結果
| 問題 | No.1533 Don't be Negative! |
| ユーザー |
 jell
|
| 提出日時 | 2021-06-04 22:25:32 |
| 言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
AC
|
| 実行時間 | 1,583 ms / 8,000 ms |
| コード長 | 62,832 bytes |
| コンパイル時間 | 5,254 ms |
| コンパイル使用メモリ | 304,916 KB |
| 実行使用メモリ | 17,544 KB |
| 最終ジャッジ日時 | 2024-11-19 21:07:17 |
| 合計ジャッジ時間 | 37,089 ms |
|
ジャッジサーバーID （参考情報） |
judge1 / judge3 |
（要ログイン）
テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | AC | 2 ms
5,248 KB |
| testcase_01 | AC | 2 ms
5,248 KB |
| testcase_02 | AC | 1 ms
5,248 KB |
| testcase_03 | AC | 41 ms
5,248 KB |
| testcase_04 | AC | 2 ms
5,248 KB |
| testcase_05 | AC | 1 ms
5,248 KB |
| testcase_06 | AC | 2 ms
5,248 KB |
| testcase_07 | AC | 2 ms
5,248 KB |
| testcase_08 | AC | 2 ms
5,248 KB |
| testcase_09 | AC | 2 ms
5,248 KB |
| testcase_10 | AC | 2 ms
5,248 KB |
| testcase_11 | AC | 417 ms
7,780 KB |
| testcase_12 | AC | 318 ms
7,336 KB |
| testcase_13 | AC | 65 ms
5,248 KB |
| testcase_14 | AC | 141 ms
6,620 KB |
| testcase_15 | AC | 344 ms
7,108 KB |
| testcase_16 | AC | 530 ms
10,964 KB |
| testcase_17 | AC | 63 ms
5,248 KB |
| testcase_18 | AC | 474 ms
10,360 KB |
| testcase_19 | AC | 144 ms
5,568 KB |
| testcase_20 | AC | 474 ms
9,728 KB |
| testcase_21 | AC | 203 ms
6,796 KB |
| testcase_22 | AC | 440 ms
9,104 KB |
| testcase_23 | AC | 176 ms
8,064 KB |
| testcase_24 | AC | 453 ms
8,604 KB |
| testcase_25 | AC | 524 ms
10,276 KB |
| testcase_26 | AC | 145 ms
5,376 KB |
| testcase_27 | AC | 351 ms
8,104 KB |
| testcase_28 | AC | 586 ms
10,972 KB |
| testcase_29 | AC | 490 ms
11,100 KB |
| testcase_30 | AC | 1,520 ms
17,544 KB |
| testcase_31 | AC | 44 ms
5,248 KB |
| testcase_32 | AC | 192 ms
6,744 KB |
| testcase_33 | AC | 991 ms
12,520 KB |
| testcase_34 | AC | 22 ms
5,248 KB |
| testcase_35 | AC | 185 ms
8,448 KB |
| testcase_36 | AC | 835 ms
11,784 KB |
| testcase_37 | AC | 220 ms
6,012 KB |
| testcase_38 | AC | 1,096 ms
17,048 KB |
| testcase_39 | AC | 694 ms
12,120 KB |
| testcase_40 | AC | 735 ms
12,360 KB |
| testcase_41 | AC | 650 ms
12,684 KB |
| testcase_42 | AC | 1,031 ms
15,400 KB |
| testcase_43 | AC | 721 ms
13,428 KB |
| testcase_44 | AC | 567 ms
11,520 KB |
| testcase_45 | AC | 680 ms
12,856 KB |
| testcase_46 | AC | 675 ms
12,856 KB |
| testcase_47 | AC | 1,375 ms
15,988 KB |
| testcase_48 | AC | 740 ms
13,832 KB |
| testcase_49 | AC | 712 ms
13,336 KB |
| testcase_50 | AC | 1,552 ms
15,724 KB |
| testcase_51 | AC | 1,513 ms
16,996 KB |
| testcase_52 | AC | 1,113 ms
13,160 KB |
| testcase_53 | AC | 1,573 ms
17,384 KB |
| testcase_54 | AC | 1,583 ms
17,384 KB |
| testcase_55 | AC | 1,572 ms
17,256 KB |
| testcase_56 | AC | 1,206 ms
16,936 KB |
ソースコード
#line 1 "other-workspace\\yuki.cc"
// #undef _GLIBCXX_DEBUG
// #define NDEBUG
#include <bits/extc++.h>
#line 2 "Library\\lib\\alias"
/**
* @file alias
* @brief Alias
*/
#line 10 "Library\\lib\\alias"
#line 2 "Library\\lib\\bit"
#if __cplusplus > 201703L
#include <bit>
#elif __cplusplus > 201402L
#ifndef _GLIBCXX_BIT
#define _GLIBCXX_BIT 1
#include <limits>
#include <type_traits>
namespace std {
template <typename _Tp> constexpr int __countl_zero(_Tp __x) noexcept {
constexpr auto _Nd = numeric_limits<_Tp>::digits;
if (__x == 0) return _Nd;
constexpr auto _Nd_ull = numeric_limits<unsigned long long>::digits;
constexpr auto _Nd_ul = numeric_limits<unsigned long>::digits;
constexpr auto _Nd_u = numeric_limits<unsigned>::digits;
if _GLIBCXX17_CONSTEXPR (_Nd <= _Nd_u) {
constexpr int __diff = _Nd_u - _Nd;
return __builtin_clz(__x) - __diff;
} else if _GLIBCXX17_CONSTEXPR (_Nd <= _Nd_ul) {
constexpr int __diff = _Nd_ul - _Nd;
return __builtin_clzl(__x) - __diff;
} else if _GLIBCXX17_CONSTEXPR (_Nd <= _Nd_ull) {
constexpr int __diff = _Nd_ull - _Nd;
return __builtin_clzll(__x) - __diff;
} else // (_Nd > _Nd_ull)
{
static_assert(_Nd <= (2 * _Nd_ull),
"Maximum supported integer size is 128-bit");
unsigned long long __high = __x >> _Nd_ull;
if (__high != 0) {
constexpr int __diff = (2 * _Nd_ull) - _Nd;
return __builtin_clzll(__high) - __diff;
}
constexpr auto __max_ull = numeric_limits<unsigned long long>::max();
unsigned long long __low = __x & __max_ull;
return (_Nd - _Nd_ull) + __builtin_clzll(__low);
}
}
template <typename _Tp> constexpr int __countr_zero(_Tp __x) noexcept {
constexpr auto _Nd = numeric_limits<_Tp>::digits;
if (__x == 0) return _Nd;
constexpr auto _Nd_ull = numeric_limits<unsigned long long>::digits;
constexpr auto _Nd_ul = numeric_limits<unsigned long>::digits;
constexpr auto _Nd_u = numeric_limits<unsigned>::digits;
if _GLIBCXX17_CONSTEXPR (_Nd <= _Nd_u)
return __builtin_ctz(__x);
else if _GLIBCXX17_CONSTEXPR (_Nd <= _Nd_ul)
return __builtin_ctzl(__x);
else if _GLIBCXX17_CONSTEXPR (_Nd <= _Nd_ull)
return __builtin_ctzll(__x);
else // (_Nd > _Nd_ull)
{
static_assert(_Nd <= (2 * _Nd_ull),
"Maximum supported integer size is 128-bit");
constexpr auto __max_ull = numeric_limits<unsigned long long>::max();
unsigned long long __low = __x & __max_ull;
if (__low != 0) return __builtin_ctzll(__low);
unsigned long long __high = __x >> _Nd_ull;
return __builtin_ctzll(__high) + _Nd_ull;
}
}
template <typename _Tp> constexpr int __popcount(_Tp __x) noexcept {
constexpr auto _Nd = numeric_limits<_Tp>::digits;
if (__x == 0) return 0;
constexpr auto _Nd_ull = numeric_limits<unsigned long long>::digits;
constexpr auto _Nd_ul = numeric_limits<unsigned long>::digits;
constexpr auto _Nd_u = numeric_limits<unsigned>::digits;
if _GLIBCXX17_CONSTEXPR (_Nd <= _Nd_u)
return __builtin_popcount(__x);
else if _GLIBCXX17_CONSTEXPR (_Nd <= _Nd_ul)
return __builtin_popcountl(__x);
else if _GLIBCXX17_CONSTEXPR (_Nd <= _Nd_ull)
return __builtin_popcountll(__x);
else // (_Nd > _Nd_ull)
{
static_assert(_Nd <= (2 * _Nd_ull),
"Maximum supported integer size is 128-bit");
constexpr auto __max_ull = numeric_limits<unsigned long long>::max();
unsigned long long __low = __x & __max_ull;
unsigned long long __high = __x >> _Nd_ull;
return __builtin_popcountll(__low) + __builtin_popcountll(__high);
}
}
template <typename _Tp> constexpr _Tp __bit_ceil(_Tp __x) noexcept {
constexpr auto _Nd = numeric_limits<_Tp>::digits;
if (__x == 0 || __x == 1) return 1;
auto __shift_exponent = _Nd - __countl_zero((_Tp)(__x - 1u));
#ifdef _GLIBCXX_HAVE_BUILTIN_IS_CONSTANT_EVALUATED
if (!__builtin_is_constant_evaluated()) {
__glibcxx_assert(__shift_exponent != numeric_limits<_Tp>::digits);
}
#endif
using __promoted_type = decltype(__x << 1);
if _GLIBCXX17_CONSTEXPR (!is_same<__promoted_type, _Tp>::value) {
const int __extra_exp = sizeof(__promoted_type) / sizeof(_Tp) / 2;
__shift_exponent |= (__shift_exponent & _Nd) << __extra_exp;
}
return (_Tp)1u << __shift_exponent;
