#line 1 "verify/math/set_power_series_exp.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/exp_of_set_power_series"
#line 1 "math/modint.hpp"
#include <cassert>
#include <cstdint>
#include <iostream>
#include <type_traits>
#include <utility>
namespace m1une {
namespace math {
template <uint32_t Modulus>
struct ModInt {
static_assert(0 < Modulus, "Modulus must be positive");
private:
uint32_t _v;
public:
static constexpr uint32_t mod() {
return Modulus;
}
static constexpr ModInt raw(uint32_t v) noexcept {
ModInt x;
x._v = v;
return x;
}
constexpr ModInt() noexcept : _v(0) {}
template <class Integer, std::enable_if_t<std::is_integral_v<Integer>, int> = 0>
constexpr ModInt(Integer v) noexcept {
if constexpr (std::is_signed_v<Integer>) {
int64_t x = static_cast<int64_t>(v) % static_cast<int64_t>(Modulus);
if (x < 0) x += Modulus;
_v = static_cast<uint32_t>(x);
} else {
_v = static_cast<uint32_t>(static_cast<uint64_t>(v) % Modulus);
}
}
constexpr uint32_t val() const noexcept {
return _v;
}
constexpr ModInt& operator++() noexcept {
_v++;
if (_v == Modulus) _v = 0;
return *this;
}
constexpr ModInt& operator--() noexcept {
if (_v == 0) _v = Modulus;
_v--;
return *this;
}
constexpr ModInt operator++(int) noexcept {
ModInt res = *this;
++*this;
return res;
}
constexpr ModInt operator--(int) noexcept {
ModInt res = *this;
--*this;
return res;
}
constexpr ModInt& operator+=(const ModInt& rhs) noexcept {
_v += rhs._v;
if (_v >= Modulus) _v -= Modulus;
return *this;
}
constexpr ModInt& operator-=(const ModInt& rhs) noexcept {
_v -= rhs._v;
if (_v >= Modulus) _v += Modulus;
return *this;
}
constexpr ModInt& operator*=(const ModInt& rhs) noexcept {
uint64_t z = _v;
z *= rhs._v;
_v = static_cast<uint32_t>(z % Modulus);
return *this;
}
constexpr ModInt& operator/=(const ModInt& rhs) noexcept {
return *this *= rhs.inv();
}
constexpr ModInt operator+(const ModInt& rhs) const noexcept {
return ModInt(*this) += rhs;
}
constexpr ModInt operator-(const ModInt& rhs) const noexcept {
return ModInt(*this) -= rhs;
}
constexpr ModInt operator*(const ModInt& rhs) const noexcept {
return ModInt(*this) *= rhs;
}
constexpr ModInt operator/(const ModInt& rhs) const noexcept {
return ModInt(*this) /= rhs;
}
constexpr bool operator==(const ModInt& rhs) const noexcept {
return _v == rhs._v;
}
constexpr bool operator!=(const ModInt& rhs) const noexcept {
return _v != rhs._v;
}
constexpr ModInt pow(long long n) const noexcept {
ModInt res = raw(1 % Modulus);
ModInt x = n < 0 ? inv() : *this;
uint64_t exponent = n < 0 ? uint64_t(-(n + 1)) + 1 : uint64_t(n);
while (exponent > 0) {
if (exponent & 1) res *= x;
x *= x;
exponent >>= 1;
}
return res;
}
constexpr ModInt inv() const noexcept {
int64_t a = _v, b = Modulus, u = 1, v = 0;
while (b) {
int64_t t = a / b;
a -= t * b;
std::swap(a, b);
u -= t * v;
std::swap(u, v);
}
assert(a == 1);
u %= Modulus;
if (u < 0) u += Modulus;
return raw(static_cast<uint32_t>(u));
}
friend std::ostream& operator<<(std::ostream& os, const ModInt& rhs) {
return os << rhs._v;
}
friend std::istream& operator>>(std::istream& is, ModInt& rhs) {
long long v;
is >> v;
rhs = ModInt(v);
return is;
}
};
using modint998244353 = ModInt<998244353>;
using modint1000000007 = ModInt<1000000007>;
template <int Id = 0>
struct DynamicModInt {
private:
uint32_t _v;
inline static uint32_t _mod = 1;
public:
static uint32_t mod() noexcept {
return _mod;
}
static void set_mod(uint32_t modulus) noexcept {
assert(modulus > 0);
assert(modulus <= uint32_t(1) << 31);
_mod = modulus;
}
static DynamicModInt raw(uint32_t v) noexcept {
assert(v < _mod);
DynamicModInt x;
x._v = v;
return x;
}
DynamicModInt() noexcept : _v(0) {}
template <class Integer, std::enable_if_t<std::is_integral_v<Integer>, int> = 0>
DynamicModInt(Integer v) noexcept {
if constexpr (std::is_signed_v<Integer>) {
int64_t x = static_cast<int64_t>(v) % static_cast<int64_t>(_mod);
if (x < 0) x += _mod;
_v = static_cast<uint32_t>(x);
} else {
_v = static_cast<uint32_t>(static_cast<uint64_t>(v) % _mod);
}
}
uint32_t val() const noexcept {
return _v;
}
DynamicModInt& operator++() noexcept {
_v++;
if (_v == _mod) _v = 0;
return *this;
}
DynamicModInt& operator--() noexcept {
if (_v == 0) _v = _mod;
