = uid(mt);
			bool f = true;
			for (const auto& i : vec) {
				if (mypow(StaticModInt(p), (modulo - 1) / i) == 1) {
					f = false;
					break;
				}
			}
			if (f) return p;
		}
	}
};
template <int modulo, class Stream>
Stream& operator>>(Stream& ist, StaticModInt<modulo>& x) {
	lint a;
	ist >> a;
	x = a;
	return ist;
}
template <int modulo, class Stream>
Stream& operator<<(Stream& ost, const StaticModInt<modulo>& x) {
	ost << int(x);
	return ost;
}

#if __cplusplus < 201703L
template <int modulo>
constexpr int StaticModInt<modulo>::inv1000000007[];
template <int modulo>
constexpr int StaticModInt<modulo>::inv998244353[];
#endif

/**
 * @title StaticModInt
 */
#line 4 "math/NumberTheoreticTransform.hpp"
// 1012924417, 5, 2^21
// 924844033, 5, 2^21
// 998244353, 3, 2^23
// 1224736769, 3, 2^24
// 167772161, 3, 2^25
// 1107296257, 10, 2^25
// 469762049, 3, 2^26
class NumberTheoreticTransform {
	static int constexpr friendly_limit(int p) { return __builtin_ffs(p - 1) - 1; }

  public:
	template <int modulo>
	static void ntt(std::vector<StaticModInt<modulo>>& a, bool inverse,
					int size = -1) {  // size should be one of powers of two
		if (size == -1) size = a.size();
		if (size == 1) return;
		a.resize(size);
		const StaticModInt<modulo> root = StaticModInt<modulo>::primitive_root().pow(
			inverse ? modulo - 1 - (modulo - 1) / size : (modulo - 1) / size);

		std::vector<StaticModInt<modulo>> b(size);
		StaticModInt<modulo> r_p = root;
		for (int i = size >> 1, w = 1; w < size; i >>= 1, w <<= 1) {
			StaticModInt<modulo> r_pp = 1;
			for (int j = 0; j < i; j++, r_pp *= r_p) {
				for (int k = 0; k < w; k++) {
					b[k + ((w * j) << 1)] = a[k + w * j] + a[k + w * j + (size >> 1)];
					b[k + ((w * j) << 1) + w] = r_pp * (a[k + w * j] - a[k + w * j + (size >> 1)]);
				}
			}
			std::swap(a, b);
			r_p *= r_p;
		}
	}

  private:
	template <class T, int modulo>
	static std::vector<StaticModInt<modulo>> internal_convolution(const std::vector<T>& f_,
																  const std::vector<T>& g_) {
		std::vector<StaticModInt<modulo>> f(f_.size()), g(g_.size());
		rep(i, f_.size()) f[i] = f_[i];
		rep(i, g_.size()) g[i] = g_[i];
		return internal_convolution(std::move(f), std::move(g));
	}
	template <int modulo>
	static std::vector<StaticModInt<modulo>> internal_convolution(
		const std::vector<StaticModInt<modulo>>& f, const std::vector<StaticModInt<modulo>>& g) {
		auto f_ = f, g_ = g;
		return internal_convolution(std::move(f_), std::move(g_));
	}
	template <int modulo>
	static std::vector<StaticModInt<modulo>> internal_convolution(
		const std::vector<StaticModInt<modulo>>& f, std::vector<StaticModInt<modulo>>&& g) {
		auto f_ = f;
		return internal_convolution(std::move(f_), std::move(g));
	}
	template <int modulo>
	static std::vector<StaticModInt<modulo>> internal_convolution(
		std::vector<StaticModInt<modulo>>& f, const std::vector<StaticModInt<modulo>>&& g) {
		auto g_ = g;
		return internal_convolution(std::move(f), std::move(g_));
	}
	template <int modulo>
	static std::vector<StaticModInt<modulo>> internal_convolution(
		std::vector<StaticModInt<modulo>>&& f, std::vector<StaticModInt<modulo>>&& g) {
		size_t target_size = f.size() + g.size() - 1, sz = 1;
		while (sz < target_size) sz <<= 1;
		f.resize(sz), g.resize(sz);
		ntt(f, false), ntt(g, false);
		rep(i, f.size()) f[i] *= g[i];
		ntt(f, true);
		StaticModInt<modulo> inv = StaticModInt<modulo>(sz).inv();
		rep(i, f.size()) f[i] *= inv;
		f.resize(target_size);
		return std::move(f);
	}