}
template <typename _Tp> constexpr _Tp __bit_floor(_Tp __x) noexcept {
constexpr auto _Nd = numeric_limits<_Tp>::digits;
if (__x == 0) return 0;
return (_Tp)1u << (_Nd - __countl_zero((_Tp)(__x >> 1)));
}
template <typename _Tp> constexpr _Tp __bit_width(_Tp __x) noexcept {
constexpr auto _Nd = numeric_limits<_Tp>::digits;
return _Nd - __countl_zero(__x);
}
} // namespace std
#endif
#endif
#line 2 "Library\\lib\\limits"
#line 4 "Library\\lib\\limits"
namespace workspace {
template <class _Tp> struct numeric_limits : std::numeric_limits<_Tp> {};
#ifdef __SIZEOF_INT128__
template <> struct numeric_limits<__uint128_t> {
constexpr static __uint128_t max() { return ~__uint128_t(0); }
constexpr static __uint128_t min() { return 0; }
};
template <> struct numeric_limits<__int128_t> {
constexpr static __int128_t max() {
return numeric_limits<__uint128_t>::max() >> 1;
}
constexpr static __int128_t min() { return -max() - 1; }
};
#endif
} // namespace workspace
#line 13 "Library\\lib\\alias"
namespace workspace {
constexpr static char eol = '\n';
using namespace std;
using i32 = int_least32_t;
using u32 = uint_least32_t;
using i64 = int_least64_t;
using u64 = uint_least64_t;
#ifdef __SIZEOF_INT128__
using i128 = __int128_t;
using u128 = __uint128_t;
#else
#warning 128-bit integer is not available.
#endif
template <class _T1, class _T2,
typename = decltype(std::declval<const _T2 &>() <
std::declval<const _T1 &>())>
constexpr
typename std::conditional<std::is_same<_T1, _T2>::value, const _T1 &,
typename std::common_type<_T1, _T2>::type>::type
min(const _T1 &__x, const _T2 &__y) noexcept {
return __y < __x ? __y : __x;
}
template <class _T1, class _T2, class _Compare,
typename = decltype(std::declval<_Compare>()(
std::declval<const _T2 &>(), std::declval<const _T1 &>()))>
constexpr
typename std::conditional<std::is_same<_T1, _T2>::value, const _T1 &,
typename std::common_type<_T1, _T2>::type>::type
min(const _T1 &__x, const _T2 &__y, _Compare __comp) noexcept {
return __comp(__y, __x) ? __y : __x;
}
template <class _Tp, typename = decltype(std::declval<const _Tp &>() <
std::declval<const _Tp &>())>
constexpr _Tp min(std::initializer_list<_Tp> __x) noexcept {
return *std::min_element(__x.begin(), __x.end());
}
template <class _Tp, class _Compare,
typename = decltype(std::declval<_Compare>()(
std::declval<const _Tp &>(), std::declval<const _Tp &>()))>
constexpr _Tp min(std::initializer_list<_Tp> __x, _Compare __comp) noexcept {
return *std::min_element(__x.begin(), __x.end(), __comp);
}
template <class _T1, class _T2,
typename = decltype(std::declval<const _T1 &>() <
std::declval<const _T2 &>())>
constexpr
typename std::conditional<std::is_same<_T1, _T2>::value, const _T1 &,
typename std::common_type<_T1, _T2>::type>::type
max(const _T1 &__x, const _T2 &__y) noexcept {
return __x < __y ? __y : __x;
}
template <class _T1, class _T2, class _Compare,
typename = decltype(std::declval<_Compare>()(
std::declval<const _T1 &>(), std::declval<const _T2 &>()))>
constexpr
typename std::conditional<std::is_same<_T1, _T2>::value, const _T1 &,
typename std::common_type<_T1, _T2>::type>::type
max(const _T1 &__x, const _T2 &__y, _Compare __comp) noexcept {
return __comp(__x, __y) ? __y : __x;
}
template <class _Tp, typename = decltype(std::declval<const _Tp &>() <
std::declval<const _Tp &>())>
constexpr _Tp max(std::initializer_list<_Tp> __x) noexcept {
return *std::max_element(__x.begin(), __x.end());
}
template <class _Tp, class _Compare,
typename = decltype(std::declval<_Compare>()(
std::declval<const _Tp &>(), std::declval<const _Tp &>()))>
constexpr _Tp max(std::initializer_list<_Tp> __x, _Compare __comp) noexcept {
return *std::max_element(__x.begin(), __x.end(), __comp);
}
#ifdef _GLIBCXX_BIT
template <typename _Tp> constexpr _Tp __bsf(_Tp __x) noexcept {
return std::__countr_zero(__x);
}
template <typename _Tp> constexpr _Tp __bsr(_Tp __x) noexcept {
return std::__bit_width(__x) - 1;
}
#endif
} // namespace workspace
#line 6 "other-workspace\\yuki.cc"
// #include "lib/cxx20"
#line 1 "Library\\lib\\direct"
#ifdef ONLINE_JUDGE
#pragma GCC optimize("O3")
#pragma GCC target("avx,avx2")
#pragma GCC optimize("unroll-loops")
#endif
#line 8 "other-workspace\\yuki.cc"
// #include "lib/opt"
#line 2 "Library\\src\\sys\\call_once.hpp"
/**
* @file call_once.hpp
* @brief Call Once
*/
#line 9 "Library\\src\\sys\\call_once.hpp"
namespace workspace {
/**
* @brief Call once.
*/
template <class _F> void call_once(_F &&__f) {
static std::unordered_set<void *> __called;
if (__called.count(std::addressof(__f))) return;
__called.emplace(std::addressof(__f));
__f();
}
} // namespace workspace
#line 2 "Library\\src\\sys\\clock.hpp"
/*
* @fn clock.hpp
* @brief Clock
*/
#line 9 "Library\\src\\sys\\clock.hpp"
namespace workspace {
using namespace std::chrono;
namespace internal {
// The start time of the program.
const auto start_time{system_clock::now()};
} // namespace internal
/*
* @fn elapsed
* @return elapsed time of the program
*/
int64_t elapsed() {
const auto end_time{system_clock::now()};
return duration_cast<milliseconds>(end_time - internal::start_time).count();
}
} // namespace workspace
#line 2 "Library\\src\\sys\\ejection.hpp"
/**
* @file ejection.hpp
* @brief Ejection
*/
#line 9 "Library\\src\\sys\\ejection.hpp"
namespace workspace {
namespace internal {
struct ejection {
bool exit = 0;
};
} // namespace internal
/**
* @brief eject from a try block, throw nullptr
* @param arg output
*/
template <class Tp> void eject(Tp const &arg) {
std::cout << arg << "\n";
throw internal::ejection{};
}
void exit() { throw internal::ejection{true}; }
} // namespace workspace
#line 2 "Library\\src\\sys\\iteration.hpp"
/**
* @file iteration.hpp
* @brief Case Iteration
*/
#line 9 "Library\\src\\sys\\iteration.hpp"
#line 11 "Library\\src\\sys\\iteration.hpp"
namespace workspace {
void main();
struct {
// 1-indexed
unsigned current{0};
unsigned total{1};
void read() { (std::cin >> total).ignore(); }
int iterate() {
static bool once = false;
assert(!once);
once = true;
while (current++ < total) {
try {
main();
} catch (internal::ejection const& status) {
if (status.exit) break;
}
}
return 0;
}
} case_info;
} // namespace workspace
#line 2 "Library\\lib\\utils"
// #include "src/utils/cached.hpp"
// #include "src/utils/cat.hpp"
// #include "src/utils/chval.hpp"
// #include "src/utils/compare.hpp"
// #include "src/utils/fixed_point.hpp"
// #include "src/utils/hash.hpp"
// #include "src/utils/io/istream.hpp"
// #include "src/utils/io/ostream.hpp"
// #include "src/utils/io/read.hpp"
// #include "src/utils/grid/motion.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 {
/**
* @brief Setup I/O.
