結果
| 問題 |
No.344 ある無理数の累乗
|
| コンテスト | |
| ユーザー |
 jell
|
| 提出日時 | 2021-01-11 15:30:20 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 2 ms / 2,000 ms |
| コード長 | 42,539 bytes |
| コンパイル時間 | 3,712 ms |
| コンパイル使用メモリ | 253,836 KB |
| 最終ジャッジ日時 | 2025-01-17 16:10:07 |
|
ジャッジサーバーID （参考情報） |
judge5 / judge5 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| other | AC * 30 |
ソースコード
#line 1 "atcoder-workspace/a.cc"
// #undef _GLIBCXX_DEBUG
// #define NDEBUG
#include <bits/extc++.h>
#line 2 "Library/src/modular/inverse.hpp"
/*
* @file inverse.hpp
* @brief Inverse Table
*/
#line 9 "Library/src/modular/inverse.hpp"
#line 2 "Library/src/modular/modint.hpp"
/**
* @file modint.hpp
*
* @brief Modular Arithmetic
*/
#line 12 "Library/src/modular/modint.hpp"
#line 2 "Library/src/utils/sfinae.hpp"
/*
* @file sfinae.hpp
* @brief SFINAE
*/
#line 10 "Library/src/utils/sfinae.hpp"
#include <type_traits>
#ifdef __SIZEOF_INT128__
#define __INT128_DEFINED__ 1
#else
#define __INT128_DEFINED__ 0
#endif
namespace std {
#if __INT128_DEFINED__
template <> struct make_signed<__uint128_t> { using type = __int128_t; };
template <> struct make_signed<__int128_t> { using type = __int128_t; };
template <> struct make_unsigned<__uint128_t> { using type = __uint128_t; };
template <> struct make_unsigned<__int128_t> { using type = __uint128_t; };
#endif
} // namespace std
namespace workspace {
template <class type, template <class> class trait>
using enable_if_trait_type = typename std::enable_if<trait<type>::value>::type;
template <class Container>
using element_type = typename std::decay<decltype(
*std::begin(std::declval<Container&>()))>::type;
template <class T, class = std::nullptr_t>
struct has_begin : std::false_type {};
template <class T>
struct has_begin<T, decltype(std::begin(std::declval<T>()), nullptr)>
: std::true_type {};
template <class T, class = int> struct mapped_of {
using type = element_type<T>;
};
template <class T>
struct mapped_of<T,
typename std::pair<int, typename T::mapped_type>::first_type> {
using type = typename T::mapped_type;
};
template <class T> using mapped_type = typename mapped_of<T>::type;
template <class T, class = void> struct is_integral_ext : std::false_type {};
template <class T>
struct is_integral_ext<
T, typename std::enable_if<std::is_integral<T>::value>::type>
: std::true_type {};
#if __INT128_DEFINED__
template <> struct is_integral_ext<__int128_t> : std::true_type {};
template <> struct is_integral_ext<__uint128_t> : std::true_type {};
#endif
#if __cplusplus >= 201402
template <class T>
constexpr static bool is_integral_ext_v = is_integral_ext<T>::value;
#endif
template <typename T, typename = void> struct multiplicable_uint {
using type = uint_least32_t;
};
template <typename T>
struct multiplicable_uint<
T, typename std::enable_if<(2 < sizeof(T)) &&
(!__INT128_DEFINED__ || sizeof(T) <= 4)>::type> {
using type = uint_least64_t;
};
#if __INT128_DEFINED__
template <typename T>
struct multiplicable_uint<T, typename std::enable_if<(4 < sizeof(T))>::type> {
using type = __uint128_t;
};
#endif
} // namespace workspace
#line 14 "Library/src/modular/modint.hpp"
namespace workspace {
namespace internal {
/**
* @brief Base of modular arithmetic.
*
* @tparam Mod identifier, which represents modulus if positive
* @tparam Storage Reserved size for inverse calculation
*/
template <auto Mod, unsigned Storage> struct modint_base {
static_assert(is_integral_ext<decltype(Mod)>::value,
"Mod must be integral type.");
using mod_type = typename std::make_signed<typename std::conditional<
0 < Mod, typename std::add_const<decltype(Mod)>::type,
decltype(Mod)>::type>::type;
using value_type = typename std::decay<mod_type>::type;
using mul_type = typename multiplicable_uint<value_type>::type;
static mod_type mod;
static value_type storage;
constexpr static void reserve(unsigned __n) noexcept { storage = __n; }
protected:
value_type value = 0;
public:
constexpr modint_base() noexcept = default;
template <class int_type,
typename std::enable_if<is_integral_ext<int_type>::value>::type * =
nullptr>
constexpr modint_base(int_type n) noexcept
: value((n %= mod) < 0 ? n += mod : n) {}
constexpr modint_base(bool n) noexcept : value(n) {}
constexpr operator value_type() const noexcept { return value; }
constexpr static modint_base one() noexcept { return 1; }
// unary operators {{
constexpr modint_base operator++(int) noexcept {
modint_base __t{*this};
operator++();
return __t;
}
constexpr modint_base operator--(int) noexcept {
modint_base __t{*this};
operator--();
return __t;
}
constexpr modint_base &operator++() noexcept {
if (++value == mod) value = 0;
return *this;
}
constexpr modint_base &operator--() noexcept {
if (!value) value = mod;
--value;
return *this;
}
constexpr modint_base operator-() const noexcept {
modint_base __t;
