Submit Info #52419

Problem Lang User Status Time Memory
Polynomial Interpolation cpp jell AC 1598 ms 71.55 MiB

ケース詳細
Name Status Time Memory
example_00 AC 1 ms 0.61 MiB
example_01 AC 1 ms 0.60 MiB
max_random_00 AC 1598 ms 71.54 MiB
max_random_01 AC 1598 ms 71.55 MiB
random_00 AC 1451 ms 67.30 MiB
random_01 AC 776 ms 36.32 MiB
random_02 AC 554 ms 27.25 MiB

#line 1 "Library\\test\\library-checker\\polynomial_interpolation.test.cpp" #define PROBLEM "https://judge.yosupo.jp/problem/polynomial_interpolation" #line 2 "Library\\src\\algebra\\interpolation.hpp" /** * @file interpolation.hpp * @brief Interpolation */ #include <vector> #line 2 "Library\\src\\algebra\\polynomial.hpp" /** * @file polynomial.hpp * @brief Polynomial */ #include <algorithm> #include <cassert> #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 #if __cplusplus < 201703L namespace std { /** * @brief Return the size of a container. * @param __cont Container. */ template <typename _Container> constexpr auto size(const _Container& __cont) noexcept(noexcept(__cont.size())) -> decltype(__cont.size()) { return __cont.size(); } /** * @brief Return the size of an array. */ template <typename _Tp, size_t _Nm> constexpr size_t size(const _Tp (&)[_Nm]) noexcept { return _Nm; } } // namespace std #endif #line 2 "Library\\src\\algebra\\ntt.hpp" /** * @file ntt.hpp * @brief Number Theoretic Transform * @see * ac-library(https://github.com/atcoder/ac-library/blob/master/atcoder/convolution.hpp) */ #line 2 "Library\\src\\number_theory\\ext_gcd.hpp" /** * @file ext_gcd.hpp * @brief Extended Euclidean Algorithm */ #include <tuple> #line 2 "Library\\src\\utils\\sfinae.hpp" /** * @file sfinae.hpp * @brief SFINAE */ #include <cstdint> #include <iterator> #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 12 "Library\\src\\algebra\\ntt.hpp" namespace workspace { namespace _ntt_impl { 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 _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 } // 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); } // Temporary aid #define _NotImplemented has_mod<_Tp>::value template <class _Iter> void _dft(_Iter __first, _Iter __last) const noexcept { // if _CXX17_CONSTEXPR (has_mod<_Tp>::value) static_assert(_NotImplemented); _ntt_impl::ntt(__first, __last); // else } template <class _Iter> void _idft(_Iter __first, _Iter __last) const noexcept { // if _CXX17_CONSTEXPR (has_mod<_Tp>::value) static_assert(_NotImplemented); _ntt_impl::intt(__first, __last); // else } void _conv_dft(poly&& __x) noexcept { // if _CXX17_CONSTEXPR (has_mod<_Tp>::value) static_assert(_NotImplemented); _conv_ntt(std::move(__x)); // else } #undef _NotImplemented 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_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_impl::ntt(vec::_M_impl._M_start, vec::_M_impl._M_finish); _ntt_impl::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); _ntt_impl::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 Rising factorial of degree n. // * @return \\prod_{i=0}^{n-1} (x+i) // */ // template <class _Tp> auto rising_factorial(_Tp __n) {} // /** // * @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 Generating function of the sum of k-th powers of the first n * non-negative integers. O(d \\log d) time in modulo x^d. * * @return \\sum_{k=0}^{d-1} x^k \\sum_{i=0}^{n-1} i^k. */ template <class _Tp> polynomial<_Tp> power_sum(_Tp __n, std::size_t __d) { if (!