  public:
	template <int modulo>
	static std::vector<StaticModInt<modulo>> convolution(
		const std::vector<StaticModInt<modulo>>& f, const std::vector<StaticModInt<modulo>>& g) {
		if (1 << friendly_limit(modulo) >= f.size() + g.size() - 1) {
			auto f_ = f, g_ = g;
			return internal_convolution<modulo>(std::move(f_), std::move(g_));
		} else if (1 << friendly_limit(modulo) + 2 >= f.size() + g.size() - 1) {
			int sz = 1 << friendly_limit(modulo) - 1;
			std::vector<std::vector<StaticModInt<modulo>>> f_, g_;
			for (int i = 0; i * sz < f.size(); i++)
				f_.emplace_back(f.begin() + i * sz,
								f.begin() + std::min((int)f.size(), (i + 1) * sz));
			for (int i = 0; i * sz < g.size(); i++)
				g_.emplace_back(g.begin() + i * sz,
								g.begin() + std::min((int)g.size(), (i + 1) * sz));
			std::vector<StaticModInt<modulo>> res(f.size() + g.size() - 1);
			rep(i, f_.size()) {
				rep(j, g_.size()) {
					auto tmp =
						internal_convolution<modulo>(j == g_.size() - 1 ? std::move(f_[i]) : f_[i],
													 i == f_.size() - 1 ? std::move(g_[j]) : g_[j]);
					rep(k, tmp.size()) res[(i + j) * sz + k] += tmp[k];
				}
			}
			return res;
		}
		constexpr int base1 = 167772161, base2 = 1107296257, base3 = 469762049;
		auto re1 = internal_convolution<StaticModInt<modulo>, base1>(f, g);
		auto re2 = internal_convolution<StaticModInt<modulo>, base2>(f, g);
		auto re3 = internal_convolution<StaticModInt<modulo>, base3>(f, g);
		std::vector<StaticModInt<modulo>> res(re1.size());
		constexpr int r12 = StaticModInt<base2>(base1).inv();
		constexpr int r13 = StaticModInt<base3>(base1).inv();
		constexpr int r23 = StaticModInt<base3>(base2).inv();
		rep(i, re1.size()) {
			re2[i] = StaticModInt<base2>(re2[i] - re1[i]) * r12;
			re3[i] = (StaticModInt<base3>(re3[i] - re1[i]) * r13 - re2[i]) * r23;
			res[i] = StaticModInt<modulo>(re1[i]) + StaticModInt<modulo>(re2[i]) * base1 +
					 StaticModInt<modulo>(re3[i]) * base1 * base2;
		}
		return res;
	}
	template <int modulo, class T>
	static std::vector<StaticModInt<modulo>> convolution(const std::vector<T>& f,
														 const std::vector<T>& g) {
		std::vector<StaticModInt<modulo>> f_(f.size()), g_(g.size());
		rep(i, f.size()) f_[i] = f[i];
		rep(i, g.size()) g_[i] = g[i];
		return convolution(f_, g_);
	}
	template <class T>
	static std::vector<lint> convolution_plain(const std::vector<T>& f, const std::vector<T>& g) {
		const int mod1 = 998244353, mod2 = 1224736769;
		std::vector<StaticModInt<mod1>> mul1 = internal_convolution<T, mod1>(f, g);
		std::vector<StaticModInt<mod2>> mul2 = internal_convolution<T, mod2>(f, g);
		std::vector<lint> res(mul1.size());
		rep(i, mul1.size()) res[i] = ChineseRem(mul1[i], mod1, mul2[i], mod2).first;
		return res;
	}
};

/**
 * @title NumberTheoreticTransform
 */
#line 4 "math/FormalPowerSeries.hpp"

template <class T, std::enable_if_t<is_ModInt_v<T>, std::nullptr_t> = nullptr>
class FormalPowerSeries : public std::vector<T> {
  private:
	using NTT = NumberTheoreticTransform;
	using FPS = FormalPowerSeries<T>;
	using std::vector<T>::vector;

  public:
	FormalPowerSeries(const std::vector<T>& vec) : std::vector<T>(vec) {}

	FPS operator-() const {
		FPS res(*this);
		for (T& i : res) i = -i;
		return res;
	}

	template <class U>
	FPS& operator+=(const U& v) {
		if (this->empty())
			this->emplace_back(v);
		else
			(*this)[0] += v;
		return *this;
	}
	template <class U>
	FPS operator+(const U& v) const {
		FPS res(*this);
		return res += v;
	}
	FPS operator+=(const FPS& f) {
		this->resize(std::max(this->size(), f.size()));
		rep(i, this->size())(*this)[i] += f[i];
		return *this;
	}
	FPS operator+(const FPS& f) const {
		FPS res(*this);
		return res += f;
	}