__t.value = value ? mod - value : 0;
return __t;
}
// }} unary operators
// operator+= {{
constexpr modint_base &operator+=(modint_base const &rhs) noexcept {
if ((value += rhs.value) >= mod) value -= mod;
return *this;
}
template <class int_type>
constexpr typename std::enable_if<is_integral_ext<int_type>::value,
modint_base>::type &
operator+=(int_type const &rhs) noexcept {
if (((value += rhs) %= mod) < 0) value += mod;
return *this;
}
// }} operator+=
// operator+ {{
template <class int_type>
constexpr typename std::enable_if<is_integral_ext<int_type>::value,
modint_base>::type
operator+(int_type const &rhs) const noexcept {
return modint_base{*this} += rhs;
}
constexpr modint_base operator+(modint_base rhs) const noexcept {
return rhs += *this;
}
template <class int_type>
constexpr friend typename std::enable_if<is_integral_ext<int_type>::value,
modint_base>::type
operator+(int_type const &lhs, modint_base rhs) noexcept {
return rhs += lhs;
}
// }} operator+
// operator-= {{
constexpr modint_base &operator-=(modint_base const &rhs) noexcept {
if ((value -= rhs.value) < 0) value += mod;
return *this;
}
template <class int_type>
constexpr typename std::enable_if<is_integral_ext<int_type>::value,
modint_base>::type &
operator-=(int_type rhs) noexcept {
if (((value -= rhs) %= mod) < 0) value += mod;
return *this;
}
// }} operator-=
// operator- {{
template <class int_type>
constexpr typename std::enable_if<is_integral_ext<int_type>::value,
modint_base>::type
operator-(int_type const &rhs) const noexcept {
return modint_base{*this} -= rhs;
}
constexpr modint_base operator-(modint_base const &rhs) const noexcept {
modint_base __t;
if (((__t.value = value) -= rhs.value) < 0) __t.value += mod;
return __t;
}
template <class int_type>
constexpr friend typename std::enable_if<is_integral_ext<int_type>::value,
modint_base>::type
operator-(int_type lhs, modint_base const &rhs) noexcept {
if (((lhs -= rhs.value) %= mod) < 0) lhs += mod;
modint_base __t;
__t.value = lhs;
return __t;
}
// }} operator-
// operator*= {{
constexpr modint_base &operator*=(modint_base const &rhs) noexcept {
if (!rhs.value) {
value = 0;
} else if (value) {
mul_type __r(value);
value = static_cast<value_type>((__r *= rhs.value) %= mod);
}
return *this;
}
template <class int_type>
constexpr typename std::enable_if<is_integral_ext<int_type>::value,
modint_base>::type &
operator*=(int_type rhs) noexcept {
if (!rhs)
value = 0;
else if (value) {
if ((rhs %= mod) < 0) rhs += mod;
mul_type __r(value);
value = static_cast<value_type>((__r *= rhs) %= mod);
}
return *this;
}
// }} operator*=
// operator* {{
constexpr modint_base operator*(modint_base const &rhs) const noexcept {
if (!value or !rhs.value) return {};
mul_type __r(value);
modint_base __t;
__t.value = static_cast<value_type>((__r *= rhs.value) %= mod);
return __t;
}
template <class int_type>
constexpr typename std::enable_if<is_integral_ext<int_type>::value,
modint_base>::type
operator*(int_type rhs) const noexcept {
if (!value or !rhs) return {};
if ((rhs %= mod) < 0) rhs += mod;
mul_type __r(value);
modint_base __t;
__t.value = static_cast<value_type>((__r *= rhs) %= mod);
return __t;
}
template <class int_type>
constexpr friend typename std::enable_if<is_integral_ext<int_type>::value,
modint_base>::type
operator*(int_type lhs, modint_base const &rhs) noexcept {
if (!lhs or !rhs.value) return {};
if ((lhs %= mod) < 0) lhs += mod;
mul_type __r(lhs);
modint_base __t;
__t.value = (__r *= rhs.value) %= mod;
return __t;
}
// }} operator*
protected:
static value_type _mem(value_type __x) {
static std::vector<value_type> __m{0, 1};
static value_type __i = (__m.reserve(Storage), 1);
while (__i < __x) {
++__i;
__m.emplace_back(mod - mul_type(mod / __i) * __m[mod % __i] % mod);
}
return __m[__x];
}
template <class int_type>
constexpr static typename std::enable_if<is_integral_ext<int_type>::value,
value_type>::type
_div(mul_type __r, int_type __x) noexcept {
assert(__x);
if (!__r) return 0;
int_type __v{};
bool __neg = __x < 0 ? __x = -__x, true : false;
if (__x < storage) {
__v = _mem(__x);
} else {
int_type __y{mod}, __u{1}, __t;
while (__x)
__t = __y / __x, __y ^= __x ^= (__y -= __t * __x) ^= __x,
__v ^= __u ^= (__v -= __t * __u) ^= __u;
if (__y < 0) __neg ^= 1;
}
if (__neg)
__v = 0 < __v ? mod - __v : -__v;
else if (__v < 0)
__v += mod;
if (__r == 1) return static_cast<value_type>(__v);
return static_cast<value_type>((__r *= __v) %= mod);
}
public:
// operator/= {{
constexpr modint_base &operator/=(modint_base const &rhs) noexcept {
if (value) value = _div(value, rhs.value);
return *this;
}
template <class int_type>
constexpr typename std::enable_if<is_integral_ext<int_type>::value,
modint_base>::type &
operator/=(int_type rhs) noexcept {
if (value) value = _div(value, rhs %= mod);
return *this;