* @param __n Standard output precision
*/
void io_setup(int __n) {
std::cin.tie(0)->sync_with_stdio(0);
std::cout << std::fixed << std::setprecision(__n);
#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 15 "Library\\lib\\utils"
// #include "src/utils/make_vector.hpp"
// #include "src/utils/py-like/enumerate.hpp"
#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 _reversed_impl {
template <class _Container> class reversed {
_Container __cont;
public:
constexpr reversed(_Container &&__cont) noexcept : __cont(__cont) {}
constexpr decltype(auto) begin() noexcept { return std::rbegin(__cont); }
constexpr decltype(auto) begin() const noexcept {
return std::rbegin(__cont);
}
constexpr decltype(auto) end() noexcept { return std::rend(__cont); }
constexpr decltype(auto) end() const noexcept { return std::rend(__cont); }
constexpr decltype(auto) size() const noexcept {
return
#if __cplusplus < 201703L
__cont.size();
#else
std::size(__cont);
#endif
}
};
} // namespace _reversed_impl
template <class _Container>
constexpr decltype(auto) reversed(_Container &&__cont) noexcept {
return _reversed_impl::reversed<_Container>{std::forward<_Container>(__cont)};
}
template <class _Tp>
constexpr decltype(auto) reversed(
std::initializer_list<_Tp> &&__cont) noexcept {
return _reversed_impl::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::random_access_iterator_tag;
constexpr iterator(const _Index &__i = _Index()) noexcept : current(__i) {}
constexpr bool operator==(const iterator &__x) const noexcept {
return current == __x.current;
}
constexpr bool operator!=(const iterator &__x) const noexcept {
return current != __x.current;
}
constexpr bool operator<(const iterator &__x) const noexcept {
return current < __x.current;
}
constexpr bool operator<=(const iterator &__x) const noexcept {
return current <= __x.current;
}
constexpr bool operator>(const iterator &__x) const noexcept {
return current > __x.current;
}
constexpr bool operator>=(const iterator &__x) const noexcept {
return current >= __x.current;
}
constexpr iterator &operator++() noexcept {
++current;
return *this;
}
constexpr iterator &operator++(int) noexcept {
auto __tmp = *this;
++current;
return __tmp;
}
constexpr iterator &operator--() noexcept {
--current;
return *this;
}
constexpr iterator &operator--(int) noexcept {
auto __tmp = *this;
--current;
return __tmp;
}
constexpr difference_type operator-(const iterator &__x) const noexcept {
return current - __x.current;
}
constexpr iterator &operator+=(difference_type __x) noexcept {
current += __x;
return *this;
}
constexpr iterator operator+(difference_type __x) const noexcept {
return iterator(*this) += __x;
}
constexpr iterator &operator-=(difference_type __x) noexcept {
current -= __x;
return *this;
}
constexpr iterator operator-(difference_type __x) const noexcept {
return iterator(*this) -= __x;
}
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());
}
constexpr size_t size() const noexcept {
return std::distance(__first, __last);
}
};
template <class... _Args>
constexpr decltype(auto) rrange(_Args &&...__args) noexcept {
return reversed(range(std::forward<_Args>(__args)...));
}
template <class _Container>
constexpr decltype(auto) iterate(_Container &&__cont) noexcept {
return range(std::begin(__cont), std::end(__cont));
}
template <class _Container>
constexpr decltype(auto) riterate(_Container &&__cont) noexcept {
return range(std::rbegin(__cont), std::rend(__cont));
}
} // namespace workspace
#endif
#line 18 "Library\\lib\\utils"
// #include "src/utils/py-like/reversed.hpp"
// #include "src/utils/py-like/zip.hpp"
// #include "src/utils/rand/rng.hpp"
// #include "src/utils/rand/shuffle.hpp"
// #include "src/utils/round_div.hpp"
// #include "src\utils\rand\tree.hpp"
// #include "src\utils\reference_list.hpp"
#line 11 "other-workspace\\yuki.cc"
signed main() {
using namespace workspace;
io_setup(15);
/* given
case_info.read(); //*/
/* unspecified
case_info.total = -1; //*/
return case_info.iterate();
}
#line 2 "Library\\src\\algebra\\polynomial.hpp"
/**
* @file polynomial.hpp
* @brief Polynomial
*/
#line 11 "Library\\src\\algebra\\polynomial.hpp"
#line 2 "Library\\lib\\cxx17"
#ifndef _CXX17_CONSTEXPR
#if __cplusplus >= 201703L
#define _CXX17_CONSTEXPR constexpr
#else
#define _CXX17_CONSTEXPR
#endif
#endif
#line 2 "Library\\src\\algebra\\ntt.hpp"
/**
* @file ntt.hpp
* @brief Number Theoretic Transform
* @date 2021-02-20
*
*
*/
#line 2 "Library\\src\\number_theory\\ext_gcd.hpp"
/**
* @file ext_gcd.hpp
* @brief Extended Euclidean Algorithm
*/
#line 9 "Library\\src\\number_theory\\ext_gcd.hpp"
#line 2 "Library\\src\\utils\\sfinae.hpp"
/**
* @file sfinae.hpp
* @brief SFINAE
*/
#line 10 "Library\\src\\utils\\sfinae.hpp"
#include <type_traits>
#ifndef __INT128_DEFINED__
#ifdef __SIZEOF_INT128__
#define __INT128_DEFINED__ 1
#else
#define __INT128_DEFINED__ 0
#endif
#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; };
template <> struct is_signed<__uint128_t> : std::false_type {};
template <> struct is_signed<__int128_t> : std::true_type {};
template <> struct is_unsigned<__uint128_t> : std::true_type {};
template <> struct is_unsigned<__int128_t> : std::false_type {};
#endif
} // namespace std
namespace workspace {
template <class Tp, class... Args> struct variadic_front { using type = Tp; };
template <class... Args> struct variadic_back;
template <class Tp> struct variadic_back<Tp> { using type = Tp; };
template <class Tp, class... Args> struct variadic_back<Tp, Args...> {
using type = typename variadic_back<Args...>::type;
};
template <class type, template <class> class trait>
using enable_if_trait_type = typename std::enable_if<trait<type>::value>::type;
/**
* @brief Return type of subscripting ( @c [] ) access.
*/
template <class _Tp>
using subscripted_type =
typename std::decay<decltype(std::declval<_Tp&>()[0])>::type;
template <class Container>
using element_type = typename std::decay<decltype(
*std::begin(std::declval<Container&>()))>::type;
template <class _Tp, class = std::nullptr_t>
struct has_begin : std::false_type {};
template <class _Tp>
struct has_begin<_Tp, decltype(std::begin(std::declval<_Tp>()), nullptr)>
: std::true_type {};
template <class _Tp, class = void> struct has_mod : std::false_type {};
template <class _Tp>
struct has_mod<_Tp, std::__void_t<decltype(_Tp::mod)>> : std::true_type {};
template <class _Tp, class = void> struct is_integral_ext : std::false_type {};
template <class _Tp>
struct is_integral_ext<
_Tp, typename std::enable_if<std::is_integral<_Tp>::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 _Tp>
constexpr static bool is_integral_ext_v = is_integral_ext<_Tp>::value;
#endif
template <typename _Tp, typename = void> struct multiplicable_uint {
using type = uint_least32_t;
};
template <typename _Tp>
struct multiplicable_uint<
_Tp,
typename std::enable_if<(2 < sizeof(_Tp)) &&
(!__INT128_DEFINED__ || sizeof(_Tp) <= 4)>::type> {
using type = uint_least64_t;
};
#if __INT128_DEFINED__
template <typename _Tp>
struct multiplicable_uint<_Tp,
typename std::enable_if<(4 < sizeof(_Tp))>::type> {
using type = __uint128_t;
};
#endif
template <typename _Tp> struct multiplicable_int {
using type =
typename std::make_signed<typename multiplicable_uint<_Tp>::type>::type;
};
template <typename _Tp> struct multiplicable {
using type = std::conditional_t<
is_integral_ext<_Tp>::value,
std::conditional_t<std::is_signed<_Tp>::value,
typename multiplicable_int<_Tp>::type,
typename multiplicable_uint<_Tp>::type>,
_Tp>;
};
template <class> struct first_arg { using type = void; };
template <class _R, class _Tp, class... _Args>
struct first_arg<_R(_Tp, _Args...)> {
using type = _Tp;
};
template <class _R, class _Tp, class... _Args>
struct first_arg<_R (*)(_Tp, _Args...)> {
using type = _Tp;
};
template <class _G, class _R, class _Tp, class... _Args>
struct first_arg<_R (_G::*)(_Tp, _Args...)> {
using type = _Tp;
};
template <class _G, class _R, class _Tp, class... _Args>
struct first_arg<_R (_G::*)(_Tp, _Args...) const> {
using type = _Tp;
};
template <class _Tp, class = void> struct parse_compare : first_arg<_Tp> {};
template <class _Tp>
struct parse_compare<_Tp, std::__void_t<decltype(&_Tp::operator())>>
: first_arg<decltype(&_Tp::operator())> {};
} // namespace workspace
#line 11 "Library\\src\\number_theory\\ext_gcd.hpp"
namespace workspace {
/**
* @param __a Integer
* @param __b Integer
* @return Pair of integers (x, y) s.t. ax + by = g = gcd(a, b), 0 <= x <
* |b/g|, -|a/g| < y <= 0. Return (0, 0) if (a, b) = (0, 0).