_v--;
return *this;
}
DynamicModInt operator++(int) noexcept {
DynamicModInt result = *this;
++*this;
return result;
}
DynamicModInt operator--(int) noexcept {
DynamicModInt result = *this;
--*this;
return result;
}
DynamicModInt& operator+=(const DynamicModInt& rhs) noexcept {
_v += rhs._v;
if (_v >= _mod) _v -= _mod;
return *this;
}
DynamicModInt& operator-=(const DynamicModInt& rhs) noexcept {
_v -= rhs._v;
if (_v >= _mod) _v += _mod;
return *this;
}
DynamicModInt& operator*=(const DynamicModInt& rhs) noexcept {
_v = static_cast<uint32_t>(uint64_t(_v) * rhs._v % _mod);
return *this;
}
DynamicModInt& operator/=(const DynamicModInt& rhs) noexcept {
return *this *= rhs.inv();
}
DynamicModInt operator+(const DynamicModInt& rhs) const noexcept {
return DynamicModInt(*this) += rhs;
}
DynamicModInt operator-(const DynamicModInt& rhs) const noexcept {
return DynamicModInt(*this) -= rhs;
}
DynamicModInt operator*(const DynamicModInt& rhs) const noexcept {
return DynamicModInt(*this) *= rhs;
}
DynamicModInt operator/(const DynamicModInt& rhs) const noexcept {
return DynamicModInt(*this) /= rhs;
}
bool operator==(const DynamicModInt& rhs) const noexcept {
return _v == rhs._v;
}
bool operator!=(const DynamicModInt& rhs) const noexcept {
return _v != rhs._v;
}
DynamicModInt pow(long long exponent) const noexcept {
DynamicModInt result = raw(1 % _mod);
DynamicModInt base = exponent < 0 ? inv() : *this;
uint64_t magnitude =
exponent < 0 ? uint64_t(-(exponent + 1)) + 1 : uint64_t(exponent);
while (magnitude > 0) {
if (magnitude & 1) result *= base;
base *= base;
magnitude >>= 1;
}
return result;
}
DynamicModInt inv() const noexcept {
int64_t a = _v, b = _mod, u = 1, v = 0;
while (b) {
int64_t quotient = a / b;
a -= quotient * b;
std::swap(a, b);
u -= quotient * v;
std::swap(u, v);
}
assert(a == 1);
u %= _mod;
if (u < 0) u += _mod;
return raw(static_cast<uint32_t>(u));
}
friend std::ostream& operator<<(std::ostream& os, const DynamicModInt& rhs) {
return os << rhs._v;
}
friend std::istream& operator>>(std::istream& is, DynamicModInt& rhs) {
long long value;
is >> value;
rhs = DynamicModInt(value);
return is;
}
};
} // namespace math
} // namespace m1une
#line 1 "math/set_power_series.hpp"
#include <algorithm>
#include <bit>
#line 7 "math/set_power_series.hpp"
#include <cstddef>
#include <iterator>
#line 10 "math/set_power_series.hpp"
#include <vector>
#line 1 "math/subset_convolution.hpp"
#line 10 "math/subset_convolution.hpp"
namespace m1une {
namespace math {
template <typename T>
std::vector<T> subset_convolution(
std::vector<T> first,
std::vector<T> second
) {
assert(first.size() == second.size());
if (first.empty()) return {};
assert((first.size() & (first.size() - 1)) == 0);
const std::size_t size = first.size();
std::size_t bit_count = 0;
while ((std::size_t(1) << bit_count) < size) ++bit_count;
const std::size_t rank_count = bit_count + 1;
std::vector<T> first_ranked(size * rank_count);
std::vector<T> second_ranked(size * rank_count);
for (std::size_t mask = 0; mask < size; ++mask) {
const std::size_t rank = std::popcount(mask);
first_ranked[mask * rank_count + rank] = std::move(first[mask]);
second_ranked[mask * rank_count + rank] = std::move(second[mask]);
}
for (std::size_t bit = 1; bit < size; bit <<= 1) {
for (std::size_t mask = 0; mask < size; ++mask) {
if ((mask & bit) == 0) continue;
const std::size_t destination = mask * rank_count;
const std::size_t source = (mask ^ bit) * rank_count;
for (std::size_t rank = 0; rank < rank_count; ++rank) {
first_ranked[destination + rank] +=
first_ranked[source + rank];
second_ranked[destination + rank] +=
second_ranked[source + rank];
}
}
}
std::vector<T> product(rank_count);
for (std::size_t mask = 0; mask < size; ++mask) {
for (T& value : product) value = T{};
const std::size_t offset = mask * rank_count;
const std::size_t rank_limit = std::popcount(mask);
for (std::size_t left = 0; left <= rank_limit; ++left) {
const std::size_t right_limit =
std::min(rank_limit, bit_count - left);
for (std::size_t right = 0; right <= right_limit; ++right) {
product[left + right] +=
first_ranked[offset + left] *
second_ranked[offset + right];
}
}
for (std::size_t rank = 0; rank < rank_count; ++rank) {