}
// }} operator/=
// operator/ {{
constexpr modint_base operator/(modint_base const &rhs) const noexcept {
if (!value) return {};
modint_base __t;
__t.value = _div(value, rhs.value);
return __t;
}
template <class int_type>
constexpr typename std::enable_if<is_integral_ext<int_type>::value,
modint_base>::type
operator/(int_type rhs) const noexcept {
if (!value) return {};
modint_base __t;
__t.value = _div(value, rhs %= mod);
return __t;
}
template <class int_type>
constexpr friend typename std::enable_if<is_integral_ext<int_type>::value,
modint_base>::type
operator/(int_type lhs, modint_base const &rhs) noexcept {
if (!lhs) return {};
if ((lhs %= mod) < 0) lhs += mod;
modint_base __t;
__t.value = _div(lhs, rhs.value);
return __t;
}
// }} operator/
constexpr modint_base inv() const noexcept { return _div(1, value); }
template <class int_type>
friend constexpr typename std::enable_if<is_integral_ext<int_type>::value,
modint_base>::type
pow(modint_base b, int_type e) noexcept {
if (e < 0) {
e = -e;
b.value = _div(1, b.value);
}
modint_base __r;
for (__r.value = 1; e; e >>= 1, b *= b)
if (e & 1) __r *= b;
return __r;
}
template <class int_type>
constexpr typename std::enable_if<is_integral_ext<int_type>::value,
modint_base>::type
pow(int_type e) const noexcept {
modint_base __r, b;
__r.value = 1;
for (b.value = e < 0 ? e = -e, _div(1, value) : value; e; e >>= 1, b *= b)
if (e & 1) __r *= b;
return __r;
}
friend std::ostream &operator<<(std::ostream &os,
const modint_base &rhs) noexcept {
return os << rhs.value;
}
friend std::istream &operator>>(std::istream &is, modint_base &rhs) noexcept {
intmax_t value;
rhs = (is >> value, value);
return is;
}
};
template <auto Mod, unsigned Storage>
typename modint_base<Mod, Storage>::mod_type modint_base<Mod, Storage>::mod =
Mod > 0 ? Mod : 0;
template <auto Mod, unsigned Storage>
typename modint_base<Mod, Storage>::value_type
modint_base<Mod, Storage>::storage = Storage;
} // namespace internal
/**
* @brief Modular arithmetic.
*
* @tparam Mod modulus
* @tparam Storage Reserved size for inverse calculation
*/
template <auto Mod, unsigned Storage = 0,
typename std::enable_if<(Mod > 0)>::type * = nullptr>
using modint = internal::modint_base<Mod, Storage>;
/**
* @brief Runtime modular arithmetic.
*
* @tparam type_id uniquely assigned
* @tparam Storage Reserved size for inverse calculation
*/
template <unsigned type_id = 0, unsigned Storage = 0>
using modint_runtime = internal::modint_base<-(signed)type_id, Storage>;
// #define modint_newtype modint_runtime<__COUNTER__>
} // namespace workspace
#line 11 "Library/src/modular/inverse.hpp"
namespace workspace {
// Modulus must be prime.
template <class Modint> struct inverse_table {
static_assert(std::is_same<std::nullptr_t,
decltype((void *)Modint::mod, nullptr)>::value);
using value_type = Modint;
constexpr value_type operator()(int n) const {
constexpr int_fast64_t mod = value_type::mod;
assert(n %= mod);
if (n < 0) n += mod;
if (inv.empty()) inv = {1, mod != 1};
for (int m(inv.size()); m <= n; ++m)
inv.emplace_back(mod / m * -inv[mod % m]);
return inv[n];
}
private:
static std::vector<value_type> inv;
};
template <class Modint> std::vector<Modint> inverse_table<Modint>::inv;
} // namespace workspace
#line 2 "Library/src/utils/cat.hpp"
/**
* @file cat.hpp
* @brief Cat
*/
#line 9 "Library/src/utils/cat.hpp"
namespace workspace {
template <class C1, class C2>
constexpr C1 &&cat(C1 &&__c1, C2 const &__c2) noexcept {
__c1.insert(__c1.end(), std::begin(__c2), std::end(__c2));
return __c1;
}
} // namespace workspace
#line 2 "Library/src/utils/chval.hpp"
/*
* @file chval.hpp
* @brief Change Less/Greater
*/
#line 9 "Library/src/utils/chval.hpp"
namespace workspace {
/*
* @fn chle
* @brief Substitute y for x if comp(y, x) is true.
* @param x Reference
* @param y Const reference
* @param comp Compare function
* @return Whether or not x is updated
*/
template <class Tp, class Comp = std::less<Tp>>
bool chle(Tp &x, const Tp &y, Comp comp = Comp()) {
return comp(y, x) ? x = y, true : false;
}
/*
* @fn chge
* @brief Substitute y for x if comp(x, y) is true.
* @param x Reference
* @param y Const reference
* @param comp Compare function
* @return Whether or not x is updated
*/
template <class Tp, class Comp = std::less<Tp>>
bool chge(Tp &x, const Tp &y, Comp comp = Comp()) {
return comp(x, y) ? x = y, true : false;
}
} // namespace workspace
#line 2 "Library/src/utils/fixed_point.hpp"
/*
* @file fixed_point.hpp
* @brief Fixed Point Combinator
*/
#line 9 "Library/src/utils/fixed_point.hpp"
namespace workspace {
/*
* @class fixed_point
* @brief Recursive calling of lambda expression.
*/
template <class lambda_type> class fixed_point {
lambda_type func;
public:
/*
* @param func 1st arg callable with the rest of args, and the return type
* specified.