*/
template <typename _T1, typename _T2> constexpr auto ext_gcd(_T1 __a, _T2 __b) {
static_assert(is_integral_ext<_T1>::value);
static_assert(is_integral_ext<_T2>::value);
using result_type = typename std::make_signed<
typename std::common_type<_T1, _T2>::type>::type;
result_type a{__a}, b{__b}, p{1}, q{}, r{}, s{1};
// Euclidean algorithm
while (b) {
result_type t = a / b;
r ^= p ^= r ^= p -= t * r;
s ^= q ^= s ^= q -= t * s;
b ^= a ^= b ^= a -= t * b;
}
// Normalize
if (a < 0) p = -p, q = -q;
if (p < 0) p += __b / a, q -= __a / a;
return std::make_pair(p, q);
}
} // namespace workspace
#line 2 "Library\\src\\number_theory\\primitive_root.hpp"
/**
* @file primitive_root.hpp
* @brief Primitive Root
* @date 2020-12-28
*/
#line 10 "Library\\src\\number_theory\\primitive_root.hpp"
namespace workspace {
/**
* @brief Compile time primitive root.
*
* @tparam __mod Positive integer
* @return Minimum positive one if it exists. Otherwise 0.
*/
template <class Tp>
constexpr typename std::enable_if<(is_integral_ext<Tp>::value), Tp>::type
primitive_root(const Tp __mod) noexcept {
assert(__mod > 0);
using int_type = typename multiplicable_uint<Tp>::type;
int_type __r = __mod, __p[16] = {}, *__q = __p;
for (int_type __i = 2; __i <= __r / __i; ++__i) {
if (__r % __i) continue;
*__q++ = __i;
while (!(__r % __i)) __r /= __i;
}
if (__r != 1) *__q++ = __r;
int_type __tot = __mod;
for (__q = __p; *__q; *__q++ = 0) (__tot /= *__q) *= *__q - 1;
__r = __tot, __q = __p + 1, __p[0] = 1;
for (int_type __i = 2; __i <= __r / __i; ++__i) {
if (__r % __i) continue;
*__q++ = __i;
while (!(__r % __i)) __r /= __i;
}
if (__r != 1) *__q++ = __r;
for (Tp __r = 1; __r != __mod; ++__r) {
auto __cnt = 0;
for (__q = __p; *__q; ++__q) {
int_type __w = 1;
for (int_type __e = __tot / *__q, __x = __r; __e;
__e >>= 1, (__x *= __x) %= __mod)
if (__e & 1) (__w *= __x) %= __mod;
if (__w == 1 && ++__cnt > 1) break;
}
if (__cnt == 1) return __r;
}
return 0;
};
} // namespace workspace
#line 13 "Library\\src\\algebra\\ntt.hpp"
namespace workspace {
namespace ntt_impl {
/**
* @see
* https://github.com/atcoder/ac-library/blob/master/atcoder/convolution.hpp
*/
template <class _Tp> struct __coef {
_Tp sum_e[30]; // sum_e[i] = ies[0] * ... * ies[i - 1] * es[i]
constexpr __coef() : sum_e{} {
if (_Tp::mod < 2) return;
int cnt2 = __builtin_ctz(_Tp::mod - 1);
_Tp e = 1;
{
auto p = (_Tp::mod - 1) >> cnt2;
_Tp w = primitive_root(_Tp::mod);
while (p) {
if (p & 1) e *= w;
p >>= 1;
w *= w;
}
}
_Tp ie = ext_gcd(decltype(_Tp::mod)(e), _Tp::mod).first;
_Tp es[30] = {}, ies[30] = {}; // es[i]^(2^(2+i)) == 1
for (int i = cnt2; i >= 2; i--) {
// e^(2^i) == 1
es[i - 2] = e;
ies[i - 2] = ie;
e *= e;
ie *= ie;
}
_Tp now = 1;
for (int i = 0; i <= cnt2 - 2; i++) {
sum_e[i] = es[i] * now;
now *= ies[i];
}
}
};
template <class _Tp> struct __icoef {
_Tp sum_ie[30]; // sum_e[i] = ies[0] * ... * ies[i - 1] * es[i]
constexpr __icoef() : sum_ie{} {
if (_Tp::mod < 2) return;
int cnt2 = __builtin_ctz(_Tp::mod - 1);
_Tp e = 1;
{
auto p = (_Tp::mod - 1) >> cnt2;
_Tp w = primitive_root(_Tp::mod);
while (p) {
if (p & 1) e *= w;
p >>= 1;
w *= w;
}
}
_Tp ie = ext_gcd(decltype(_Tp::mod)(e), _Tp::mod).first;
_Tp es[30] = {}, ies[30] = {}; // es[i]^(2^(2+i)) == 1
for (int i = cnt2; i >= 2; i--) {
// e^(2^i) == 1
es[i - 2] = e;
ies[i - 2] = ie;
e *= e;
ie *= ie;
}
_Tp now = 1;
for (int i = 0; i <= cnt2 - 2; i++) {
sum_ie[i] = ies[i] * now;
now *= es[i];
}
}
};
template <class _Tp> struct __ipow2 {
_Tp __ip2[30];
constexpr __ipow2() : __ip2{1, (1 + _Tp::mod) / 2} {
for (size_t __i = 1; __i + 1 != std::size(__ip2); ++__i)
__ip2[__i + 1] = __ip2[__i] * __ip2[1];
}
};
template <class _FIter>
constexpr void ntt(_FIter __first, _FIter __last) noexcept {
using value_type = typename std::decay<decltype(*__first)>::type;
constexpr __coef<value_type> _;
auto __h = __builtin_ctz(std::distance(__first, __last));
for (ptrdiff_t __p = 1 << __h; __p >>= 1;) {
value_type now = -1;
auto __l = __first;
for (size_t __s = 1 << __h; __l != __last;
now *= _.sum_e[__builtin_ctz(--__s)]) {
auto __r = __l + __p;
for (auto __mid = __r; __l != __mid; ++__l, ++__r) {
auto __tmp = *__l;
*__l -= *__r *= now;
*__r += __tmp;
}
__l = __r;
}
}
}
template <class _A> constexpr void ntt(_A &a) noexcept {
ntt(std::begin(a), std::end(a));
}
template <class _FIter>
constexpr void intt(_FIter __first, _FIter __last) noexcept {
using value_type = typename std::decay<decltype(*__first)>::type;
constexpr __icoef<value_type> _;
auto __h = __builtin_ctz(std::distance(__first, __last));
for (ptrdiff_t __p = 1; __p >> __h ^ 1; __p <<= 1) {
value_type inow = 1;
auto __l = __first;
for (size_t __s = 1 << __h; __l != __last;
inow *= _.sum_ie[__builtin_ctz(--__s)]) {
auto __r = __l + __p;
for (auto __mid = __r; __l != __mid; ++__l, ++__r) {
auto __tmp = (*__l - *__r) * inow;
*__l += *__r;
*__r = __tmp;
}
__l = __r;
}
}
constexpr __ipow2<value_type> __;
while (__first != __last) *--__last *= __.__ip2[__h];
} // namespace ntt_impl
template <class _A> constexpr void intt(_A &a) noexcept {
intt(std::begin(a), std::end(a));
}
} // namespace ntt_impl
using ntt_impl::intt;
using ntt_impl::ntt;
} // namespace workspace
#line 15 "Library\\src\\algebra\\polynomial.hpp"
namespace workspace {
/**
* @brief Polynomial.