first_ranked[offset + rank] = std::move(product[rank]);
}
}
for (std::size_t bit = 1; bit < size; bit <<= 1) {
for (std::size_t mask = 0; mask < size; ++mask) {
if ((mask & bit) == 0) continue;
const std::size_t destination = mask * rank_count;
const std::size_t source = (mask ^ bit) * rank_count;
for (std::size_t rank = 0; rank < rank_count; ++rank) {
first_ranked[destination + rank] -=
first_ranked[source + rank];
}
}
}
std::vector<T> result(size);
for (std::size_t mask = 0; mask < size; ++mask) {
result[mask] = std::move(
first_ranked[mask * rank_count + std::popcount(mask)]
);
}
return result;
}
} // namespace math
} // namespace m1une
#line 13 "math/set_power_series.hpp"
namespace m1une {
namespace math {
namespace set_power_series_detail {
inline bool is_power_of_two(std::size_t size) {
return size != 0 && (size & (size - 1)) == 0;
}
template <class T>
std::vector<T> divide(
const std::vector<T>& numerator,
const std::vector<T>& denominator
) {
assert(numerator.size() == denominator.size());
assert(is_power_of_two(numerator.size()));
assert(denominator[0] != T{});
const std::size_t size = numerator.size();
const int bit_count = std::countr_zero(size);
const std::size_t rank_count = std::size_t(bit_count) + 1;
std::vector<T> denominator_ranked(size * rank_count);
std::vector<T> quotient_ranked(size * rank_count);
for (std::size_t mask = 0; mask < size; mask++) {
std::size_t rank = std::popcount(mask);
denominator_ranked[mask * rank_count + rank] = denominator[mask];
}
for (std::size_t bit = 1; bit < size; bit <<= 1) {
for (std::size_t mask = 0; mask < size; mask++) {
if ((mask & bit) == 0) continue;
std::size_t source_mask = mask ^ bit;
std::size_t source = source_mask * rank_count;
std::size_t destination = mask * rank_count;
std::size_t rank_limit = std::popcount(source_mask);
for (std::size_t rank = 0; rank <= rank_limit; rank++) {
denominator_ranked[destination + rank] +=
denominator_ranked[source + rank];
}
}
}
const T inverse_constant = T(1) / denominator[0];
std::vector<T> transformed_product(size);
std::vector<T> quotient(size);
for (int rank = 0; rank <= bit_count; rank++) {
std::fill(
transformed_product.begin(),
transformed_product.end(),
T{}
);
for (std::size_t mask = 0; mask < size; mask++) {
std::size_t offset = mask * rank_count;
for (int left_rank = 0; left_rank <= rank; left_rank++) {
transformed_product[mask] +=
denominator_ranked[offset + left_rank] *
quotient_ranked[offset + rank - left_rank];
}
}
for (std::size_t bit = 1; bit < size; bit <<= 1) {
for (std::size_t mask = 0; mask < size; mask++) {
if (mask & bit) {
transformed_product[mask] -=
transformed_product[mask ^ bit];
}
}
}
for (std::size_t mask = 0; mask < size; mask++) {
if (int(std::popcount(mask)) != rank) continue;
quotient[mask] =
(numerator[mask] - transformed_product[mask]) *
inverse_constant;
quotient_ranked[mask * rank_count + rank] = quotient[mask];
}
for (std::size_t bit = 1; bit < size; bit <<= 1) {
for (std::size_t mask = 0; mask < size; mask++) {
if (mask & bit) {
quotient_ranked[mask * rank_count + rank] +=
quotient_ranked[(mask ^ bit) * rank_count + rank];
}
}
}
}
return quotient;
}
template <class T>
std::vector<T> normalized_power(std::vector<T> series, T exponent) {
assert(is_power_of_two(series.size()));
assert(series[0] == T(1));
std::vector<T> logarithm(series.size());
logarithm[0] = T{};
for (std::size_t half = 1; half < series.size(); half <<= 1) {
std::vector<T> low(series.begin(), series.begin() + half);
std::vector<T> high(
series.begin() + half,
series.begin() + 2 * half
);
std::vector<T> next = divide(high, low);
std::move(next.begin(), next.end(), logarithm.begin() + half);
}
for (T& value : logarithm) value *= exponent;
std::vector<T> result(1, T(1));
result.reserve(series.size());
for (std::size_t half = 1; half < series.size(); half <<= 1) {
std::vector<T> high(
logarithm.begin() + half,
logarithm.begin() + 2 * half
);
std::vector<T> next = subset_convolution(std::move(high), result);
result.insert(
result.end(),
std::make_move_iterator(next.begin()),
std::make_move_iterator(next.end())
);
}
return result;
}
} // namespace set_power_series_detail
// Returns numerator / denominator under subset convolution.