__d) return {}; polynomial<_Tp> __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\\algebra\\system\\operation.hpp" /** * @file operation.hpp * @brief Operation Traits */ #line 9 "Library\\src\\algebra\\system\\operation.hpp" namespace workspace { // Unary `+` template <class _Tp> using require_unary_plus = std::enable_if_t< std::is_convertible<decltype(+std::declval<const _Tp &>()), _Tp>::value>; template <class _Tp, class = void> struct has_unary_plus : std::false_type {}; template <class _Tp> struct has_unary_plus<_Tp, require_unary_plus<_Tp>> : std::true_type {}; // Unary `-` template <class _Tp> using require_unary_minus = std::enable_if_t< std::is_convertible<decltype(-std::declval<const _Tp &>()), _Tp>::value>; template <class _Tp, class = void> struct has_unary_minus : std::false_type {}; template <class _Tp> struct has_unary_minus<_Tp, require_unary_minus<_Tp>> : std::true_type {}; // Binary `+` template <class _Tp1, class _Tp2 = _Tp1> using require_binary_plus = std::enable_if_t<std::is_convertible<decltype(std::declval<const _Tp1 &>() + std::declval<const _Tp2 &>()), _Tp1>::value>; template <class _Tp1, class _Tp2 = _Tp1, class = void> struct has_binary_plus : std::false_type {}; template <class _Tp1, class _Tp2> struct has_binary_plus<_Tp1, _Tp2, require_binary_plus<_Tp1, _Tp2>> : std::true_type {}; // Binary `-` template <class _Tp1, class _Tp2 = _Tp1> using require_binary_minus = std::__void_t<decltype(std::declval<const _Tp1 &>() - std::declval<const _Tp2 &>())>; template <class _Tp1, class _Tp2 = _Tp1, class = void> struct has_binary_minus : std::false_type {}; template <class _Tp1, class _Tp2> struct has_binary_minus<_Tp1, _Tp2, require_binary_minus<_Tp1, _Tp2>> : std::true_type {}; // Binary `*` template <class _Tp1, class _Tp2 = _Tp1> using require_binary_multiplies = std::enable_if_t<std::is_convertible<decltype(std::declval<const _Tp1 &>() * std::declval<const _Tp2 &>()), _Tp1>::value>; template <class _Tp1, class _Tp2 = _Tp1, class = void> struct has_binary_multiplies : std::false_type {}; template <class _Tp1, class _Tp2> struct has_binary_multiplies<_Tp1, _Tp2, require_binary_multiplies<_Tp1, _Tp2>> : std::true_type {}; // Binary `/` template <class _Tp1, class _Tp2 = _Tp1> using require_binary_divides = std::enable_if_t<std::is_convertible<decltype(std::declval<const _Tp1 &>() / std::declval<const _Tp2 &>()), _Tp1>::value>; template <class _Tp1, class _Tp2 = _Tp1, class = void> struct has_binary_divides : std::false_type {}; template <class _Tp1, class _Tp2> struct has_binary_divides<_Tp1, _Tp2, require_binary_divides<_Tp1, _Tp2>> : std::true_type {}; // Binary `%` template <class _Tp1, class _Tp2 = _Tp1> using require_binary_modulus = std::enable_if_t<std::is_convertible<decltype(std::declval<const _Tp1 &>() % std::declval<const _Tp2 &>()), _Tp1>::value>; template <class _Tp1, class _Tp2 = _Tp1, class = void> struct has_binary_modulus : std::false_type {}; template <class _Tp1, class _Tp2> struct has_binary_modulus<_Tp1, _Tp2, require_binary_modulus<_Tp1, _Tp2>> : std::true_type {}; template <class _Tp1, class _Tp2 = _Tp1, class = void, class = void, class = void, class = void> struct has_arithmetic : std::false_type {}; template <class _Tp1, class _Tp2> struct has_arithmetic<_Tp1, _Tp2, require_binary_plus<_Tp1, _Tp2>, require_binary_minus<_Tp1, _Tp2>, require_binary_multiplies<_Tp1, _Tp2>, require_binary_divides<_Tp1, _Tp2>> : std::true_type {}; template <class _Tp1, class _Tp2 = _Tp1> using require_arithmetic = std::enable_if_t<has_arithmetic<_Tp1, _Tp2>::value>; } // namespace workspace #line 12 "Library\\src\\algebra\\interpolation.hpp" namespace workspace { /** * @brief Lagrange interpolation on the points 0, 1, 2, ... * @param __x Point to evaluate