*
* @tparam _Tp Ring structure
* @tparam _Conv_threshold Threshold for convolution method
*/
template <class _Tp, std::size_t _Conv_threshold = 64>
class polynomial : public std::vector<_Tp> {
using vec = std::vector<_Tp>;
using poly = polynomial;
template <class _Os> friend _Os& operator<<(_Os& __os, const poly& __x) {
bool __head = true;
for (const auto& __a : __x) {
if (!__head) __os << ' ';
__head = false;
__os << __a;
}
return __os;
}
public:
using vec::vec;
using size_type = typename vec::size_type;
protected:
void _erase_leading_zeros() noexcept {
auto __i = vec::_M_impl._M_finish;
while (__i != vec::_M_impl._M_start && *(__i - 1) == _Tp(0)) --__i;
vec::_M_erase_at_end(__i);
}
template <class _Iter> void _dft(_Iter __first, _Iter __last) const noexcept {
if _CXX17_CONSTEXPR (has_mod<_Tp>::value)
ntt(__first, __last);
else {
// fft(__first, __last);
assert(0); // Not implemented!
}
}
template <class _Iter>
void _idft(_Iter __first, _Iter __last) const noexcept {
if _CXX17_CONSTEXPR (has_mod<_Tp>::value)
intt(__first, __last);
else {
// ifft(__first, __last);
assert(0); // Not implemented!
}
}
void _conv_naive(const poly& __x) noexcept {
if (vec::_M_impl._M_start == vec::_M_impl._M_finish) return;
if (__x._M_impl._M_start == __x._M_impl._M_finish) {
vec::_M_erase_at_end(vec::_M_impl._M_start);
return;
}
vec::_M_default_append(__x._M_impl._M_finish - __x._M_impl._M_start - 1);
for (auto __i = vec::_M_impl._M_finish; __i-- != vec::_M_impl._M_start;) {
auto __j = __i, __k = __x._M_impl._M_start;
*__i *= *__k++;
while (__j != vec::_M_impl._M_start && __k != __x._M_impl._M_finish)
*__i += *--__j * *__k++;
}
}
void _conv_dft(poly&& __x) noexcept {
if _CXX17_CONSTEXPR (has_mod<_Tp>::value)
_conv_ntt(std::move(__x));
else {
// _conv_fft(std::move(__x));
assert(0); // Not implemented!
}
}
void _conv_fft(poly&& __x) noexcept;
void _conv_ntt(poly&& __x) noexcept {
size_type __n = vec::_M_impl._M_finish - vec::_M_impl._M_start,
__m = __x._M_impl._M_finish - __x._M_impl._M_start,
__len = 1 << (32 - __builtin_clz(__n + __m - 1));
vec::_M_default_append(__len - __n);
__x._M_default_append(__len - __m);
ntt(vec::_M_impl._M_start, vec::_M_impl._M_finish);
ntt(__x._M_impl._M_start, __x._M_impl._M_finish);
for (auto __i = vec::_M_impl._M_start, __j = __x._M_impl._M_start;
__i != vec::_M_impl._M_finish; ++__i, ++__j)
*__i *= std::move(*__j);
intt(vec::_M_impl._M_start, vec::_M_impl._M_finish);
vec::_M_erase_at_end(vec::_M_impl._M_start + __n + __m - 1);
}
/**
* @brief
*
* @param __x
* @return Degree of __x.
*/
size_type _divmod_naive(const poly& __x) {
auto __xfin = __x._M_impl._M_finish;
auto __xlen = __x.size();
while (__xfin != __x._M_impl._M_start && *(__xfin - 1) == _Tp(0))
--__xfin, --__xlen;
assert(__xlen != 0);
_erase_leading_zeros();
auto __p = vec::_M_impl._M_finish;
while (size_type(__p - vec::_M_impl._M_start) >= __xlen) {
--__p;
auto __src = __xfin;
auto __dst = __p;
*__dst /= *--__src;
while (__src != __x._M_impl._M_start) *--__dst -= *--__src * *__p;
}
return std::min<size_type>(__xlen - 1, __p - vec::_M_impl._M_start);
}
void _div_naive(const poly& __x) { operator>>=(_divmod_naive(__x)); }
void _div_doubling(poly&& __x) noexcept {
_erase_leading_zeros();
__x._erase_leading_zeros();
auto __n = vec::_M_impl._M_finish - vec::_M_impl._M_start;
auto __m = __x._M_impl._M_finish - __x._M_impl._M_start;
if (__n < __m)
vec::clear();
else {
assert(__m != 0);
std::reverse(__x._M_impl._M_start, __x._M_impl._M_finish);
__x = __x.inv(__n - __m + 1);
std::reverse(vec::_M_impl._M_start, vec::_M_impl._M_finish);
vec::_M_erase_at_end(vec::_M_impl._M_finish - (__m - 1));
operator*=(__x).resize(__n - __m + 1);
std::reverse(vec::_M_impl._M_start, vec::_M_impl._M_finish);
}
}
public:
/**
* @return Degree of %polynomial. Return -1 if it equals zero.
*/
size_type deg() const noexcept { return vec::size() - 1; }
/**
* @param __i Not exceeding the degree.
* @return Coefficient of x^i.
*/
typename vec::reference operator[](size_type __i) noexcept {
assert(__i < vec::size());
return *(vec::_M_impl._M_start + __i);
}
/**
* @param __i Not exceeding the degree.
* @return Coefficient of x^i.
*/
typename vec::const_reference operator[](size_type __i) const noexcept {
assert(__i < vec::size());
return *(vec::_M_impl._M_start + __i);
}
/**
* @brief Evaluate at given point.
*/
_Tp eval(const _Tp& __a) const noexcept {
_Tp __v(0), __p(1);
for (auto __i = vec::_M_impl._M_start; __i != vec::_M_impl._M_finish;
++__i, __p *= __a)
__v += *__i * __p;
return __v;
}
/**
* @brief In-place multipoint evaluation.
*/
template <class _Iter, typename = std::_RequireInputIter<_Iter>>
_Iter eval(_Iter __first, _Iter __last) const noexcept {
return eval(__first, __last, __first);
}
/**
* @brief Multipoint evaluation.
*/
template <class _InputIter, class _OutputIter,
typename = std::_RequireInputIter<_InputIter>>
_OutputIter eval(_InputIter __first, _InputIter __last,
_OutputIter __result) const noexcept {
size_type __n = std::distance(__first, __last);
if (!__n) return __result;
auto __tree = new poly[__n << 1];
for (auto __p = __tree + __n; __first != __last; ++__p, ++__first)
*__p = {-*__first, 1};
for (size_type __i = __n; --__i;)
__tree[__i] = __tree[__i << 1] * __tree[__i << 1 | 1];
__tree[1] = operator%(std::move(__tree[1]));
for (size_type __i = 2; __i != __n << 1; __i += 2)
__tree[__i] = __tree[__i >> 1] % std::move(__tree[__i]),
__tree[__i | 1] =
std::move(__tree[__i >> 1] %= std::move(__tree[__i | 1]));
for (size_type __i = 0; __i != __n; ++__i)
*__result++ = std::move(*__tree[__n + __i]._M_impl._M_start);
delete[] __tree;
return __result;
}
/**
* @brief Conversion to bool.
*
* @return Whether the %polynomial is not zero.
*/
operator bool() const noexcept {
auto __first = vec::_M_impl._M_start, __last = vec::_M_impl._M_finish;
while (__first != __last)
if (*__first++ != _Tp(0)) return true;
return false;
}
bool operator==(const poly& __x) const noexcept {
auto __first1 = vec::_M_impl._M_start, __last1 = vec::_M_impl._M_finish;
auto __first2 = __x._M_impl._M_start, __last2 = __x._M_impl._M_finish;
if (__last1 - __first1 < __last2 - __first2) {
while (__first1 != __last1)
if (*__first1++ != *__first2++) return false;
while (__first2 != __last2)
if (*__first2++ != _Tp(0)) return false;
}
else {
while (__first2 != __last2)
if (*__first1++ != *__first2++) return false;
while (__first1 != __last1)
if (*__first1++ != _Tp(0)) return false;
}
return true;
}
bool operator!=(const poly& __x) const noexcept { return !operator==(__x); }
/**
* @brief Multiply by x^i.
*/
poly& operator<<=(size_type __i) noexcept {
vec::insert(vec::begin(), __i, _Tp(0));
return *this;
}
/**
* @brief Divide by x^i.
*/
poly& operator>>=(size_type __i) noexcept {
vec::_M_erase_at_end(
std::move(vec::_M_impl._M_start + std::min(__i, vec::size()),
vec::_M_impl._M_finish, vec::_M_impl._M_start));
return *this;
}
/**
* @brief Multiply by x^i.
*/
poly operator<<(size_type __i) const noexcept {
return poly(*this).operator<<=(__i);
}
/**
* @brief Divide by x^i.