template <class T>
std::vector<T> set_power_series_divide(
const std::vector<T>& numerator,
const std::vector<T>& denominator
) {
return set_power_series_detail::divide(numerator, denominator);
}
template <class T>
std::vector<T> set_power_series_inverse(const std::vector<T>& series) {
assert(set_power_series_detail::is_power_of_two(series.size()));
std::vector<T> identity(series.size());
identity[0] = T(1);
return set_power_series_divide(identity, series);
}
template <class T>
std::vector<T> set_power_series_exp(const std::vector<T>& series) {
assert(set_power_series_detail::is_power_of_two(series.size()));
assert(series[0] == T{});
std::vector<T> result(1, T(1));
result.reserve(series.size());
for (std::size_t half = 1; half < series.size(); half <<= 1) {
std::vector<T> high(
series.begin() + half,
series.begin() + 2 * half
);
std::vector<T> next = subset_convolution(std::move(high), result);
result.insert(
result.end(),
std::make_move_iterator(next.begin()),
std::make_move_iterator(next.end())
);
}
return result;
}
template <class T>
std::vector<T> set_power_series_log(const std::vector<T>& series) {
assert(set_power_series_detail::is_power_of_two(series.size()));
assert(series[0] == T(1));
std::vector<T> result(series.size());
for (std::size_t half = 1; half < series.size(); half <<= 1) {
std::vector<T> low(series.begin(), series.begin() + half);
std::vector<T> high(
series.begin() + half,
series.begin() + 2 * half
);
std::vector<T> next = set_power_series_divide(high, low);
std::move(next.begin(), next.end(), result.begin() + half);
}
return result;
}
template <class T>
std::vector<T> set_power_series_pow(
const std::vector<T>& series,
long long exponent
) {
return set_power_series_detail::normalized_power(
series,
T(exponent)
);
}
template <class T>
std::vector<T> set_power_series_sqrt(const std::vector<T>& series) {
return set_power_series_detail::normalized_power(
series,
T(1) / T(2)
);
}
} // namespace math
} // namespace m1une
#line 1 "utilities/fast_io.hpp"
#line 5 "utilities/fast_io.hpp"
#include <array>
#include <cerrno>
#include <charconv>
#line 9 "utilities/fast_io.hpp"
#include <cstdio>
#include <cstdlib>
#line 12 "utilities/fast_io.hpp"
#include <cstring>
#line 14 "utilities/fast_io.hpp"
#include <string>
#include <sys/stat.h>
#line 18 "utilities/fast_io.hpp"
#include <unistd.h>
#line 20 "utilities/fast_io.hpp"
namespace m1une {
namespace utilities {
struct FastOutput;
namespace internal {
// Shared with the convenience helpers in template.hpp.
inline FastOutput* standard_output_instance = nullptr;
// Detect std::begin(x), std::end(x).
template <class T, class = void>
struct is_range : std::false_type {};
template <class T>
struct is_range<T, std::void_t<
decltype(std::begin(std::declval<T&>())),
decltype(std::end(std::declval<T&>()))
>> : std::true_type {};
template <class T>
inline constexpr bool is_range_v = is_range<T>::value;
template <class T>
using range_reference_t = decltype(*std::begin(std::declval<T&>()));
template <class T>
using range_value_t = std::remove_cv_t<std::remove_reference_t<range_reference_t<T>>>;
template <class T, class = void>
struct range_stored_value {
using type = range_value_t<T>;
};
template <class T>
struct range_stored_value<T, std::void_t<typename std::remove_cv_t<std::remove_reference_t<T>>::value_type>> {
using type = typename std::remove_cv_t<std::remove_reference_t<T>>::value_type;
};
template <class T>
using range_stored_value_t = typename range_stored_value<T>::type;
// Treat strings and C strings as scalar output objects, not as ranges.
template <class T>
struct is_char_array : std::false_type {};
template <class T, std::size_t N>
struct is_char_array<T[N]>
: std::bool_constant<std::is_same_v<std::remove_cv_t<T>, char>> {};
template <class T>
struct is_string_like
: std::bool_constant<
std::is_same_v<std::decay_t<T>, std::string>
|| std::is_same_v<std::decay_t<T>, const char*>
|| std::is_same_v<std::decay_t<T>, char*>
|| is_char_array<std::remove_reference_t<T>>::value
> {};
template <class T>
inline constexpr bool is_string_like_v = is_string_like<T>::value;
// ModInt-like type: x.val() is printable, and x can be assigned from long long.
