#line 1 "other-workspace\\y.cc" // #undef _GLIBCXX_DEBUG // #define NDEBUG #include #line 2 "Library\\lib\\alias" /** * @file alias * @brief Alias */ #line 10 "Library\\lib\\alias" #line 2 "Library\\lib\\bit" #if __cplusplus > 201703L #include #elif __cplusplus > 201402L #ifndef _GLIBCXX_BIT #define _GLIBCXX_BIT 1 #include #include namespace std { template 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::digits; constexpr auto _Nd_ul = numeric_limits::digits; constexpr auto _Nd_u = numeric_limits::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::max(); unsigned long long __low = __x & __max_ull; return (_Nd - _Nd_ull) + __builtin_clzll(__low); } } template 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::digits; constexpr auto _Nd_ul = numeric_limits::digits; constexpr auto _Nd_u = numeric_limits::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::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 constexpr int __popcount(_Tp __x) noexcept { constexpr auto _Nd = numeric_limits<_Tp>::digits; if (__x == 0) return 0; constexpr auto _Nd_ull = numeric_limits::digits; constexpr auto _Nd_ul = numeric_limits::digits; constexpr auto _Nd_u = numeric_limits::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::max(); unsigned long long __low = __x & __max_ull; unsigned long long __high = __x >> _Nd_ull; return __builtin_popcountll(__low) + __builtin_popcountll(__high); } } template 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 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 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 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 () < std::declval())> constexpr typename std::conditional::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 ()( std::declval(), std::declval()))> constexpr typename std::conditional::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 () < std::declval())> constexpr _Tp min(std::initializer_list<_Tp> __x) noexcept { return *std::min_element(__x.begin(), __x.end()); } template ()( std::declval(), std::declval()))> constexpr _Tp min(std::initializer_list<_Tp> __x, _Compare __comp) noexcept { return *std::min_element(__x.begin(), __x.end(), __comp); } template () < std::declval())> constexpr typename std::conditional::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 ()( std::declval(), std::declval()))> constexpr typename std::conditional::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 () < std::declval())> constexpr _Tp max(std::initializer_list<_Tp> __x) noexcept { return *std::max_element(__x.begin(), __x.end()); } template ()( std::declval(), std::declval()))> constexpr _Tp max(std::initializer_list<_Tp> __x, _Compare __comp) noexcept { return *std::max_element(__x.begin(), __x.end(), __comp); } #ifdef _GLIBCXX_BIT template constexpr _Tp __bsf(_Tp __x) noexcept { return std::__countr_zero(__x); } template constexpr _Tp __bsr(_Tp __x) noexcept { return std::__bit_width(__x) - 1; } #endif } // namespace workspace #line 6 "other-workspace\\y.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\\y.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 void call_once(_F &&__f) { static std::unordered_set __called; if (__called.count(std::addressof(__f))) return; __called.emplace(std::addressof(__f)); __f(); } } // namespace workspace #line 2 "Library\\src\\sys\\clock.hpp" /** * @file 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 /** * @return Elapsed time of the program. */ decltype(auto) elapsed() noexcept { const auto end_time{system_clock::now()}; return duration_cast(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 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\\src\\utils\\cached.hpp" /** * @file cached.hpp * @brief Cached */ #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 { /** * @brief Fixed Point Combinator. */ template class fixed_point { public: // Construct a new fixed-point object. fixed_point(_F __x) noexcept : __fn(__x) {} // Function call. template decltype(auto) operator()(_Args... __args) { return _wrapper{__fn}(std::forward<_Args>(__args)...); } private: _F __fn; struct _wrapper { _F &__ref; template decltype(auto) operator()(_Args... __args) { return __ref(*this, std::forward<_Args>(__args)...); } }; }; } // namespace workspace #line 2 "Library\\lib\\cxx17" #ifndef _CXX17_CONSTEXPR #if __cplusplus >= 201703L #define _CXX17_CONSTEXPR constexpr #else #define _CXX17_CONSTEXPR #endif #endif #if __cplusplus < 201703L namespace std { /** * @brief Return the size of a container. * @param __cont Container. */ template constexpr auto size(const _Container& __cont) noexcept(noexcept(__cont.size())) -> decltype(__cont.size()) { return __cont.size(); } /** * @brief Return the size of an array. */ template constexpr size_t size(const _Tp (&)[_Nm]) noexcept { return _Nm; } } // namespace std #endif #line 10 "Library\\src\\utils\\cached.hpp" namespace workspace { namespace _cached_impl { // Convert keys to tuple. template struct as_tuple { using type = decltype(std::tuple_cat( std::declval, _Args>::value, std::decay_t<_Args>, _Args>>>()...)); }; // Associative array. template struct assoc : std::integral_constant::value>, std::conditional_t::value, std::set::type>, std::map::type, _Value>> { }; // Non-resursive lambda type. template struct is_recursive : std::false_type {}; // Resursive lambda type. template struct is_recursive< _F, std::__void_t &>)>> : std::true_type {}; // Recursive ver. template class _recursive { template struct _cache; template struct _cache<_R (_G::*)(_H, _Args...)> : assoc<_R, _Args...> {}; template struct _cache<_R (_G::*)(_H, _Args...) const> : assoc<_R, _Args...> {}; public: using cache_type = _cache &>)>; _recursive(_F &&__x) noexcept : __fn(__x) {} // Function call. template decltype(auto) operator()(_Args &&...__args) { return _wrapper{__fn, __c}(std::forward<_Args>(__args)...); } private: _F __fn; cache_type __c; struct _wrapper { _F &__fn; cache_type &__c; template decltype(auto) operator()(_Args &&...__args) { typename cache_type::key_type __key{__args...}; auto __i = __c.lower_bound(__key); if _CXX17_CONSTEXPR (cache_type::value) { if (__i != __c.end() && __i->first == __key) return __i->second; return __c .emplace_hint(__i, std::move(__key), __fn(*this, std::forward<_Args>(__args)...)) ->second; } else if (__i == __c.end() || *__i != __key) __c.emplace_hint(__i, std::move(__key)), __fn(*this, std::forward<_Args>(__args)...); } }; }; // Non-recursive ver. template class _non_recursive { template struct _get_func { using type = _T; }; template struct _get_func<_T, std::__void_t> { using type = decltype(&_T::operator()); }; template struct _cache; template struct _cache<_R(_Args...)> : assoc<_R, _Args...> {}; template struct _cache<_R (*)(_Args...)> : assoc<_R, _Args...> {}; template struct _cache<_R (_G::*)(_Args...)> : assoc<_R, _Args...> {}; template struct _cache<_R (_G::*)(_Args...) const> : assoc<_R, _Args...> {}; public: using cache_type = _cache::type>; _non_recursive(_F &&__x) noexcept : __fn(__x) {} // Function call. template decltype(auto) operator()(_Args &&...__args) { typename cache_type::key_type __key{__args...