*/
poly operator>>(size_type __i) const noexcept {
return poly(*this).operator>>=(__i);
}
poly operator+() const noexcept { return *this; }
poly operator-() const noexcept {
poly __x = *this;
for (auto __i = __x._M_impl._M_start; __i != __x._M_impl._M_finish; ++__i)
*__i = -*__i;
return __x;
}
poly& operator+=(const poly& __x) noexcept {
if (vec::size() < __x.size())
vec::_M_default_append(__x.size() - vec::size());
for (auto __i = vec::_M_impl._M_start, __j = __x._M_impl._M_start;
__j != __x._M_impl._M_finish; ++__i, ++__j)
*__i += *__j;
_erase_leading_zeros();
return *this;
}
poly& operator+=(const _Tp& __c) noexcept {
if (__c != static_cast<_Tp>(0)) {
if (vec::_M_impl._M_start == vec::_M_impl._M_finish)
vec::emplace_back(__c);
else
*vec::_M_impl._M_start += __c, _erase_leading_zeros();
}
return *this;
}
poly& operator-=(const poly& __x) noexcept {
if (vec::size() < __x.size())
vec::_M_default_append(__x.size() - vec::size());
for (auto __i = vec::_M_impl._M_start, __j = __x._M_impl._M_start;
__j != __x._M_impl._M_finish; ++__i, ++__j)
*__i -= *__j;
_erase_leading_zeros();
return *this;
}
poly& operator-=(const _Tp& __c) noexcept {
if (__c != static_cast<_Tp>(0)) {
if (vec::_M_impl._M_start == vec::_M_impl._M_finish)
vec::emplace_back(-__c);
else
*vec::_M_impl._M_start -= __c, _erase_leading_zeros();
}
return *this;
}
poly& operator*=(const poly& __x) noexcept {
std::min(vec::size(), __x.size()) > _Conv_threshold
? _conv_dft(poly(__x))
: _conv_naive(this == std::addressof(__x) ? poly(__x) : __x);
return *this;
}
poly& operator*=(poly&& __x) noexcept {
std::min(vec::size(), __x.size()) > _Conv_threshold
? _conv_dft(std::move(__x))
: _conv_naive(__x);
return *this;
}
poly& operator*=(const _Tp& __c) noexcept {
if (__c == static_cast<_Tp>(0))
vec::_M_erase_at_end(vec::_M_impl._M_start);
else
for (auto __i = vec::_M_impl._M_start; __i != vec::_M_impl._M_finish;
++__i)
*__i *= __c;
return *this;
}
poly& operator/=(const _Tp& __c) noexcept {
assert(__c != static_cast<_Tp>(0));
for (auto __i = vec::_M_impl._M_start; __i != vec::_M_impl._M_finish; ++__i)
*__i /= __c;
return *this;
}
poly rev() const noexcept { return rev(vec::size()); }
poly rev(size_type __n) const noexcept {
poly __r(__n);
auto __src = vec::_M_impl._M_start;
auto __dst = __r._M_impl._M_finish;
for (size_type __i = std::min(__n, vec::size()); __i; --__i)
*--__dst = *__src++;
return __r;
}
poly inv() const noexcept { return inv(vec::size()); }
/**
* @brief Multiplicative inverse modulo x^n.
*
* @param __n Degree of modulus
* @return
*/
poly inv(size_type __n) const noexcept {
if (!__n) return {};
assert(*vec::_M_impl._M_start != _Tp(0));
size_type __len = 1;
while (__len < __n) __len <<= 1;
poly __y(__len);
auto __xp = new _Tp[__len], __yp = __y._M_impl._M_start,
__zp = new _Tp[__len];
*__yp = _Tp(1) / *vec::_M_impl._M_start;
for (size_type __i = 1; __i != __len; __i <<= 1) {
std::fill(std::copy_n(__yp, __i, __zp), __zp + (__i << 1), _Tp(0));
_dft(__zp, __zp + (__i << 1));
std::fill(std::copy_n(vec::_M_impl._M_start,
std::min(__i << 1, vec::size()), __xp),
__xp + (__i << 1), _Tp(0));
_dft(__xp, __xp + (__i << 1));
for (size_type __j = 0; __j != (__i << 1); ++__j) __xp[__j] *= -__zp[__j];
_idft(__xp, __xp + (__i << 1));
std::fill(std::move(__xp + __i, __xp + (__i << 1), __xp),
__xp + (__i << 1), _Tp(0));
_dft(__xp, __xp + (__i << 1));
for (size_type __j = 0; __j != (__i << 1); ++__j)
__xp[__j] *= static_cast<_Tp&&>(__zp[__j]);
_idft(__xp, __xp + (__i << 1));
std::move(__xp, __xp + __i, __yp + __i);
}
delete[] __xp;
delete[] __zp;
__y._M_erase_at_end(__yp + __n);
return __y;
}
poly& operator/=(const poly& __x) noexcept {
if (__x.size() > _Conv_threshold)
_div_doubling(poly(__x));
else
_div_naive(__x);
return *this;
}
poly& operator/=(poly&& __x) noexcept {
if (__x.size() > _Conv_threshold)
_div_doubling(std::move(__x));
else
_div_naive(__x);
return *this;
}
poly& operator%=(const poly& __x) noexcept {
if (__x.size() > _Conv_threshold)
return operator-=(__x.operator*(operator/(__x)));
vec::_M_erase_at_end(vec::_M_impl._M_start + _divmod_naive(__x));
return *this;
}
template <class _T> poly operator+(_T&& __x) const noexcept {
return poly(*this).operator+=(std::forward<_T>(__x));
}
template <class _T> poly operator-(_T&& __x) const noexcept {
return poly(*this).operator-=(std::forward<_T>(__x));
}
template <class _T> poly operator*(_T&& __x) const noexcept {
return poly(*this).operator*=(std::forward<_T>(__x));
}
template <class _T> poly operator/(_T&& __x) const noexcept {
return poly(*this).operator/=(std::forward<_T>(__x));
}
template <class _T> poly operator%(_T&& __x) const noexcept {
return poly(*this).operator%=(std::forward<_T>(__x));
}
std::pair<poly, poly> divmod(const poly& __x) const {
if (__x.size() > _Conv_threshold) return {operator/(__x), operator%(__x)};
poly __rem(*this);
auto __p = __rem._M_impl._M_start + __rem._divmod_naive(__x);
poly __quot(__p, __rem._M_impl._M_finish);
__rem._M_erase_at_end(__p);
return {__quot, __rem};
}
/**
* @brief Differentiate.
*
* @return Derivative.
*/
poly deriv() const noexcept {
if (auto __s = vec::_M_impl._M_start, __f = vec::_M_impl._M_finish;
__s != __f) {
poly __der(++__s, __f);
__s = __der._M_impl._M_start, __f = __der._M_impl._M_finish;
for (_Tp __i(1); __s != __f; ++__s, __i += 1) *__s *= __i;
__der._erase_leading_zeros();
return __der;
}
return {};
}
/**
* @brief Differentiate at given point.
*
* @return Derivative coefficient.
*/
_Tp deriv(const _Tp& __a) const noexcept {
_Tp __der(0);
if (auto __s = vec::_M_impl._M_start, __f = vec::_M_impl._M_finish;
__s != __f)
for (_Tp __i(1), __p(1); ++__s != __f; __i += 1, __p *= __a)
__der += *__s * __i * __p;
return __der;
}
/**
* @brief Integrate.
*
* @return Integral indefinite at the degrees divisible by the characteristic
* of `_Tp`. Coefficients are set as 0 there.
*/
poly integ() const noexcept {
if (auto __s = vec::_M_impl._M_start, __f = vec::_M_impl._M_finish;
__s != __f) {
poly __int(__f - __s + 1);
__f = std::copy(__s, __f, __int._M_impl._M_start + 1);
__s = __int._M_impl._M_start + 1;
for (_Tp __i(1); __s != __f; ++__s, __i += 1)
__i == _Tp(0) ? assert(*__s == _Tp(0)) : void(*__s /= __i);
return __int;
}
return {};
}
/**
* @brief Integrate in given range.
*
* @return Definite integral over [0, __a].
*/
_Tp integ(const _Tp& __a) const noexcept {
_Tp __int(0);
auto __s = vec::_M_impl._M_start, __f = vec::_M_impl._M_finish;
for (_Tp __p(__a), __i(1); __s != __f; ++__s, __p *= __a, __i += 1)
__int += *__s / __i * __p;
return __int;
}
/**
* @brief Integrate in given range.
*
* @return Definite integral over [__a, __b].
*/
_Tp integ(const _Tp& __a, const _Tp& __b) const noexcept {
_Tp __int(0);
auto __s = vec::_M_impl._M_start, __f = vec::_M_impl._M_finish;
for (_Tp __pa(__a), __pb(__b), __i(1); __s != __f;
++__s, __pa *= __a, __pb *= __b, __i += 1)
__int += *__s / __i * (__pb - __pa);
return __int;
}
};
/**
* @brief Polynomial interpolation in O(n log(n)^2) time.