	template <class U>
	FPS& operator-=(const U& v) {
		if (this->empty())
			this->emplace_back(-v);
		else
			(*this)[0] -= v;
		return *this;
	}
	template <class U>
	FPS operator-(const U& v) const {
		FPS res(*this);
		return res -= v;
	}
	FPS operator-=(const FPS& f) {
		this->resize(std::max(this->size(), f.size()));
		rep(i, std::min(this->size(), f.size()))(*this)[i] -= f[i];
		return *this;
	}
	FPS operator-(const FPS& f) const {
		FPS res(*this);
		return res -= f;
	}

	template <class U>
	FPS& operator*=(const U& v) {
		for (T& i : *this) i *= v;
		return *this;
	}
	template <class U>
	FPS operator*(const U& v) const {
		FPS res(*this);
		return res *= v;
	}
	FPS operator*=(const FPS& f) {
		*this = NTT::convolution(*this, f);
		return *this;
	}
	FPS operator*(const FPS& f) const { return NTT::convolution(*this, f); }

	template <class U>
	FPS& operator/=(const U& v) {
		return *this *= T(v).inv();
	}
	template <class U>
	FPS operator/(const U& v) const {
		return *this * T(v).inv();
	}
	FPS operator/=(const FPS& f) {
		*this = *this * f.inv();
		return *this;
	}
	FPS operator/(const FPS& f) const { return *this * f.inv(); }

	void differentiate() {
		this->erase(this->begin());
		REP(i, this->size())(*this)[i - 1] *= i;
	}
	[[nodiscard]] FPS differential() {
		FPS res = *this;
		res.differentiate();
		return res;
	}

	void integrate() {
		this->insert(this->begin(), 0);
		REP(i, this->size() - 1)(*this)[i] /= i;
	}
	[[nodiscard]] FPS integral() {
		FPS res = *this;
		res.integrate();
		return res;
	}

	void invert() { invert(this->size()); }
	void invert(size_t len) { *this = FPS(len); }
	[[nodiscard]] FPS inv() const { return inv(this->size()); }
	[[nodiscard]] FPS inv(size_t len) const {
		FPS res;
		size_t n = 1;
		res.emplace_back((*this)[0].inv());
		while (n < len) {
			n <<= 1;
			FPS f(n), g(n);
			rep(i, std::min(this->size(), n)) f[i] = (*this)[i];
			rep(i, res.size()) g[i] = res[i];
			NTT::ntt(f, false, n);
			NTT::ntt(g, false, n);
			rep(i, n) f[i] *= g[i];
			NTT::ntt(f, true, n);
			T inv = T(n).inv();
			rep(i, n >> 1) f[i] = 0, f[i + (n >> 1)] *= inv;
			NTT::ntt(f, false, n);
			rep(i, n) f[i] *= g[i];
			NTT::ntt(f, true, n);
			rep(i, n >> 1) f[i + (n >> 1)] *= -inv;
			res.insert(res.end(), f.begin() + (n >> 1), f.begin() + n);
		}
		res.resize(len);
		return std::move(res);
	}

	[[nodiscard]] FPS log() { return log(this->size()); }
	[[nodiscard]] FPS log(size_t len) {
		FPS differentiated = differential();
		FPS tmp = differentiated / *this;
		tmp.resize(len - 1);
		return tmp.integral();
	}

	[[nodiscard]] FPS exp() { return exp(this->size()); }
	[[nodiscard]] FPS exp(size_t len) {
		FPS res(1, 1);
		size_t n = 1;
		while (n < len) {
			n <<= 1;
			auto tmp = *this + 1;
			tmp -= res.log(n);
			res *= tmp;
			res.resize(std::min(len, 2 * n));
		}
		return res;
	}

	[[nodiscard]] FPS pow(lint k) { return pow(k, this->size()); }
	[[nodiscard]] FPS pow(lint k, size_t len) {
		rep(i, len) {
			if (i && (len < k || len < k * i)) break;
			if ((*this)[i]) {
				FPS res = FPS(this->begin() + i, this->end()) / (*this)[i];
				res = (res.log() * k).exp();
				res.resize(len);
				T c = (*this)[i].pow(k);
				for (int j = len - 1; j >= 0; j--) {
					if (i && (j < k || j < k * i))
						res[j] = 0;
					else
						res[j] = res[j - i * k] * c;
				}
				return res;
			}
		}
		FPS res(len);
		if (!k) res[0] = 1;
		return res;
	}
};
#line 5 "test/yosupo/exp_of_formal_power_series.test.cpp"

using ModInt = StaticModInt<998244353>;
using FPS = FormalPowerSeries<ModInt>;
int main() {
	int N;
	FPS vec;
	std::cin >> N >> vec;
	std::cout << vec.exp() << std::endl;
}

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