}; auto __i = __c.lower_bound(__key); if _CXX17_CONSTEXPR (cache_type::value) { if (__i != __c.end() && __i->first == __key) return __i->second; return __c .emplace_hint(__i, std::move(__key), __fn(std::forward<_Args>(__args)...)) ->second; } else if (__i == __c.end() || *__i != __key) __c.emplace_hint(__i, std::move(__key)), __fn(std::forward<_Args>(__args)...); } private: _F __fn; cache_type __c; }; template using _cached = std::conditional_t::value, _recursive<_F>, _non_recursive<_F>>; } // namespace _cached_impl /** * @brief Cached caller of function */ template class cached : public _cached_impl::_cached<_F> { public: // Construct a new cached object. cached() noexcept : _cached_impl::_cached<_F>(_F{}) {} // Construct a new cached object. cached(_F __x) noexcept : _cached_impl::_cached<_F>(std::move(__x)) {} }; } // namespace workspace #line 2 "Library\\src\\utils\\cat.hpp" /** * @file cat.hpp * @brief Cat */ #line 9 "Library\\src\\utils\\cat.hpp" #line 11 "Library\\src\\utils\\cat.hpp" namespace workspace { /** * @brief Concatenate two sequences. * * @param __c1 * @param __c2 * @return Concatenated sequence. */ template constexpr decltype(auto) cat(_C1 &&__c1, _C2 &&__c2) noexcept { auto __c = std::forward<_C1>(__c1); if _CXX17_CONSTEXPR (std::is_rvalue_reference::value) __c.insert(std::end(__c), std::make_move_iterator(std::begin(__c2)), std::make_move_iterator(std::end(__c2))); else __c.insert(std::end(__c), std::cbegin(__c2), std::cend(__c2)); return __c; } /** * @return Concatenated sequence. */ template constexpr decltype(auto) cat(_C1 &&__c1, _C2 &&__c2, _Args &&...__args) noexcept { return cat(cat(std::forward<_C1>(__c1), std::forward<_C2>(__c2)), std::forward<_Args>(__args)...); } } // 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 { /** * @brief Substitute __y for __x if __y < __x. * @param __x Reference * @param __y Comparison target * @return Whether or not __x is updated. */ template () < std::declval<_T1 &>())> typename std::enable_if::value, bool>::type chle( _T1 &__x, _T2 &&__y) noexcept { return __y < __x ? __x = std::forward<_T2>(__y), true : false; } /** * @brief Substitute __y for __x if __x < __y. * @param __x Reference * @param __y Comparison target * @return Whether or not __x is updated. */ template () < std::declval<_T2>())> typename std::enable_if::value, bool>::type chgr( _T1 &__x, _T2 &&__y) noexcept { return __x < __y ? __x = std::forward<_T2>(__y), true : false; } /** * @brief Substitute __y for __x if __comp(__y, __x) is true. * @param __x Reference * @param __y Comparison target * @param __comp Compare function object * @return Whether or not __x is updated. */ template ()(std::declval<_T2>(), std::declval<_T1 &>()))> typename std::enable_if::value, bool>::type chle( _T1 &__x, _T2 &&__y, _Compare __comp) noexcept { return __comp(__y, __x) ? __x = std::forward<_T2>(__y), true : false; } /** * @brief Substitute __y for __x if __comp(__x, __y) is true. * @param __x Reference * @param __y Comparison target * @param __comp Compare function object * @return Whether or not __x is updated. */ template ()(std::declval<_T1 &>(), std::declval<_T2>()))> typename std::enable_if::value, bool>::type chgr( _T1 &__x, _T2 &&__y, _Compare __comp) noexcept { return __comp(__x, __y) ? __x = std::forward<_T2>(__y), true : false; } } // namespace workspace #line 1 "Library\\src\\utils\\compare.hpp" /** * @file compare.hpp * @brief Compare */ #line 2 "Library\\src\\utils\\sfinae.hpp" /** * @file sfinae.hpp * @brief SFINAE */ #line 10 "Library\\src\\utils\\sfinae.hpp" #include #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 struct variadic_front { using type = Tp; }; template struct variadic_back; template struct variadic_back { using type = Tp; }; template struct variadic_back { using type = typename variadic_back::type; }; template class trait> using enable_if_trait_type = typename std::enable_if::value>::type; /** * @brief Return type of subscripting ( @c [] ) access. */ template using subscripted_type = typename std::decay()[0])>::type; template using element_type = typename std::decay()))>::type; template struct has_begin : std::false_type {}; template struct has_begin<_Tp, decltype(std::begin(std::declval<_Tp>()), nullptr)> : std::true_type {}; template struct has_mod : std::false_type {}; template struct has_mod<_Tp, std::__void_t> : std::true_type {}; template struct is_integral_ext : std::false_type {}; template struct is_integral_ext< _Tp, typename std::enable_if::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 constexpr static bool is_integral_ext_v = is_integral_ext<_Tp>::value; #endif template struct multiplicable_uint { using type = uint_least32_t; }; template 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 struct multiplicable_uint<_Tp, typename std::enable_if<(4 < sizeof(_Tp))>::type> { using type = __uint128_t; }; #endif template struct multiplicable_int { using type = typename std::make_signed::type>::type; }; template struct multiplicable { using type = std::conditional_t< is_integral_ext<_Tp>::value, std::conditional_t::value, typename multiplicable_int<_Tp>::type, typename multiplicable_uint<_Tp>::type>, _Tp>; }; template struct first_arg { using type = void; }; template struct first_arg<_R(_Tp, _Args...)> { using type = _Tp; }; template struct first_arg<_R (*)(_Tp, _Args...)> { using type = _Tp; }; template struct first_arg<_R (_G::*)(_Tp, _Args...)> { using type = _Tp; }; template struct first_arg<_R (_G::*)(_Tp, _Args...) const> { using type = _Tp; }; template struct parse_compare : first_arg<_Tp> {}; template struct parse_compare<_Tp, std::__void_t> : first_arg {}; } // namespace workspace #line 7 "Library\\src\\utils\\compare.hpp" #if __cplusplus >= 201703L namespace workspace { /** * @brief Compare 2 points by their value of `atan2`. * * @return */ template bool compare_arg(const _Tp& __p1, const _Tp& __p2) noexcept { const auto& [__x1, __y1] = __p1; const auto& [__x2, __y2] = __p2; using value_type = std::decay_t; using mul_type = typename multiplicable::type; if (__y1 == value_type(0)) return value_type(0) <= __x1 && (value_type(0) < __y2 || (__y2 == value_type(0) && __x2 < value_type(0))); return value_type(0) < __y1 ? value_type(0) <= __y2 && mul_type(__y1) * __x2 < mul_type(__x1) * __y2 : value_type(0) <= __y2 || mul_type(__y1) * __x2 < mul_type(__x1) * __y2; } } // namespace workspace #endif #line 7 "Library\\lib\\utils" // #include "src/utils/hash.hpp" #line 2 "Library\\src\\utils\\io\\istream.hpp" /** * @file istream.hpp * @brief Input Stream */ #include #line 13 "Library\\src\\utils\\io\\istream.hpp" #line 16 "Library\\src\\utils\\io\\istream.hpp" namespace workspace { namespace _istream_impl { template struct helper { helper(std::istream &__is, _Tp &__x) { if _CXX17_CONSTEXPR (has_begin<_Tp &>::value) for (auto &&__e : __x) helper>(__is, __e); else static_assert(has_begin<_Tp>::value, "istream unsupported type."); } }; template struct helper<_Tp, std::__void_t() >> std::declval<_Tp &>())>> { helper(std::istream &__is, _Tp &__x) { __is >> __x; } }; #ifdef __SIZEOF_INT128__ template <> struct helper<__uint128_t, void> { helper(std::istream &__is, __uint128_t &__x) { std::string __s; __is >> __s; bool __neg = false; if (__s.front() == '-') __neg = true, __s.erase(__s.begin()); __x = 0; for (char __d : __s) { __x *= 10; __d -= '0'; if (__neg) __x -= __d; else __x += __d; } } }; template <> struct helper<__int128_t, void> { helper(std::istream &__is, __int128_t &__x) { std::string __s; __is >> __s; bool __neg = false; if (__s.front() == '-') __neg = true, __s.erase(__s.begin()); __x = 0; for (char __d : __s) { __x *= 10; __d -= '0'; if (__neg) __x -= __d; else __x += __d; } } }; #endif // INT128 template struct helper> { helper(std::istream &__is, std::pair<_T1, _T2> &__x) { helper<_T1>(__is, __x.first), helper<_T2>(__is, __x.second); } }; template struct helper> { helper(std::istream &__is, std::tuple<_Tp...