template <class T, class = void>
struct has_val_method : std::false_type {};
template <class T>
struct has_val_method<T, std::void_t<decltype(std::declval<const T&>().val())>>
: std::true_type {};
template <class T>
inline constexpr bool has_val_method_v = has_val_method<T>::value;
template <class T, class = void>
struct has_static_mod_raw : std::false_type {};
template <class T>
struct has_static_mod_raw<
T, std::void_t<decltype(T::mod()), decltype(T::raw(std::declval<uint32_t>()))>>
: std::true_type {};
template <class T>
inline constexpr bool has_static_mod_raw_v = has_static_mod_raw<T>::value;
// libstdc++ before GCC 16 does not classify __int128 as an integral type in
// strict ISO modes such as -std=c++23. Keep the fast-I/O interface independent
// of that implementation detail.
template <class T>
inline constexpr bool is_integral_v =
std::is_integral_v<T>
|| std::is_same_v<std::remove_cv_t<T>, __int128_t>
|| std::is_same_v<std::remove_cv_t<T>, __uint128_t>;
template <class T>
inline constexpr bool is_signed_v =
std::is_signed_v<T>
|| std::is_same_v<std::remove_cv_t<T>, __int128_t>;
template <class T>
struct make_unsigned {
using type = std::make_unsigned_t<T>;
};
template <>
struct make_unsigned<__int128_t> {
using type = __uint128_t;
};
template <>
struct make_unsigned<__uint128_t> {
using type = __uint128_t;
};
template <class T>
using make_unsigned_t = typename make_unsigned<std::remove_cv_t<T>>::type;
} // namespace internal
struct FastInput {
static constexpr int buffer_size = 1 << 20;
private:
std::FILE* _stream;
char _buffer[buffer_size];
int _position;
int _length;
int _file_descriptor;
bool _streaming;
bool refill() {
_position = 0;
if (_streaming) {
ssize_t length;
do {
length = ::read(_file_descriptor, _buffer, buffer_size);
} while (length < 0 && errno == EINTR);
if (length <= 0) {
_length = 0;
return false;
}
_length = int(length);
} else {
_length = int(std::fread(_buffer, 1, buffer_size, _stream));
}
return _length != 0;
}
template <class T>
bool read_integer_from_stream(T& value) {
if (!skip_spaces()) return false;
int c = read_char_raw();
bool negative = false;
if (c == '-') {
negative = true;
c = read_char_raw();
}
if constexpr (internal::is_signed_v<T>) {
T result = 0;
while ('0' <= c && c <= '9') {
result = negative ? result * 10 - (c - '0')
: result * 10 + (c - '0');
c = read_char_raw();
}
value = result;
} else {
T result = 0;
while ('0' <= c && c <= '9') {
result = result * 10 + T(c - '0');
c = read_char_raw();
}
value = negative ? T(0) - result : result;
}
return true;
}
bool prepare_number() {
if (_length - _position >= 64) return true;
const int remaining = _length - _position;
if (remaining > 0) std::memmove(_buffer, _buffer + _position, remaining);
const int added = int(std::fread(_buffer + remaining, 1, buffer_size - remaining, _stream));
_position = 0;
_length = remaining + added;
if (_length < buffer_size) _buffer[_length] = '\0';
return _length != 0;
}
public:
explicit FastInput(std::FILE* stream = stdin)
: _stream(stream),
_position(0),
_length(0),
_file_descriptor(::fileno(stream)),
_streaming([&] {
struct stat status;
return _file_descriptor >= 0
&& ::fstat(_file_descriptor, &status) == 0
&& !S_ISREG(status.st_mode);
}()) {}
FastInput(const FastInput&) = delete;
FastInput& operator=(const FastInput&) = delete;
int read_char_raw() {
if (_position == _length && !refill()) return EOF;
return _buffer[_position++];
}
bool skip_spaces() {
int c = read_char_raw();
while (c != EOF && c <= ' ') c = read_char_raw();
if (c == EOF) return false;
--_position;
return true;
}
bool read(char& value) {
if (!skip_spaces()) return false;
value = char(read_char_raw());
return true;
}
bool read(std::string& value) {
if (!skip_spaces()) return false;
value.clear();
while (true) {
const int begin = _position;
while (_position < _length &&
static_cast<unsigned char>(_buffer[_position]) > ' ') {
++_position;
}
value.append(_buffer + begin, _position - begin);
if (_position < _length) {
++_position;
return true;
}
if (!refill()) return true;
}
}
bool read(bool& value) {
int x;
if (!read(x)) return false;
value = x != 0;
return true;
}
template <class T>
std::enable_if_t<
internal::is_integral_v<T>
&& !std::is_same_v<std::remove_cv_t<T>, bool>
&& !std::is_same_v<std::remove_cv_t<T>, char>,
bool
>
read(T& value) {
if (_streaming) return read_integer_from_stream(value);
if (!prepare_number()) return false;
int c = static_cast<unsigned char>(_buffer[_position++]);
while (c <= ' ') c = static_cast<unsigned char>(_buffer[_position++]);