*
* @param __first
* @param __last
* @return
*/
template <class _InputIter, typename = std::_RequireInputIter<_InputIter>>
auto interpolate(_InputIter __first, _InputIter __last) {
size_t __n = std::distance(__first, __last);
auto [__1, __2] =
typename std::iterator_traits<decltype(__first)>::value_type{};
using poly = polynomial<decltype(__1)>;
if (!__n) return poly{};
struct node {
poly __all, __lack;
};
auto __tree = new node[__n << 1];
auto __iter = __first;
for (size_t __i = 0; __i != __n; ++__i) {
auto&& [__a, __b] = *__iter++;
__tree[__i + __n].__all = {-__a, 1}, __tree[__i + __n].__lack = {1};
}
for (size_t __i = __n; --__i;)
__tree[__i].__all = __tree[__i << 1].__all * __tree[__i << 1 | 1].__all,
__tree[__i].__lack =
__tree[__i << 1].__all * std::move(__tree[__i << 1 | 1].__lack) +
__tree[__i << 1 | 1].__all * std::move(__tree[__i << 1].__lack);
for (size_t __i = 2; __i != __n << 1; __i += 2)
__tree[__i].__lack = __tree[__i >> 1].__lack % __tree[__i].__all,
__tree[__i | 1].__lack =
std::move(__tree[__i >> 1].__lack %= __tree[__i | 1].__all);
for (size_t __i = 0; __i != __n; ++__i) {
auto&& [__a, __b] = *__first++;
__tree[__i + __n].__lack[0] =
std::move(__b) / std::move(__tree[__i + __n].__lack[0]);
}
for (size_t __i = __n; --__i;)
__tree[__i].__lack = std::move(__tree[__i << 1].__all) *
std::move(__tree[__i << 1 | 1].__lack) +
std::move(__tree[__i << 1 | 1].__all) *
std::move(__tree[__i << 1].__lack);
auto __result = std::move(__tree[1].__lack);
delete[] __tree;
return __result;
}
// /**
// * @brief \\prod_{i=0}^{n-1} (x+i) \\bmod x^d.
// */
// template <class _Tp> auto rising_factorial(_Tp __n, std::size_t __d) {}
// /**
// * @brief \\prod_{i=0}^{n-1} (x+i).
// */
// template <class _Tp> auto rising_factorial(_Tp __n) {
// return rising_factorial(__n, __n);
// }
// /**
// * @brief \\prod_{i=0}^{n-1} (x-i) \\bmod x^d.
// */
// template <class _Tp> auto falling_factorial(_Tp __n, std::size_t __d) {
// auto __f = rising_factorial(__n, __d);
// for (std::size_t __i = (__n & 1) ^ 1; __i < __d; __i += 2)
// __f[__i] = -__f[__i];
// return __f;
// }
// /**
// * @brief \\prod_{i=0}^{n-1} (x-i).
// */
// template <class _Tp> auto falling_factorial(_Tp __n) {
// return falling_factorial(__n, __n);
// }
/**
* @brief \\sum_{j=0}^{d-1} x^j \\sum_{i=0}^{n-1} i^j.
*/
template <class _Tp> auto power_sums(_Tp __n, std::size_t __d) {
using return_type = polynomial<_Tp>;
if (!__d) return return_type{};
return_type __f(__d), __e(__d);
__f[0] = __n;
for (std::size_t __i = 1; __i != __d; ++__i) __f[__i] = __f[__i - 1] * __n;
_Tp __c{1};
for (std::size_t __i = 0; __i != __d; ++__i)
__c /= __i + 1, __f[__i] *= __c, __e[__i] = __c;
(__f *= __e.inv(__d)).resize(__d);
__c = 1;
for (std::size_t __i = 0; __i != __d; __c *= ++__i) __f[__i] *= __c;
return __f;
}
} // namespace workspace
#line 2 "Library\\src\\modular\\modint.hpp"
/**
* @file modint.hpp
*
* @brief Modular Arithmetic
*/
#line 12 "Library\\src\\modular\\modint.hpp"
#line 2 "Library\\src\\number_theory\\sqrt_mod.hpp"
/**
* @file sqrt_mod.hpp
* @brief Tonelli-Shanks Algorithm
*/
#line 2 "Library\\src\\number_theory\\pow_mod.hpp"
/**
* @file mod_pow.hpp
* @brief Modular Exponentiation
*/
#line 9 "Library\\src\\number_theory\\pow_mod.hpp"
#line 11 "Library\\src\\number_theory\\pow_mod.hpp"
namespace workspace {
/**
* @brief Compile time modular exponentiation.
*
* @param __x
* @param __n Exponent
* @param __mod Modulus
* @return
*/
template <class _Tp>
constexpr std::enable_if_t<(is_integral_ext<_Tp>::value), _Tp> pow_mod(
_Tp __x, _Tp __n, _Tp __mod) noexcept {
assert(__mod > 0);
using mul_type = typename multiplicable_uint<_Tp>::type;
if ((__x %= __mod) < 0) __x += __mod;
mul_type __y{1};
while (__n) {
if (__n & 1) (__y *= __x) %= __mod;
__x = (mul_type)__x * __x % __mod;
__n >>= 1;
}
return __y;
};
} // namespace workspace
#line 10 "Library\\src\\number_theory\\sqrt_mod.hpp"
namespace workspace {
/**
* @brief Compile time modular square root.
*
* @param __x
* @param __mod Modulus
* @return One if it exists. Otherwise -1.
*/
template <class _Tp>
constexpr std::enable_if_t<(is_integral_ext<_Tp>::value), _Tp> sqrt_mod(
_Tp __x, _Tp __mod) noexcept {
assert(__mod > 0);
using mul_type = typename multiplicable_uint<_Tp>::type;
if ((__x %= __mod) < 0) __x += __mod;
if (!__x) return 0;
if (__mod == 2) return __x;
if (pow_mod(__x, __mod >> 1, __mod) != 1) return -1;
_Tp __z = __builtin_ctz(__mod - 1), __q = __mod >> __z;
mul_type __a = pow_mod(__x, (__q + 1) >> 1, __mod), __b = 2;
while (pow_mod<_Tp>(__b, __mod >> 1, __mod) == 1) ++__b;
__b = pow_mod<_Tp>(__b, __q, __mod);
_Tp __shift = 0;
for (auto __r = __a * __a % __mod * pow_mod(__x, __mod - 2, __mod) % __mod;
__r != 1; (__r *= (__b *= __b) %= __mod) %= __mod) {
auto __bsf = __z;
for (auto __e = __r; __e != 1; --__bsf) (__e *= __e) %= __mod;
while (++__shift != __bsf) (__b *= __b) %= __mod;
(__a *= __b) %= __mod;
}
return __a;
};
} // namespace workspace
#line 15 "Library\\src\\modular\\modint.hpp"
namespace workspace {
namespace _modint_impl {
template <auto _Mod, unsigned _Storage> struct modint {
static_assert(is_integral_ext<decltype(_Mod)>::value,
"_Mod must be integral type.");
using mod_type = std::make_signed_t<typename std::conditional<
0 < _Mod, std::add_const_t<decltype(_Mod)>, decltype(_Mod)>::type>;
using value_type = std::decay_t<mod_type>;
using mul_type = typename multiplicable_uint<value_type>::type;
// Modulus
static mod_type mod;
static unsigned storage;
private:
value_type value = 0;
struct direct_ctor_t {};
constexpr static direct_ctor_t direct_ctor_tag{};
// Direct constructor
template <class _Tp>
constexpr modint(_Tp __n, direct_ctor_t) noexcept : value(__n) {}
public:
constexpr modint() noexcept = default;
template <class _Tp, typename = std::enable_if_t<is_integral_ext<_Tp>::value>>
constexpr modint(_Tp __n) noexcept
: value((__n %= mod) < 0 ? __n += mod : __n) {}
constexpr modint(bool __n) noexcept : value(__n) {}
constexpr operator value_type() const noexcept { return value; }
// unary operators {{
constexpr modint operator++(int) noexcept {
modint __t{*this};
operator++();
return __t;
}
constexpr modint operator--(int) noexcept {
modint __t{*this};
operator--();
return __t;
}
constexpr modint &operator++() noexcept {
if (++value == mod) value = 0;
return *this;
}
constexpr modint &operator--() noexcept {
if (!value)
value = mod - 1;
else
--value;
return *this;
}
constexpr modint operator+() const noexcept { return *this; }
constexpr modint operator-() const noexcept {
return {value ? mod - value : 0, direct_ctor_tag};
}
// }} unary operators
// operator+= {{
constexpr modint &operator+=(const modint &__x) noexcept {
if ((value += __x.value) >= mod) value -= mod;
return *this;
}
template <class _Tp>
constexpr std::enable_if_t<is_integral_ext<_Tp>::value, modint> &operator+=(
_Tp const &__x) noexcept {
if (((value += __x) %= mod) < 0) value += mod;
return *this;