> &__x) { iterate(__is, __x); } private: template void iterate(std::istream &__is, _Tuple &__x) { if _CXX17_CONSTEXPR (_Nm != std::tuple_size<_Tuple>::value) { helper::type>( __is, std::get<_Nm>(__x)), iterate<_Tuple, _Nm + 1>(__is, __x); } } }; } // namespace _istream_impl /** * @brief A wrapper class for std::istream. */ class istream : public std::istream { public: /** * @brief Wrapped operator. */ template istream &operator>>(_Tp &__x) { _istream_impl::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; } }; decltype(auto) cin = static_cast(std::cin); } // namespace workspace #line 9 "Library\\lib\\utils" // #include "src/utils/io/ostream.hpp" // #include "src/utils/io/read.hpp" #line 2 "Library\\src\\utils\\grid\\motion.hpp" /** * @file motion.hpp * @brief Motion */ #line 9 "Library\\src\\utils\\grid\\motion.hpp" #line 11 "Library\\src\\utils\\grid\\motion.hpp" namespace workspace { /** * @brief Transpose. * @param __grid */ template >()[0].resize(0))> constexpr decltype(auto) transpose(_Grid &&__grid) noexcept { #if __cplusplus < 201703L auto __h = __grid.size(), __w = __grid[0].size(); #else auto __h = std::size(__grid), __w = std::size(__grid[0]); #endif std::decay_t<_Grid> __t(__w); for (auto &&__r : __t) __r.resize(__h); for (size_t __i = 0; __i != __h; ++__i) for (size_t __j = 0; __j != __w; ++__j) if _CXX17_CONSTEXPR (std::is_rvalue_reference::value) __t[__j][__i] = std::move(__grid[__i][__j]); else __t[__j][__i] = __grid[__i][__j]; return __t; } /** * @brief Transpose. * @param __grid */ template constexpr decltype(auto) transpose(const _Tp (&__grid)[_Rows][_Cols]) noexcept { std::array, _Cols> __t; for (size_t __i = 0; __i != _Rows; ++__i) for (size_t __j = 0; __j != _Cols; ++__j) __t[__j][__i] = __grid[__i][__j]; return __t; } /** * @brief Transpose. * @param __grid */ template constexpr decltype(auto) transpose(_Tp(&&__grid)[_Rows][_Cols]) noexcept { std::array, _Cols> __t; for (size_t __i = 0; __i != _Rows; ++__i) for (size_t __j = 0; __j != _Cols; ++__j) __t[__j][__i] = std::move(__grid[__i][__j]); return __t; } /** * @brief Transpose. * @param __grid */ template constexpr decltype(auto) transpose( const std::array, _Rows> &__grid) noexcept { std::array, _Cols> __t; for (size_t __i = 0; __i != _Rows; ++__i) for (size_t __j = 0; __j != _Cols; ++__j) __t[__j][__i] = __grid[__i][__j]; return __t; } /** * @brief Transpose. * @param __grid */ template constexpr decltype(auto) transpose( std::array, _Rows> &&__grid) noexcept { std::array, _Cols> __t; for (size_t __i = 0; __i != _Rows; ++__i) for (size_t __j = 0; __j != _Cols; ++__j) __t[__j][__i] = std::move(__grid[__i][__j]); return __t; } /** * @brief Roll the grid counter-clockwise. * @param __grid */ template decltype(auto) roll_ccw(_Grid &&__grid) noexcept { if _CXX17_CONSTEXPR (std::is_rvalue_reference::value) { auto __t = transpose(std::move(__grid)); std::reverse(std::begin(__t), std::end(__t)); return __t; } else { auto __t = transpose(__grid); std::reverse(std::begin(__t), std::end(__t)); return __t; } } /** * @brief Roll the grid clockwise. * @param __grid */ template decltype(auto) roll_cw(_Grid &&__grid) noexcept { if _CXX17_CONSTEXPR (std::is_rvalue_reference::value) { std::reverse(std::begin(__grid), std::end(__grid)); return transpose(std::move(__grid)); } else { auto __t = transpose(__grid); for (auto &&__r : __t) std::reverse(std::begin(__r), std::end(__r)); return __t; } } } // namespace workspace #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 ::value - 1> struct common_iterator_category { using type = typename std::common_type< typename common_iterator_category::type, typename std::iterator_traits::type>::iterator_category>::type; }; template struct common_iterator_category { 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 #include namespace workspace { /* * @class reverse_iterator * @brief Wrapper class for `std::reverse_iterator`. * @see http://gcc.gnu.org/PR51823 */ template class reverse_iterator : public std::reverse_iterator { using base_std = std::reverse_iterator; std::optional 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 #include namespace workspace { /** * @brief Make a multi-dimensional vector. * * @param __dim Dimension * @param __x Initial value */ template constexpr decltype(auto) make_vector([[maybe_unused]] _Dim* __dim, const _Tp& __x = _Tp()) { static_assert(std::is_convertible<_Dim, size_t>::value); if constexpr (_Nm) return std::vector(*__dim, make_vector<_Tp, _Dim, _Nm - 1>(std::next(__dim), __x)); else return __x; } /** * @brief Make a multi-dimensional vector. * * @param __dim Dimension * @param __x Initial value */ template constexpr decltype(auto) make_vector(const _Dim (&__dim)[_Nm], const _Tp& __x = _Tp()) { return make_vector<_Tp, _Dim, _Nm>((_Dim*)__dim, __x); } /** * @brief Make a multi-dimensional vector. * * @param __dim Dimension * @param __x Initial value */ template constexpr decltype(auto) make_vector([[maybe_unused]] const _Dim& __dim, const _Tp& __x = _Tp()) { if constexpr (_Nm == std::tuple_size<_Dim>::value) return __x; else { static_assert( std::is_convertible, size_t>::value); return std::vector(std::get<_Nm>(__dim), make_vector<_Tp, _Dim, _Nm + 1>(__dim, __x)); } } } // namespace workspace #endif #line 16 "Library\\lib\\utils" // #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 #line 10 "Library\\src\\utils\\py-like\\reversed.hpp" namespace workspace { namespace _reversed_impl { template 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 constexpr decltype(auto) reversed(_Container &&__cont) noexcept { return _reversed_impl::reversed<_Container>{std::forward<_Container>(__cont)}; } template constexpr decltype(auto) reversed( std::initializer_list<_Tp> &&__cont) noexcept { return _reversed_impl::reversed>{ std::forward>(__cont)}; } } // namespace workspace #line 12 "Library\\src\\utils\\py-like\\range.hpp" #if __cplusplus >= 201703L namespace workspace { template 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 rbegin() const noexcept { return reverse_iterator(end()); } constexpr reverse_iterator rend() const noexcept { return reverse_iterator(begin()); } constexpr size_t size() const noexcept { return std::distance(__first, __last); } }; template constexpr decltype(auto) rrange(_Args &&...__args) noexcept { return reversed(range(std::forward<_Args>(__args)...)); } template constexpr decltype(auto) iterate(_Container &&__cont) noexcept { return range(std::begin(__cont), std::end(__cont)); } template 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" #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 using uniform_distribution = typename std::conditional< std::is_integral<_Arithmetic>::value, std::uniform_int_distribution<_Arithmetic>, std::uniform_real_distribution<_Arithmetic>>::type; template class random_number_generator : uniform_distribution<_Arithmetic> { using base = uniform_distribution<_Arithmetic>; _Engine __engine; public: random_number_generator(_Arithmetic __min, _Arithmetic __max) : base(__min, __max), __engine(std::random_device{}()) {} random_number_generator(_Arithmetic __max = 1) : random_number_generator(0, __max) {} random_number_generator(typename base::param_type const& __param) : base(__param), __engine(std::random_device{}()) {} decltype(auto) operator()() noexcept { 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 void shuffle(_RAIter __first, _RAIter __last) { static _Engine __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 constexpr typename std::enable_if<(is_integral_ext::value && is_integral_ext::value), typename std::common_type::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 constexpr typename std::enable_if<(is_integral_ext::value && is_integral_ext::value), typename