bool negative = false;
if (c == '-') {
negative = true;
c = static_cast<unsigned char>(_buffer[_position++]);
}
if constexpr (internal::is_signed_v<T>) {
T result = 0;
while ('0' <= c && c <= '9') {
const int first = c - '0';
const int second = static_cast<unsigned char>(_buffer[_position]) - '0';
if (0 <= second && second <= 9) {
result = negative ? result * 100 - (first * 10 + second)
: result * 100 + (first * 10 + second);
++_position;
} else {
result = negative ? result * 10 - first : result * 10 + first;
}
c = static_cast<unsigned char>(_buffer[_position++]);
}
value = result;
} else {
T result = 0;
while ('0' <= c && c <= '9') {
const unsigned first = unsigned(c - '0');
const int second = static_cast<unsigned char>(_buffer[_position]) - '0';
if (0 <= second && second <= 9) {
result = result * 100 + T(first * 10 + unsigned(second));
++_position;
} else {
result = result * 10 + T(first);
}
c = static_cast<unsigned char>(_buffer[_position++]);
}
value = negative ? T(0) - result : result;
}
if (_position > _length) _position = _length;
return true;
}
template <class T>
std::enable_if_t<std::is_floating_point_v<T>, bool>
read(T& value) {
if (!skip_spaces()) return false;
int c = read_char_raw();
bool negative = false;
if (c == '-' || c == '+') {
negative = c == '-';
c = read_char_raw();
}
long double result = 0;
while ('0' <= c && c <= '9') {
result = result * 10 + (c - '0');
c = read_char_raw();
}
if (c == '.') {
long double place = 0.1L;
c = read_char_raw();
while ('0' <= c && c <= '9') {
result += (c - '0') * place;
place *= 0.1L;
c = read_char_raw();
}
}
if (c == 'e' || c == 'E') {
c = read_char_raw();
bool exponent_negative = false;
if (c == '-' || c == '+') {
exponent_negative = c == '-';
c = read_char_raw();
}
int exponent = 0;
while ('0' <= c && c <= '9') {
exponent = exponent * 10 + (c - '0');
c = read_char_raw();
}
long double scale = 1;
long double power = 10;
while (exponent > 0) {
if (exponent & 1) scale *= power;
power *= power;
exponent >>= 1;
}
result = exponent_negative ? result / scale : result * scale;
}
value = static_cast<T>(negative ? -result : result);
return true;
}
template <class T>
std::enable_if_t<
internal::has_val_method_v<T>
&& !internal::is_integral_v<T>
&& !internal::is_range_v<T>,
bool
>
read(T& value) {
long long x;
if (!read(x)) return false;
if constexpr (internal::has_static_mod_raw_v<T>) {
if (x >= 0 && uint64_t(x) < uint64_t(T::mod())) {
value = T::raw(uint32_t(x));
} else {
value = T(x);
}
} else {
value = T(x);
}
return true;
}
template <class First, class Second>
bool read(std::pair<First, Second>& value) {
if (!read(value.first)) return false;
return read(value.second);
}
template <class Range>
std::enable_if_t<
internal::is_range_v<Range>
&& !internal::is_string_like_v<Range>,
bool
>
read(Range& range) {
using StoredValue = internal::range_stored_value_t<Range>;
constexpr bool nested = internal::is_range_v<StoredValue>
&& !internal::is_string_like_v<StoredValue>;
for (auto&& value : range) {
if constexpr (std::is_same_v<StoredValue, bool> && !nested) {
bool x;
if (!read(x)) return false;
value = x;
} else {
if (!read(value)) return false;
}
}
return true;
}
template <class First, class Second, class... Rest>
bool read(First& first, Second& second, Rest&... rest) {
if (!read(first)) return false;
return read(second, rest...);
}
template <class T>
FastInput& operator>>(T& value) {
if (!read(value)) std::abort();
return *this;
}
};
struct FastOutput {
static constexpr int buffer_size = 1 << 20;
private:
inline static const auto digit_quads = [] {
std::array<char, 40000> result{};
for (int i = 0; i < 10000; i++) {
int value = i;
for (int j = 3; j >= 0; j--) {
result[4 * i + j] = char('0' + value % 10);
value /= 10;
}
}
return result;
}();
std::FILE* _stream;
char _buffer[buffer_size];
int _position;
int _precision;
std::chars_format _float_format;
char _range_separator;
std::string* _capture = nullptr;
template <class T>
std::string format_cell(const T& value) {
std::string result;
struct CaptureGuard {
std::string*& target;
std::string* previous;
~CaptureGuard() { target = previous; }
} guard{_capture, _capture};
_capture = &result;
write(value);
return result;
}
template <class Matrix>
void write_aligned_matrix(const Matrix& matrix) {
std::vector<std::vector<std::string>> rows;
std::vector<std::size_t> widths;
for (const auto& row : matrix) {
auto& cells = rows.emplace_back();
std::size_t column = 0;
for (const auto& value : row) {
cells.push_back(format_cell(value));