*/
fixed_point(lambda_type &&func) : func(std::move(func)) {}
/*
* @brief Recursively apply *this to 1st arg of func.
* @param args Arguments of the recursive method.
*/
template <class... Args> auto operator()(Args &&... args) const {
return func(*this, std::forward<Args>(args)...);
}
};
} // namespace workspace
#line 2 "Library/src/utils/grid.hpp"
/**
* @file grid.hpp
* @brief Grid
* @date 2021-01-09
*/
#line 10 "Library/src/utils/grid.hpp"
namespace workspace {
template <class Grid> Grid transpose(Grid const &grid) {
Grid __t;
for (auto &&__r : grid) {
auto __i = std::begin(__t);
for (auto &&__x : __r) {
if (__i == std::end(__t))
__i = __t.insert(__t.end(), typename std::decay<decltype(__r)>::type{});
__i->insert(__i->end(), __x);
++__i;
}
}
return __t;
}
// template <class _Tp, size_t _Row, size_t _Col>
// std::array<std::array<_Tp, _Row>, _Col> transpose(_Tp (&__g)[_Row][_Col]) {}
template <class Grid> Grid roll_ccw(Grid const &grid) {
auto __t = transpose(grid);
std::reverse(std::begin(__t), std::end(__t));
return __t;
}
template <class Grid> Grid roll_cw(Grid const &grid) {
auto __t = grid;
std::reverse(std::begin(__t), std::end(__t));
return transpose(__t);
}
} // namespace workspace
#line 2 "Library/src/utils/hash.hpp"
#line 8 "Library/src/utils/hash.hpp"
#line 10 "Library/src/utils/hash.hpp"
namespace workspace {
template <class T, class = void> struct hash : std::hash<T> {};
#if __cplusplus >= 201703L
template <class Unique_bits_type>
struct hash<Unique_bits_type,
enable_if_trait_type<Unique_bits_type,
std::has_unique_object_representations>> {
size_t operator()(uint64_t x) const {
static const uint64_t m = std::random_device{}();
x ^= x >> 23;
x ^= m;
x ^= x >> 47;
return x - (x >> 32);
}
};
#endif
template <class Key> size_t hash_combine(const size_t &seed, const Key &key) {
return seed ^
(hash<Key>()(key) + 0x9e3779b9 /* + (seed << 6) + (seed >> 2) */);
}
template <class T1, class T2> struct hash<std::pair<T1, T2>> {
size_t operator()(const std::pair<T1, T2> &pair) const {
return hash_combine(hash<T1>()(pair.first), pair.second);
}
};
template <class... T> class hash<std::tuple<T...>> {
template <class Tuple, size_t index = std::tuple_size<Tuple>::value - 1>
struct tuple_hash {
static uint64_t apply(const Tuple &t) {
return hash_combine(tuple_hash<Tuple, index - 1>::apply(t),
std::get<index>(t));
}
};
template <class Tuple> struct tuple_hash<Tuple, size_t(-1)> {
static uint64_t apply(const Tuple &t) { return 0; }
};
public:
uint64_t operator()(const std::tuple<T...> &t) const {
return tuple_hash<std::tuple<T...>>::apply(t);
}
};
template <class hash_table> struct hash_table_wrapper : hash_table {
using key_type = typename hash_table::key_type;
size_t count(const key_type &key) const {
return hash_table::find(key) != hash_table::end();
}
template <class... Args> auto emplace(Args &&... args) {
return hash_table::insert(typename hash_table::value_type(args...));
}
};
template <class Key, class Mapped = __gnu_pbds::null_type>
using cc_hash_table =
hash_table_wrapper<__gnu_pbds::cc_hash_table<Key, Mapped, hash<Key>>>;
template <class Key, class Mapped = __gnu_pbds::null_type>
using gp_hash_table =
hash_table_wrapper<__gnu_pbds::gp_hash_table<Key, Mapped, hash<Key>>>;
template <class Key, class Mapped>
using unordered_map = std::unordered_map<Key, Mapped, hash<Key>>;
template <class Key> using unordered_set = std::unordered_set<Key, hash<Key>>;
} // namespace workspace
#line 2 "Library/src/utils/io/istream.hpp"
/**
* @file istream.hpp
* @brief Input Stream
*/
#include <cxxabi.h>
#line 13 "Library/src/utils/io/istream.hpp"
#line 15 "Library/src/utils/io/istream.hpp"
namespace workspace {
namespace internal {
template <class Tp, typename = std::nullptr_t> struct istream_helper {
istream_helper(std::istream &is, Tp &x) {
if constexpr (has_begin<Tp>::value)
for (auto &&e : x)
istream_helper<typename std::decay<decltype(e)>::type>(is, e);
else
static_assert(has_begin<Tp>::value, "istream unsupported type.");
}
};
template <class Tp>
struct istream_helper<
Tp,
decltype(std::declval<std::decay<decltype(std::declval<std::istream &>() >>
std::declval<Tp &>())>>(),
nullptr)> {
istream_helper(std::istream &is, Tp &x) { is >> x; }
};
#ifdef __SIZEOF_INT128__
template <> struct istream_helper<__int128_t, std::nullptr_t> {
istream_helper(std::istream &is, __int128_t &x) {
std::string s;
is >> s;
bool negative = s.front() == '-' ? s.erase(s.begin()), true : false;
x = 0;
for (char e : s) x = x * 10 + e - '0';
if (negative) x = -x;
}
};
template <> struct istream_helper<__uint128_t, std::nullptr_t> {
istream_helper(std::istream &is, __uint128_t &x) {
std::string s;
is >> s;
bool negative = s.front() == '-' ? s.erase(s.begin()), true : false;
x = 0;
for (char e : s) x = x * 10 + e - '0';
if (negative) x = -x;
}
};
#endif // INT128
template <class T1, class T2> struct istream_helper<std::pair<T1, T2>> {
istream_helper(std::istream &is, std::pair<T1, T2> &x) {
istream_helper<T1>(is, x.first), istream_helper<T2>(is, x.second);
}
};
template <class... Tps> struct istream_helper<std::tuple<Tps...>> {
istream_helper(std::istream &is, std::tuple<Tps...> &x) { iterate(is, x); }
private:
template <class Tp, size_t N = 0> void iterate(std::istream &is, Tp &x) {
if constexpr (N == std::tuple_size<Tp>::value)
return;
else
istream_helper<typename std::tuple_element<N, Tp>::type>(is,
std::get<N>(x)),
iterate<Tp, N + 1>(is, x);
}
};
} // namespace internal
/**
* @brief A wrapper class for std::istream.