std::common_type::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 23 "Library\\lib\\utils" // #include "src\utils\rand\tree.hpp" // #include "src\utils\reference_list.hpp" #line 2 "Library\\src\\utils\\io\\input.hpp" /** * @file input.hpp * @brief Input */ #line 9 "Library\\src\\utils\\io\\input.hpp" namespace workspace { namespace _input_impl { template class input { _Tp __value; template struct is_same : std::false_type {}; template struct is_same<_Arg, _Arg> : std::true_type {}; public: operator _Tp &() noexcept { return __value; } operator const _Tp &() const noexcept { return __value; } template input(_Args &&...__args) noexcept : __value(std::forward<_Args>(__args)...) { if _CXX17_CONSTEXPR (!is_same::value && !is_same<_Tp, _Args...>::value) cin >> __value; } input &operator=(const _Tp &__x) noexcept { return __value = __x, *this; } }; template class input<_Tp, true> : public _Tp { template struct is_same : std::false_type {}; template struct is_same<_Arg, _Arg> : std::true_type {}; public: operator _Tp &() noexcept { return *this; } operator const _Tp &() const noexcept { return *this; } template input(_Args &&...__args) noexcept : _Tp(std::forward<_Args>(__args)...) { if _CXX17_CONSTEXPR (!is_same::value && !is_same<_Tp, _Args...>::value) cin >> *this; } input &operator=(const _Tp &__x) noexcept { _Tp::operator=(__x); return *this; } }; } // namespace _input_impl template using input = _input_impl::input<_Tp, std::is_class<_Tp>::value>; } // namespace workspace #line 11 "other-workspace\\y.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\\rational.hpp" /** * @file rational.hpp * @brief Rational */ #line 9 "Library\\src\\algebra\\rational.hpp" namespace workspace { /** * @brief Rational * * @tparam _Tp Ring structure */ template class rational { constexpr void normalize() noexcept; public: _Tp __num{0}, __den{1}; constexpr rational() noexcept = default; constexpr rational(const _Tp &__x) noexcept : __num(__x) {} constexpr rational(const _Tp &__x, const _Tp __y) noexcept : __num(__x), __den(__y) {} constexpr operator bool() const noexcept { return operator!=(0); } constexpr rational operator+() const noexcept { return *this; } constexpr rational operator-() const noexcept { return {-__num, __den}; } constexpr rational operator+(const rational &__x) const noexcept { return {__num * __x.__den + __x.__num * __den, __den * __x.__den}; } constexpr rational operator-(const rational &__x) const noexcept { return {__num * __x.__den - __x.__num * __den, __den * __x.__den}; } constexpr rational operator*(const rational &__x) noexcept { return {__num * __x.__num, __den * __x.__den}; } constexpr rational operator/(const rational &__x) noexcept { assert(__x.__num != _Tp(0)); return {__num * __x.__den, __den * __x.__num}; } constexpr rational &operator+=(const rational &__x) noexcept { (__num *= __x.__den) += __den * __x.__num, __den *= __x.__den; return *this; } constexpr rational &operator-=(const rational &__x) noexcept { (__num *= __x.__den) -= __den * __x.__num, __den *= __x.__den; return *this; } constexpr rational &operator*=(const rational &__x) noexcept { __num *= __x.__num, __den *= __x.__den; return *this; } constexpr rational &operator/=(const rational &__x) noexcept { assert(__x.__num != _Tp(0)); __num *= __x.__den, __den *= __x.__num; return *this; } constexpr bool operator==(const rational &__x) const noexcept { return __num == __x.__num && __den == __x.den; } constexpr bool operator!=(const rational &__x) const noexcept { return __num != __x.__num || __den != __x.den; } constexpr bool operator<(const rational &__x) const noexcept { return __num * __x.__den < __den * __x.