at. * @param __first * @param __last */ template <class _Tp, class _InputIter, typename = std::_RequireInputIter<_InputIter>, typename = require_arithmetic< typename std::iterator_traits<_InputIter>::value_type>> auto interpolate(_Tp __x, _InputIter __first, _InputIter __last) noexcept { using value_type = typename std::iterator_traits<_InputIter>::value_type; value_type __c{1}, __k{1}, __y{}; std::vector<value_type> __f(__first, __last); auto __i = __f.begin(); while (__i != __f.end()) { *__i++ *= __c; __c /= __k, __k += 1; __c *= __x, __x -= 1; } __c = __k = 1; while (__i != __f.begin()) { __y += *--__i * __c; __c /= -__k, __k += 1; __x += 1, __c *= __x; } return __y; } /** * @brief Polynomial interpolation in O(n log(n)^2) time. * @param __first * @param __last */ template <class _InputIter, typename = std::_RequireInputIter<_InputIter>> auto interpolate(_InputIter __first, _InputIter __last) noexcept { size_t __n = std::distance(__first, __last); auto [__1, __2] = typename std::iterator_traits<_InputIter>::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; } } // namespace workspace #line 2 "Library\\src\\modular\\modint.hpp" /** * @file modint.hpp * * @brief Modular Arithmetic */ #line 10 "Library\\src\\modular\\modint.hpp" #include <iostream> #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> 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 __x) noexcept { __x %= mod, value += __x; if (value < 0) value += mod; else if (value >= mod) 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 { __x %= mod, value -= __x; if (value < 0) value += mod; else if (value >= mod) 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{mod != 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{mod != 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}; } 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 2 "Library\\src\\utils\\io\\istream.hpp" /** * @file istream.hpp * @brief Input Stream */ #include <cxxabi.h> #line 13 "Library\\src\\utils\\io\\istream.hpp" #line 16 "Library\\src\\utils\\io\\istream.hpp" namespace workspace { namespace _istream_impl { template <class _Tp, typename = void> struct helper { helper(std::istream &__is, _Tp &__x) { if _CXX17_CONSTEXPR (has_begin<_Tp &>::value) for (auto &&__e : __x) helper<std::decay_t<decltype(__e)>>(__is, __e); else static_assert(has_begin<_Tp>::value, "istream unsupported type."); } }; template <class _Tp> struct helper<_Tp, std::__void_t<decltype(std::declval<std::istream &>() >> 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 <class _T1, class _T2> struct helper<std::pair<_T1, _T2>> { helper(std::istream &__is, std::pair<_T1, _T2> &__x) { helper<_T1>(__is, __x.first), helper<_T2>(__is, __x.second); } }; template <class... _Tp> struct helper<std::tuple<_Tp...>> { helper(std::istream &__is, std::tuple<_Tp...> &__x) { iterate(__is, __x); } private: template <class _Tuple, size_t _Nm = 0> void iterate(std::istream &__is, _Tuple &__x) { if _CXX17_CONSTEXPR (_Nm != std::tuple_size<_Tuple>::value) { helper<typename std::tuple_element<_Nm, _Tuple>::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 <typename _Tp> 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<istream &>(std::cin); } // namespace workspace #line 2 "Library\\src\\utils\\io\\ostream.hpp" /** * @file ostream.hpp * @brief Output Stream */ #line 9 "Library\\src\\utils\\io\\ostream.hpp" #line 11 "Library\\src\\utils\\io\\ostream.hpp" namespace workspace { template <class _Os> struct is_ostream { template <typename... _Args> static std::true_type __test(std::basic_ostream<_Args...