*/
class istream : public std::istream {
public:
/**
* @brief Wrapped operator.
*/
template <typename Tp> istream &operator>>(Tp &x) {
internal::istream_helper<Tp>(*this, x);
if (std::istream::fail()) {
static auto once = atexit([] {
std::cerr << "\n\033[43m\033[30mwarning: failed to read \'"
<< abi::__cxa_demangle(typeid(Tp).name(), 0, 0, 0)
<< "\'.\033[0m\n\n";
});
assert(!once);
}
return *this;
}
};
namespace internal {
auto *const cin_ptr = (istream *)&std::cin;
}
auto &cin = *internal::cin_ptr;
} // namespace workspace
#line 2 "Library/src/utils/io/ostream.hpp"
/*
* @file ostream.hpp
* @brief Output Stream
*/
#line 10 "Library/src/utils/io/ostream.hpp"
namespace workspace {
template <class T, class U>
std::ostream &operator<<(std::ostream &os, const std::pair<T, U> &p) {
return os << p.first << ' ' << p.second;
}
template <class tuple_t, size_t index> struct tuple_os {
static std::ostream &apply(std::ostream &os, const tuple_t &t) {
tuple_os<tuple_t, index - 1>::apply(os, t);
return os << ' ' << std::get<index>(t);
}
};
template <class tuple_t> struct tuple_os<tuple_t, 0> {
static std::ostream &apply(std::ostream &os, const tuple_t &t) {
return os << std::get<0>(t);
}
};
template <class tuple_t> struct tuple_os<tuple_t, SIZE_MAX> {
static std::ostream &apply(std::ostream &os, const tuple_t &t) { return os; }
};
template <class... T>
std::ostream &operator<<(std::ostream &os, const std::tuple<T...> &t) {
return tuple_os<std::tuple<T...>,
std::tuple_size<std::tuple<T...>>::value - 1>::apply(os, t);
}
template <class Container,
typename = decltype(std::begin(std::declval<Container>()))>
typename std::enable_if<
!std::is_same<typename std::decay<Container>::type, std::string>::value &&
!std::is_same<typename std::decay<Container>::type, char *>::value,
std::ostream &>::type
operator<<(std::ostream &os, const Container &cont) {
bool head = true;
for (auto &&e : cont) head ? head = 0 : (os << ' ', 0), os << e;
return os;
}
} // namespace workspace
#line 9 "Library/lib\\utils"
// #include "src/utils/io/read.hpp"
#line 2 "Library/src/utils/io/setup.hpp"
/*
* @file setup.hpp
* @brief I/O Setup
*/
#line 10 "Library/src/utils/io/setup.hpp"
namespace workspace {
/*
* @fn io_setup
* @brief Setup I/O.
* @param precision Standard output precision
*/
void io_setup(int precision) {
std::ios::sync_with_stdio(false);
std::cin.tie(nullptr);
std::cout << std::fixed << std::setprecision(precision);
#ifdef _buffer_check
atexit([] {
char bufc;
if (std::cin >> bufc)
std::cerr << "\n\033[43m\033[30mwarning: buffer not empty.\033[0m\n\n";
});
#endif
}
} // namespace workspace
#line 2 "Library/src/utils/iterator/category.hpp"
/*
* @file category.hpp
* @brief Iterator Category
*/
#line 10 "Library/src/utils/iterator/category.hpp"
namespace workspace {
/*
* @tparam Tuple Tuple of iterator types
*/
template <class Tuple, size_t N = std::tuple_size<Tuple>::value - 1>
struct common_iterator_category {
using type = typename std::common_type<
typename common_iterator_category<Tuple, N - 1>::type,
typename std::iterator_traits<typename std::tuple_element<
N, Tuple>::type>::iterator_category>::type;
};
template <class Tuple> struct common_iterator_category<Tuple, 0> {
using type = typename std::iterator_traits<
typename std::tuple_element<0, Tuple>::type>::iterator_category;
};
} // namespace workspace
#line 2 "Library/src/utils/iterator/reverse.hpp"
/*
* @file reverse_iterator.hpp
* @brief Reverse Iterator
*/
#if __cplusplus >= 201703L
#include <iterator>
#include <optional>
namespace workspace {
/*
* @class reverse_iterator
* @brief Wrapper class for `std::reverse_iterator`.