if (column == widths.size()) widths.push_back(0);
widths[column] = std::max(widths[column], cells.back().size());
++column;
}
}
bool first = true;
for (const auto& row : rows) {
if (!first) write_char('\n');
first = false;
for (std::size_t column = 0; column < row.size(); ++column) {
if (column != 0) write_char(_range_separator);
for (std::size_t padding = row[column].size();
padding < widths[column]; ++padding) {
write_char(' ');
}
write(row[column]);
}
}
}
public:
explicit FastOutput(std::FILE* stream = stdout)
: _stream(stream),
_position(0),
_precision(6),
_float_format(std::chars_format::general),
_range_separator(' ') {
if (_stream == stdout
&& internal::standard_output_instance == nullptr) {
internal::standard_output_instance = this;
}
}
FastOutput(const FastOutput&) = delete;
FastOutput& operator=(const FastOutput&) = delete;
~FastOutput() {
flush();
if (internal::standard_output_instance == this) {
internal::standard_output_instance = nullptr;
}
}
void flush() {
if (_position != 0) {
std::fwrite(_buffer, 1, _position, _stream);
_position = 0;
}
std::fflush(_stream);
}
void write_char(char c) {
if (_capture != nullptr) {
_capture->push_back(c);
return;
}
if (_position == buffer_size) flush();
_buffer[_position++] = c;
}
void write(const char* s) {
while (*s != '\0') write_char(*s++);
}
void write(const std::string& s) {
if (_capture != nullptr) {
_capture->append(s);
return;
}
std::size_t position = 0;
while (position < s.size()) {
if (_position == buffer_size) flush();
const std::size_t copied =
std::min<std::size_t>(buffer_size - _position, s.size() - position);
std::memcpy(_buffer + _position, s.data() + position, copied);
_position += int(copied);
position += copied;
}
}
void write(char c) {
write_char(c);
}
void write(bool value) {
write_char(value ? '1' : '0');
}
template <class T>
std::enable_if_t<std::is_floating_point_v<T>>
write(T value) {
char digits[128];
auto [end, error] = std::to_chars(
digits,
digits + sizeof(digits),
value,
_float_format,
_precision
);
if (error != std::errc()) std::abort();
for (const char* pointer = digits; pointer != end; pointer++) {
write_char(*pointer);
}
}
template <class T>
std::enable_if_t<
internal::is_integral_v<T>
&& !std::is_same_v<std::remove_cv_t<T>, bool>
&& !std::is_same_v<std::remove_cv_t<T>, char>
>
write(T value) {
using Raw = std::remove_cv_t<T>;
using Unsigned = internal::make_unsigned_t<Raw>;
Unsigned magnitude;
if constexpr (internal::is_signed_v<Raw>) {
if (value < 0) {
write_char('-');
magnitude = Unsigned(0) - Unsigned(value);
} else {
magnitude = Unsigned(value);
}
} else {
magnitude = value;
}
if (magnitude == 0) {
write_char('0');
return;
}
unsigned chunks[16];
int count = 0;
while (magnitude >= 10000) {
const Unsigned quotient = magnitude / 10000;
chunks[count++] = unsigned(magnitude - quotient * 10000);
magnitude = quotient;
}
if (_capture == nullptr && _position > buffer_size - 64) flush();
char captured[64];
char* const begin = _capture != nullptr ? captured : _buffer + _position;
char* destination = begin;
const unsigned leading = unsigned(magnitude);
const char* first = digit_quads.data() + 4 * leading;
int skip = leading < 10 ? 3 : leading < 100 ? 2 : leading < 1000 ? 1 : 0;
for (; skip < 4; skip++) *destination++ = first[skip];
while (count--) {
const char* digits = digit_quads.data() + 4 * chunks[count];
std::memcpy(destination, digits, 4);
destination += 4;
}
if (_capture != nullptr) {
_capture->append(begin, destination - begin);
} else {
_position += int(destination - begin);
}
}
template <class T>
std::enable_if_t<
internal::has_val_method_v<T>
&& !internal::is_integral_v<T>
&& !internal::is_range_v<T>
>
write(const T& value) {
write(value.val());
}
template <class First, class Second>
void write(const std::pair<First, Second>& value) {
write(value.first);
write_char(' ');
write(value.second);
}
template <class Range>
std::enable_if_t<
internal::is_range_v<Range>
&& !internal::is_string_like_v<Range>
>
write(const Range& range) {
using StoredValue = internal::range_stored_value_t<const Range>;
constexpr bool nested = internal::is_range_v<StoredValue>
&& !internal::is_string_like_v<StoredValue>;
bool first = true;
for (const auto& value : range) {
if (!first) write_char(nested ? '\n' : _range_separator);
first = false;
if constexpr (std::is_same_v<StoredValue, bool> && !nested) {
write(static_cast<bool>(value));
} else {
write(value);
}
}
}
template <class First, class... Rest>
void print(const First& first, const Rest&... rest) {
write(first);
((write_char(' '), write(rest)), ...);