__num; } }; } // 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 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 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 struct modint { static_assert(is_integral_ext::value, "_Mod must be integral type."); using mod_type = std::make_signed_t, decltype(_Mod)>::type>; using value_type = std::decay_t; using mul_type = typename multiplicable_uint::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 constexpr modint(_Tp __n, direct_ctor_t) noexcept : value(__n) {} public: constexpr modint() noexcept = default; template ::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 constexpr std::enable_if_t::value, modint> &operator+=( _Tp const &__x) noexcept { if (((value += __x) %= mod) < 0) value += mod; return *this; } // }} operator+= // operator+ {{ template constexpr std::enable_if_t::value, modint> operator+( _Tp const &__x) const noexcept { return modint{*this} += __x; } constexpr modint operator+(modint __x) const noexcept { return __x += *this; } template constexpr friend std::enable_if_t::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 constexpr std::enable_if_t::value, modint> &operator-=( _Tp __x) noexcept { if (((value -= __x) %= mod) < 0) value += mod; return *this; } // }} operator-= // operator- {{ template constexpr std::enable_if_t::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 constexpr friend std::enable_if_t::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 * static_cast(__x.value) % mod); return *this; } template constexpr std::enable_if_t::value, modint> &operator*=( _Tp __x) noexcept { value = static_cast( 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(value) * __x.value % mod, direct_ctor_tag}; } template constexpr std::enable_if_t::value, modint> operator*( _Tp __x) const noexcept { __x %= mod; if (__x < 0) __x += mod; return {static_cast(value) * __x % mod, direct_ctor_tag}; } template constexpr friend std::enable_if_t::value, modint> operator*(_Tp __x, const modint &__y) noexcept { __x %= mod; if (__x < 0) __x += mod; return {static_cast(__x) * __y.value % mod, direct_ctor_tag}; } // }} operator* protected: static value_type _mem(value_type __x) { static std::vector __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 __v{}; bool __neg = __x < 0 ? __x = -__x, true : false; if (static_cast(__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(__v) : static_cast(__r * __v % mod); } public: // operator/= {{ constexpr modint &operator/=(const modint &__x) noexcept { if (value) value = _div(value, __x.value); return *this; } template constexpr std::enable_if_t::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 constexpr std::enable_if_t::value, modint> operator/( _Tp __x) const noexcept { if (!value) return {}; return {_div(value, __x %= mod), direct_ctor_tag}; } template constexpr friend std::enable_if_t::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 constexpr std::enable_if_t::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 constexpr friend std::enable_if_t::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 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 typename modint<_Mod, _Storage>::mod_type modint<_Mod, _Storage>::mod = _Mod > 0 ? _Mod : 0; template unsigned modint<_Mod, _Storage>::storage = _Storage; } // namespace _modint_impl template 0)>> using modint = _modint_impl::modint<_Mod, _Storage>; template using modint_runtime = _modint_impl::modint<-(signed)_Id, 0>; } // namespace workspace #line 28 "other-workspace\\y.cc" namespace workspace { using mint = modint<998244353>; template () + 1)> void f(T) {} void main() { // start here! input n, k; priority_queue> Q; mint sum; while (n--) { input a; Q.emplace(a, 1); sum += (int)a; } mint ans{1}; for (auto i : range((int)k)) { ans *= i + 1; ans /= sum; } while (k--) { auto [x, y] = Q.top(); Q.pop(); ans *= x; ans /= y++; Q.emplace(x, y); } cout << ans << "\n"; } } // namespace workspace