* @see http://gcc.gnu.org/PR51823
*/
template <class Iterator>
class reverse_iterator : public std::reverse_iterator<Iterator> {
using base_std = std::reverse_iterator<Iterator>;
std::optional<typename base_std::value_type> deref;
public:
using base_std::reverse_iterator;
constexpr typename base_std::reference operator*() noexcept {
if (!deref) {
Iterator tmp = base_std::current;
deref = *--tmp;
}
return deref.value();
}
constexpr reverse_iterator &operator++() noexcept {
base_std::operator++();
deref.reset();
return *this;
}
constexpr reverse_iterator &operator--() noexcept {
base_std::operator++();
deref.reset();
return *this;
}
constexpr reverse_iterator operator++(int) noexcept {
base_std::operator++();
deref.reset();
return *this;
}
constexpr reverse_iterator operator--(int) noexcept {
base_std::operator++();
deref.reset();
return *this;
}
};
} // namespace workspace
#endif
#line 2 "Library/src/utils/make_vector.hpp"
/*
* @file make_vector.hpp
* @brief Multi-dimensional Vector
*/
#if __cplusplus >= 201703L
#include <tuple>
#include <vector>
namespace workspace {
/*
* @brief Make a multi-dimensional vector.
* @tparam Tp type of the elements
* @tparam N dimension
* @tparam S integer type
* @param sizes The size of each dimension
* @param init The initial value
*/
template <typename Tp, size_t N, typename S>
constexpr auto make_vector([[maybe_unused]] S* sizes, Tp const& init = Tp()) {
static_assert(std::is_convertible_v<S, size_t>);
if constexpr (N)
return std::vector(*sizes,
make_vector<Tp, N - 1, S>(std::next(sizes), init));
else
return init;
}
/*
* @brief Make a multi-dimensional vector.
* @param sizes The size of each dimension
* @param init The initial value
*/
template <typename Tp, size_t N, typename S>
constexpr auto make_vector(const S (&sizes)[N], Tp const& init = Tp()) {
return make_vector<Tp, N, S>((S*)sizes, init);
}
/*
* @brief Make a multi-dimensional vector.
* @param sizes The size of each dimension
* @param init The initial value
*/
template <typename Tp, size_t N, typename S, size_t I = 0>
constexpr auto make_vector([[maybe_unused]] std::array<S, N> const& sizes,
Tp const& init = Tp()) {
static_assert(std::is_convertible_v<S, size_t>);
if constexpr (I == N)
return init;
else
return std::vector(sizes[I], make_vector<Tp, N, S, I + 1>(sizes, init));
}
/*
* @brief Make a multi-dimensional vector.
* @param sizes The size of each dimension
* @param init The initial value
*/
template <typename Tp, size_t N = SIZE_MAX, size_t I = 0, class... Args>
constexpr auto make_vector([[maybe_unused]] std::tuple<Args...> const& sizes,
Tp const& init = Tp()) {
using tuple_type = std::tuple<Args...>;
if constexpr (I == std::tuple_size_v<tuple_type> || I == N)
return init;
else {
static_assert(
std::is_convertible_v<std::tuple_element_t<I, tuple_type>, size_t>);
return std::vector(std::get<I>(sizes),
make_vector<Tp, N, I + 1>(sizes, init));
}
}
/*
* @brief Make a multi-dimensional vector.
* @param sizes The size of each dimension
* @param init The initial value
*/
template <typename Tp, class Fst, class Snd>
constexpr auto make_vector(std::pair<Fst, Snd> const& sizes,
Tp const& init = Tp()) {
static_assert(std::is_convertible_v<Fst, size_t>);
static_assert(std::is_convertible_v<Snd, size_t>);
return make_vector({(size_t)sizes.first, (size_t)sizes.second}, init);
}
} // namespace workspace
#endif
#line 2 "Library/src/utils/py-like/enumerate.hpp"
/*
* @file enumerate.hpp
* @brief Enumerate
*/
#line 2 "Library/src/utils/py-like/range.hpp"
/**
* @file range.hpp
* @brief Range
*/
#line 9 "Library/src/utils/py-like/range.hpp"
#line 2 "Library/src/utils/py-like/reversed.hpp"
/**
* @file reversed.hpp
* @brief Reversed
*/
#include <initializer_list>
#line 10 "Library/src/utils/py-like/reversed.hpp"
namespace workspace {
namespace internal {
template <class Container> class reversed {
Container cont;
public:
constexpr reversed(Container &&cont) : cont(cont) {}
constexpr auto begin() { return std::rbegin(cont); }
constexpr auto end() { return std::rend(cont); }
};
} // namespace internal
template <class Container> constexpr auto reversed(Container &&cont) noexcept {
return internal::reversed<Container>{std::forward<Container>(cont)};
}
template <class Tp>
constexpr auto reversed(std::initializer_list<Tp> &&cont) noexcept {
return internal::reversed<std::initializer_list<Tp>>{
std::forward<std::initializer_list<Tp>>(cont)};
}
} // namespace workspace
#line 12 "Library/src/utils/py-like/range.hpp"
#if __cplusplus >= 201703L
namespace workspace {
template <class Index> class range {
Index first, last;
public:
class iterator {
Index current;
public:
using difference_type = std::ptrdiff_t;
using value_type = Index;
using reference = typename std::add_const<Index>::type &;
using pointer = iterator;
using iterator_category = std::bidirectional_iterator_tag;
constexpr iterator(Index const &__i = Index()) noexcept : current(__i) {}
constexpr bool operator==(iterator const &rhs) const noexcept {
return current == rhs.current;
}
constexpr bool operator!=(iterator const &rhs) const noexcept {
return current != rhs.current;
}
constexpr iterator &operator++() noexcept {
++current;
return *this;
}