> *); static std::false_type __test(void *); constexpr static bool value = decltype(__test(std::declval<_Os *>()))::value; }; template <class _Os> using ostream_ref = typename std::enable_if<is_ostream<_Os>::value, _Os &>::type; /** * @brief Stream insertion operator for C-style array. * * @param __os Output stream * @param __a Array * @return Reference to __os. */ template <class _Os, class _Tp, size_t _Nm> typename std::enable_if<bool(sizeof(_Tp) > 2), ostream_ref<_Os>>::type operator<<(_Os &__os, const _Tp (&__a)[_Nm]) { if _CXX17_CONSTEXPR (_Nm) { __os << *__a; for (auto __i = __a + 1, __e = __a + _Nm; __i != __e; ++__i) __os << ' ' << *__i; } return __os; } /** * @brief Stream insertion operator for std::array. * * @param __os Output stream * @param __a Array * @return Reference to __os. */ template <class _Os, class _Tp, size_t _Nm> ostream_ref<_Os> operator<<(_Os &__os, const std::array<_Tp, _Nm> &__a) { if _CXX17_CONSTEXPR (_Nm) { __os << __a[0]; for (size_t __i = 1; __i != _Nm; ++__i) __os << ' ' << __a[__i]; } return __os; } /** * @brief Stream insertion operator for std::pair. * * @param __os Output stream * @param __p Pair * @return Reference to __os. */ template <class _Os, class _T1, class _T2> ostream_ref<_Os> operator<<(_Os &__os, const std::pair<_T1, _T2> &__p) { return __os << __p.first << ' ' << __p.second; } /** * @brief Stream insertion operator for std::tuple. * * @param __os Output stream * @param __t Tuple * @return Reference to __os. */ template <class _Os, class _Tp, size_t _Nm = 0> typename std::enable_if<bool(std::tuple_size<_Tp>::value + 1), ostream_ref<_Os>>::type operator<<(_Os &__os, const _Tp &__t) { if _CXX17_CONSTEXPR (_Nm != std::tuple_size<_Tp>::value) { if _CXX17_CONSTEXPR (_Nm) __os << ' '; __os << std::get<_Nm>(__t); operator<<<_Os, _Tp, _Nm + 1>(__os, __t); } return __os; } template <class _Os, class _Container, typename = decltype(std::begin(std::declval<_Container>()))> typename std::enable_if< !std::is_same<std::decay_t<_Container>, std::string>::value && !std::is_same<std::decay_t<_Container>, char *>::value, ostream_ref<_Os>>::type operator<<(_Os &__os, const _Container &__cont) { bool __h = true; for (auto &&__e : __cont) __h ? __h = 0 : (__os << ' ', 0), __os << __e; return __os; } #ifdef __SIZEOF_INT128__ /** * @brief Stream insertion operator for __int128_t. * * @param __os Output Stream * @param __x 128-bit integer * @return Reference to __os. */ template <class _Os> ostream_ref<_Os> operator<<(_Os &__os, __int128_t __x) { if (!__x) return __os << '0'; if (__x < 0) __os << '-'; char __s[40], *__p = __s; while (__x) { auto __d = __x % 10; *__p++ = '0' + (__x < 0 ? -__d : __d); __x /= 10; } *__p = 0; for (char *__t = __s; __t < --__p; ++__t) *__t ^= *__p ^= *__t ^= *__p; return __os << __s; } /** * @brief Stream insertion operator for __uint128_t. * * @param __os Output Stream * @param __x 128-bit unsigned integer * @return Reference to __os. */ template <class _Os> ostream_ref<_Os> operator<<(_Os &__os, __uint128_t __x) { if (!__x) return __os << '0'; char __s[40], *__p = __s; while (__x) *__p++ = '0' + __x % 10, __x /= 10; *__p = 0; for (char *__t = __s; __t < --__p; ++__t) *__t ^= *__p ^= *__t ^= *__p; return __os << __s; } #endif } // namespace workspace #line 7 "Library\\test\\library-checker\\polynomial_interpolation.test.cpp" int main() { using namespace workspace; using mint = modint<998244353>; int n; cin >> n; std::vector<std::pair<mint, mint>> xy(n); for (auto&& [x, y] : xy) cin >> x; for (auto&& [x, y] : xy) cin >> y; auto p = interpolate(begin(xy), end(xy)); p.resize(n); std::cout << p << "\n"; }