}
// }} operator+=
// operator+ {{
template <class _Tp>
constexpr std::enable_if_t<is_integral_ext<_Tp>::value, modint> operator+(
_Tp const &__x) const noexcept {
return modint{*this} += __x;
}
constexpr modint operator+(modint __x) const noexcept { return __x += *this; }
template <class _Tp>
constexpr friend std::enable_if_t<is_integral_ext<_Tp>::value, modint>
operator+(_Tp const &__x, modint __y) noexcept {
return __y += __x;
}
// }} operator+
// operator-= {{
constexpr modint &operator-=(const modint &__x) noexcept {
if ((value -= __x.value) < 0) value += mod;
return *this;
}
template <class _Tp>
constexpr std::enable_if_t<is_integral_ext<_Tp>::value, modint> &operator-=(
_Tp __x) noexcept {
if (((value -= __x) %= mod) < 0) value += mod;
return *this;
}
// }} operator-=
// operator- {{
template <class _Tp>
constexpr std::enable_if_t<is_integral_ext<_Tp>::value, modint> operator-(
_Tp const &__x) const noexcept {
return modint{*this} -= __x;
}
constexpr modint operator-(const modint &__x) const noexcept {
return modint{*this} -= __x;
}
template <class _Tp>
constexpr friend std::enable_if_t<is_integral_ext<_Tp>::value, modint>
operator-(_Tp __x, const modint &__y) noexcept {
if (((__x -= __y.value) %= mod) < 0) __x += mod;
return {__x, direct_ctor_tag};
}
// }} operator-
// operator*= {{
constexpr modint &operator*=(const modint &__x) noexcept {
value =
static_cast<value_type>(value * static_cast<mul_type>(__x.value) % mod);
return *this;
}
template <class _Tp>
constexpr std::enable_if_t<is_integral_ext<_Tp>::value, modint> &operator*=(
_Tp __x) noexcept {
value = static_cast<value_type>(
value * mul_type((__x %= mod) < 0 ? __x + mod : __x) % mod);
return *this;
}
// }} operator*=
// operator* {{
constexpr modint operator*(const modint &__x) const noexcept {
return {static_cast<mul_type>(value) * __x.value % mod, direct_ctor_tag};
}
template <class _Tp>
constexpr std::enable_if_t<is_integral_ext<_Tp>::value, modint> operator*(
_Tp __x) const noexcept {
__x %= mod;
if (__x < 0) __x += mod;
return {static_cast<mul_type>(value) * __x % mod, direct_ctor_tag};
}
template <class _Tp>
constexpr friend std::enable_if_t<is_integral_ext<_Tp>::value, modint>
operator*(_Tp __x, const modint &__y) noexcept {
__x %= mod;
if (__x < 0) __x += mod;
return {static_cast<mul_type>(__x) * __y.value % mod, direct_ctor_tag};
}
// }} 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];
}
static value_type _div(mul_type __r, value_type __x) noexcept {
assert(__x != value_type(0));
if (!__r) return 0;
std::make_signed_t<value_type> __v{};
bool __neg = __x < 0 ? __x = -__x, true : false;
if (static_cast<decltype(storage)>(__x) < storage)
__v = _mem(__x);
else {
value_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;
return __r == mul_type(1) ? static_cast<value_type>(__v)
: static_cast<value_type>(__r * __v % mod);
}
public:
// operator/= {{
constexpr modint &operator/=(const modint &__x) noexcept {
if (value) value = _div(value, __x.value);
return *this;
}
template <class _Tp>
constexpr std::enable_if_t<is_integral_ext<_Tp>::value, modint> &operator/=(
_Tp __x) noexcept {
if (value) value = _div(value, __x %= mod);
return *this;
}
// }} operator/=
// operator/ {{
constexpr modint operator/(const modint &__x) const noexcept {
if (!value) return {};
return {_div(value, __x.value), direct_ctor_tag};
}
template <class _Tp>
constexpr std::enable_if_t<is_integral_ext<_Tp>::value, modint> operator/(
_Tp __x) const noexcept {
if (!value) return {};
return {_div(value, __x %= mod), direct_ctor_tag};
}
template <class _Tp>
constexpr friend std::enable_if_t<is_integral_ext<_Tp>::value, modint>
operator/(_Tp __x, const modint &__y) noexcept {
if (!__x) return {};
if ((__x %= mod) < 0) __x += mod;
return {_div(__x, __y.value), direct_ctor_tag};
}
// }} operator/
constexpr modint inv() const noexcept { return _div(1, value); }
template <class _Tp>
constexpr std::enable_if_t<is_integral_ext<_Tp>::value, modint> pow(
_Tp __e) const noexcept {
modint __r{1, direct_ctor_tag};
for (modint __b{__e < 0 ? __e = -__e, _div(1, value) : value,
direct_ctor_tag};
__e; __e >>= 1, __b *= __b)
if (__e & 1) __r *= __b;
return __r;
}
template <class _Tp>
constexpr friend std::enable_if_t<is_integral_ext<_Tp>::value, modint> pow(
modint __b, _Tp __e) noexcept {
if (__e < 0) {
__e = -__e;
__b.value = _div(1, __b.value);
}
modint __r{1, direct_ctor_tag};
for (; __e; __e >>= 1, __b *= __b)
if (__e & 1) __r *= __b;
return __r;
}
constexpr modint sqrt() const noexcept {
return {sqrt_mod(value, mod), direct_ctor_tag};
}
friend constexpr modint sqrt(const modint &__x) noexcept {
return {sqrt_mod(__x.value, mod), direct_ctor_tag};
}
template <class _Os>
friend _Os &operator<<(_Os &__os, const modint &__x) noexcept {
return __os << __x.value;
}
friend std::istream &operator>>(std::istream &__is, modint &__x) noexcept {
std::string __s;
__is >> __s;
bool __neg = false;
if (__s.front() == '-') {
__neg = true;
__s.erase(__s.begin());
}
__x = 0;
for (char __c : __s) __x = __x * 10 + (__c - '0');
if (__neg) __x = -__x;
return __is;
}
};
template <auto _Mod, unsigned _Storage>
typename modint<_Mod, _Storage>::mod_type modint<_Mod, _Storage>::mod =
_Mod > 0 ? _Mod : 0;
template <auto _Mod, unsigned _Storage>
unsigned modint<_Mod, _Storage>::storage = _Storage;
} // namespace _modint_impl
template <auto _Mod, unsigned _Storage = 0,
typename = std::enable_if_t<(_Mod > 0)>>
using modint = _modint_impl::modint<_Mod, _Storage>;
template <unsigned _Id = 0>
using modint_runtime = _modint_impl::modint<-(signed)_Id, 0>;
} // namespace workspace
#line 28 "other-workspace\\yuki.cc"
namespace workspace {
using mint = modint<998244353>;
using poly = polynomial<mint>;
struct A : polynomial<mint> {
using P = polynomial<mint>;
int zero = 0;
using P::P;
A& operator+=(A x) {
if (x.zero < zero) {
x <<= (zero - x.zero);
} else {
*this <<= (x.zero - zero);
zero = x.zero;
}
P::operator+=(x);
return *this;
}
A& operator*=(const A& x) {
zero += x.zero;
P::operator*=(x);
return *this;
}
A operator+(const A& x) const { return A(*this) += x; }
A operator*(const A& x) const { return A(*this) *= x; }
};
void main() {
// start here!
int n, m, k;
cin >> n >> m >> k;
auto c = 0;
A f;
f.zero = m;
f.resize(m * 2 + 1);
for (auto j : range(-m, m + 1)) {
if (abs(j) != k) {
f[j + f.zero] = 1;
++c;
}
}
for (auto&& x : f) {
x /= c;
}
queue<pair<A, A>> Q;
for (auto i : range(n)) {
auto f2 = f;
for (auto&& x : f2) {
x *= i + 1;
}
Q.emplace(f, f2);
}
while (Q.size() > 1) {
decltype(Q) nxt;
while (Q.size() > 1) {
auto f = Q.front();
Q.pop();
const auto g = Q.front();
Q.pop();
f.first *= g.first;
f.second *= g.first;
f.second += g.second;
nxt.emplace(f);
}
if (!Q.empty()) nxt.emplace(Q.front());
Q.swap(nxt);
}
mint ans;
auto all = Q.front().second;
for (auto i : range(all.zero)) {
ans += all[i];
}
for (auto i : range(n)) {
ans *= c;
}
cout << ans << "\n";
}
} // namespace workspace