constexpr iterator &operator--() noexcept {
--current;
return *this;
}
constexpr reference operator*() const noexcept { return current; }
};
constexpr range(Index first, Index last) noexcept
: first(first), last(last) {}
constexpr range(Index last) noexcept : first(), last(last) {}
constexpr iterator begin() const noexcept { return iterator{first}; }
constexpr iterator end() const noexcept { return iterator{last}; }
constexpr reverse_iterator<iterator> rbegin() const noexcept {
return reverse_iterator<iterator>(end());
}
constexpr reverse_iterator<iterator> rend() const noexcept {
return reverse_iterator<iterator>(begin());
}
};
template <class... Args> constexpr auto rrange(Args &&... args) noexcept {
return internal::reversed(range(std::forward<Args>(args)...));
}
} // namespace workspace
#endif
#line 2 "Library/src/utils/py-like/zip.hpp"
/**
* @file zip.hpp
* @brief Zip
*/
#line 11 "Library/src/utils/py-like/zip.hpp"
#line 14 "Library/src/utils/py-like/zip.hpp"
#if __cplusplus >= 201703L
namespace workspace {
namespace internal {
template <class> struct zipped_iterator;
template <class...> struct zipped_iterator_tuple;
template <class... Args> class zipped {
using ref_tuple = std::tuple<Args...>;
ref_tuple args;
template <size_t N = 0> constexpr auto begin_cat() const noexcept {
if constexpr (N != std::tuple_size<ref_tuple>::value) {
return std::tuple_cat(std::tuple(std::begin(std::get<N>(args))),
begin_cat<N + 1>());
} else
return std::tuple<>();
}
template <size_t N = 0> constexpr auto end_cat() const noexcept {
if constexpr (N != std::tuple_size<ref_tuple>::value) {
return std::tuple_cat(std::tuple(std::end(std::get<N>(args))),
end_cat<N + 1>());
} else
return std::tuple<>();
}
public:
constexpr zipped(Args &&... args) noexcept : args(args...) {}
class iterator {
using base_tuple = typename zipped_iterator_tuple<Args...>::type;
public:
using iterator_category =
typename common_iterator_category<base_tuple>::type;
using difference_type = std::ptrdiff_t;
using value_type = zipped_iterator<base_tuple>;
using reference = zipped_iterator<base_tuple> &;
using pointer = iterator;
protected:
value_type current;
template <size_t N = 0>
constexpr bool equal(const iterator &rhs) const noexcept {
if constexpr (N != std::tuple_size<base_tuple>::value) {
return std::get<N>(current) == std::get<N>(rhs.current) ||
equal<N + 1>(rhs);
} else
return false;
}
template <size_t N = 0> constexpr void increment() noexcept {
if constexpr (N != std::tuple_size<base_tuple>::value) {
++std::get<N>(current);
increment<N + 1>();
}
}
template <size_t N = 0> constexpr void decrement() noexcept {
if constexpr (N != std::tuple_size<base_tuple>::value) {
--std::get<N>(current);
decrement<N + 1>();
}
}
template <size_t N = 0>
constexpr void advance(difference_type __d) noexcept {
if constexpr (N != std::tuple_size<base_tuple>::value) {
std::get<N>(current) += __d;
advance<N + 1>(__d);
}
}
public:
constexpr iterator() noexcept = default;
constexpr iterator(base_tuple const ¤t) noexcept : current(current) {}
constexpr bool operator==(const iterator &rhs) const noexcept {
return equal(rhs);
}
constexpr bool operator!=(const iterator &rhs) const noexcept {
return !equal(rhs);
}
constexpr iterator &operator++() noexcept {
increment();
return *this;
}
constexpr iterator &operator--() noexcept {
decrement();
return *this;
}
constexpr bool operator<(const iterator &rhs) const noexcept {
return std::get<0>(current) < std::get<0>(rhs.current);
}
constexpr bool operator<=(const iterator &rhs) const noexcept {
return std::get<0>(current) <= std::get<0>(rhs.current);
}
constexpr iterator &operator+=(difference_type __d) noexcept {
advance(__d);
return *this;
}
constexpr iterator &operator-=(difference_type __d) noexcept {
advance(-__d);
return *this;
}
constexpr iterator operator+(difference_type __d) const noexcept {
return iterator{*this} += __d;
}
constexpr iterator operator-(difference_type __d) const noexcept {
return iterator{*this} -= __d;
}
constexpr difference_type operator-(const iterator &rhs) const noexcept {
return std::get<0>(current) - std::get<0>(rhs.current);
}
constexpr reference operator*() noexcept { return current; }
};
constexpr iterator begin() const noexcept { return iterator{begin_cat()}; }
constexpr iterator end() const noexcept { return iterator{end_cat()}; }
constexpr reverse_iterator<iterator> rbegin() const noexcept {
return reverse_iterator<iterator>{end()};
}
constexpr reverse_iterator<iterator> rend() const noexcept {
return reverse_iterator<iterator>{begin()};
}
};
template <class Tp, class... Args> struct zipped_iterator_tuple<Tp, Args...> {
using type = decltype(std::tuple_cat(
std::declval<std::tuple<decltype(std::begin(std::declval<Tp>()))>>(),
std::declval<typename zipped_iterator_tuple<Args...>::type>()));
};
template <> struct zipped_iterator_tuple<> { using type = std::tuple<>; };
template <class Iter_tuple> struct zipped_iterator : Iter_tuple {
constexpr zipped_iterator(Iter_tuple const &__t) noexcept
: Iter_tuple::tuple(__t) {}
constexpr zipped_iterator(zipped_iterator const &__t) = default;
constexpr zipped_iterator &operator=(zipped_iterator const &__t) = default;
// Avoid move initialization.