}
void println() {
write_char('\n');
}
void set_precision(int precision) {
_precision = precision;
}
void set_fixed(int precision = 6) {
_float_format = std::chars_format::fixed;
_precision = precision;
}
void set_general(int precision = 6) {
_float_format = std::chars_format::general;
_precision = precision;
}
void set_range_separator(char separator) {
_range_separator = separator;
}
template <class Matrix>
void write_aligned(const Matrix& matrix) {
using Row = internal::range_stored_value_t<const Matrix>;
using Cell = internal::range_stored_value_t<const Row>;
static_assert(internal::is_range_v<Row> && !internal::is_string_like_v<Row>,
"write_aligned requires a two-dimensional range");
static_assert(!internal::is_range_v<Cell> || internal::is_string_like_v<Cell>,
"write_aligned requires scalar cells");
write_aligned_matrix(matrix);
}
template <class Matrix>
void println_aligned(const Matrix& matrix) {
write_aligned(matrix);
write_char('\n');
}
template <class... Args>
void println(const Args&... args) {
print(args...);
write_char('\n');
}
template <class T>
FastOutput& operator<<(const T& value) {
write(value);
return *this;
}
};
} // namespace utilities
} // namespace m1une
#line 6 "verify/math/set_power_series_exp.test.cpp"
#line 11 "verify/math/set_power_series_exp.test.cpp"
namespace {
using Mint = m1une::math::modint998244353;
std::vector<Mint> naive_product(
const std::vector<Mint>& first,
const std::vector<Mint>& second
) {
assert(first.size() == second.size());
std::vector<Mint> result(first.size());
for (int mask = 0; mask < int(first.size()); mask++) {
int submask = mask;
while (true) {
result[mask] += first[submask] * second[mask ^ submask];
if (submask == 0) break;
submask = (submask - 1) & mask;
}
}
return result;
}
std::vector<Mint> naive_exp(const std::vector<Mint>& series) {
int bit_count = std::countr_zero(series.size());
std::vector<Mint> result(series.size());
std::vector<Mint> power(series.size());
power[0] = 1;
Mint factorial = 1;
for (int exponent = 0; exponent <= bit_count; exponent++) {
if (exponent > 0) factorial *= exponent;
Mint inverse_factorial = Mint(1) / factorial;
for (int mask = 0; mask < int(series.size()); mask++) {
result[mask] += power[mask] * inverse_factorial;
}
power = naive_product(power, series);
}
return result;
}
void test_randomized() {
std::uint64_t state = 0x9e3779b97f4a7c15ULL;
auto random = [&]() {
state ^= state << 7;
state ^= state >> 9;
return state;
};
for (int trial = 0; trial < 300; trial++) {
int bit_count = int(random() % 6);
int size = 1 << bit_count;
std::vector<Mint> logarithm(size);
logarithm[0] = 0;
for (int mask = 1; mask < size; mask++) logarithm[mask] = random();
std::vector<Mint> series =
m1une::math::set_power_series_exp(logarithm);
assert(series == naive_exp(logarithm));
assert(m1une::math::set_power_series_log(series) == logarithm);
std::vector<Mint> quotient(size), denominator(size);
denominator[0] = Mint(random() % 998244352ULL + 1);
for (int mask = 0; mask < size; mask++) quotient[mask] = random();
for (int mask = 1; mask < size; mask++) denominator[mask] = random();
std::vector<Mint> numerator = naive_product(quotient, denominator);
assert(
m1une::math::set_power_series_divide(numerator, denominator) ==
quotient
);
std::vector<Mint> inverse =
m1une::math::set_power_series_inverse(denominator);
std::vector<Mint> identity(size);
identity[0] = 1;
assert(naive_product(denominator, inverse) == identity);
std::vector<Mint> normalized = series;
std::vector<Mint> cube = naive_product(
naive_product(normalized, normalized),
normalized
);
assert(m1une::math::set_power_series_pow(normalized, 3) == cube);
assert(
naive_product(
normalized,
m1une::math::set_power_series_pow(normalized, -1)
) == identity
);
assert(m1une::math::set_power_series_pow(normalized, 0) == identity);
std::vector<Mint> square = naive_product(normalized, normalized);
std::vector<Mint> root =
m1une::math::set_power_series_sqrt(square);
assert(naive_product(root, root) == square);
}
}
} // namespace
int main() {
m1une::utilities::FastInput fast_input;
m1une::utilities::FastOutput fast_output;
test_randomized();
int bit_count = 0;
fast_input >> bit_count;
int size = 1 << bit_count;
std::vector<Mint> series(size);
for (Mint& value : series) fast_input >> value;
std::vector<Mint> result = m1une::math::set_power_series_exp(series);
for (int mask = 0; mask < size; mask++) {
if (mask != 0) fast_output << ' ';
fast_output << result[mask].val();
}
fast_output << '\n';
}
verify/math/set_power_series_exp.test.cpp