constexpr zipped_iterator(zipped_iterator &&__t)
: zipped_iterator(static_cast<zipped_iterator const &>(__t)) {}
// Avoid move assignment.
zipped_iterator &operator=(zipped_iterator &&__t) {
return operator=(static_cast<zipped_iterator const &>(__t));
}
template <size_t N>
friend constexpr auto &get(zipped_iterator<Iter_tuple> const &__z) noexcept {
return *std::get<N>(__z);
}
template <size_t N>
friend constexpr auto get(zipped_iterator<Iter_tuple> &&__z) noexcept {
return *std::get<N>(__z);
}
};
} // namespace internal
} // namespace workspace
namespace std {
template <size_t N, class Iter_tuple>
struct tuple_element<N, workspace::internal::zipped_iterator<Iter_tuple>> {
using type = typename remove_reference<typename iterator_traits<
typename tuple_element<N, Iter_tuple>::type>::reference>::type;
};
template <class Iter_tuple>
struct tuple_size<workspace::internal::zipped_iterator<Iter_tuple>>
: tuple_size<Iter_tuple> {};
} // namespace std
namespace workspace {
template <class... Args> constexpr auto zip(Args &&... args) noexcept {
return internal::zipped<Args...>(std::forward<Args>(args)...);
}
template <class... Args>
constexpr auto zip(std::initializer_list<Args> const &... args) noexcept {
return internal::zipped<const std::initializer_list<Args>...>(args...);
}
} // namespace workspace
#endif
#line 10 "Library/src/utils/py-like/enumerate.hpp"
#if __cplusplus >= 201703L
namespace workspace {
constexpr size_t min_size() noexcept { return SIZE_MAX; }
template <class Container, class... Args>
constexpr size_t min_size(Container const &cont, Args &&... args) noexcept {
return std::min(std::size(cont), min_size(std::forward<Args>(args)...));
}
template <class... Args> constexpr auto enumerate(Args &&... args) noexcept {
return zip(range(min_size(args...)), std::forward<Args>(args)...);
}
template <class... Args>
constexpr auto enumerate(std::initializer_list<Args> const &... args) noexcept {
return zip(range(min_size(args...)), std::vector(args)...);
}
} // namespace workspace
#endif
#line 2 "Library/src/utils/rand/rng.hpp"
/**
* @file rng.hpp
* @brief Random Number Generator
*/
#line 9 "Library/src/utils/rand/rng.hpp"
namespace workspace {
template <typename Arithmetic>
using uniform_distribution =
typename std::conditional<std::is_integral<Arithmetic>::value,
std::uniform_int_distribution<Arithmetic>,
std::uniform_real_distribution<Arithmetic>>::type;
template <typename Arithmetic>
class random_number_generator : uniform_distribution<Arithmetic> {
using base = uniform_distribution<Arithmetic>;
std::mt19937 engine;
public:
template <class... Args>
random_number_generator(Args&&... args)
: base(args...), engine(std::random_device{}()) {}
auto operator()() { return base::operator()(engine); }
};
} // namespace workspace
#line 2 "Library/src/utils/rand/shuffle.hpp"
/**
* @file shuffle.hpp
* @brief Shuffle
*/
#line 10 "Library/src/utils/rand/shuffle.hpp"
namespace workspace {
template <class RAIter>
void shuffle(RAIter const& __first, RAIter const& __last) {
static std::mt19937 engine(std::random_device{}());
std::shuffle(__first, __last, engine);
}
} // namespace workspace
#line 2 "Library/src/utils/round_div.hpp"
/*
* @file round_div.hpp
* @brief Round Integer Division
*/
#line 9 "Library/src/utils/round_div.hpp"
#line 11 "Library/src/utils/round_div.hpp"
namespace workspace {
/*
* @fn floor_div
* @brief floor of fraction.
* @param x the numerator
* @param y the denominator
* @return maximum integer z s.t. z <= x / y
* @note y must be nonzero.
*/
template <typename T1, typename T2>
constexpr typename std::enable_if<(is_integral_ext<T1>::value &&
is_integral_ext<T2>::value),
typename std::common_type<T1, T2>::type>::type
floor_div(T1 x, T2 y) {
assert(y != 0);
if (y < 0) x = -x, y = -y;
return x < 0 ? (x - y + 1) / y : x / y;
}
/*
* @fn ceil_div
* @brief ceil of fraction.
* @param x the numerator
* @param y the denominator
* @return minimum integer z s.t. z >= x / y
* @note y must be nonzero.
*/
template <typename T1, typename T2>
constexpr typename std::enable_if<(is_integral_ext<T1>::value &&
is_integral_ext<T2>::value),
typename std::common_type<T1, T2>::type>::type
ceil_div(T1 x, T2 y) {
assert(y != 0);
if (y < 0) x = -x, y = -y;
return x < 0 ? x / y : (x + y - 1) / y;
}
} // namespace workspace
#line 7 "atcoder-workspace/a.cc"
namespace workspace {
using namespace std;
using mint = modint<1000>;
void main() {
// start here!
int n;
cin >> n;
bool even = !(n % 2);
valarray<valarray<mint>> a = {{0, 2}, {1, 2}};
valarray<mint> v = {2, 2};
while (n) {
if (n % 2) v = v[0] * a[0] + v[1] * a[1];
valarray nx(valarray<mint>(2), 2);
for (auto i : range(2))
for (auto j : range(2)) nx[i] += a[i][j] * a[j];
a.swap(nx);
n /= 2;
}
cout << v[0] - even << "\n";
}
} // namespace workspace
int main() { workspace::main(); }