#line 2 "Library\\src\\algebra\\polynomial.hpp" /** * @file polynomial.hpp * @brief Polynomial */ #include #include #include #line 2 "Library\\lib\\cxx17" #ifndef _CXX17_CONSTEXPR #if __cplusplus >= 201703L #define _CXX17_CONSTEXPR constexpr #else #define _CXX17_CONSTEXPR #endif #endif #line 2 "Library\\src\\algebra\\ntt.hpp" /** * @file ntt.hpp * @brief Number Theoretic Transform * @date 2021-02-20 * * */ #line 2 "Library\\src\\number_theory\\ext_gcd.hpp" /** * @file ext_gcd.hpp * @brief Extended Euclidean Algorithm */ #include #line 2 "Library\\src\\utils\\sfinae.hpp" /** * @file sfinae.hpp * @brief SFINAE */ #include #include #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 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 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 constexpr typename std::enable_if<(is_integral_ext::value), Tp>::type primitive_root(const Tp __mod) noexcept { assert(__mod > 0); using int_type = typename multiplicable_uint::type; int_type __r = __mod, __p[16] = {}, *__q = __p; for (int_type __i = 2; __i <= __r / __i; ++__i) { if (__r % __i) continue; *__q++ = __i; while (!(__r % __i)) __r /= __i; } if (__r != 1) *__q++ = __r; int_type __tot = __mod; for (__q = __p; *__q; *__q++ = 0) (__tot /= *__q) *= *__q - 1; __r = __tot, __q = __p + 1, __p[0] = 1; for (int_type __i = 2; __i <= __r / __i; ++__i) { if (__r % __i) continue; *__q++ = __i; while (!(__r % __i)) __r /= __i; } if (__r != 1) *__q++ = __r; for (Tp __r = 1; __r != __mod; ++__r) { auto __cnt = 0; for (__q = __p; *__q; ++__q) { int_type __w = 1; for (int_type __e = __tot / *__q, __x = __r; __e; __e >>= 1, (__x *= __x) %= __mod) if (__e & 1) (__w *= __x) %= __mod; if (__w == 1 && ++__cnt > 1) break; } if (__cnt == 1) return __r; } return 0; }; } // namespace workspace #line 13 "Library\\src\\algebra\\ntt.hpp" namespace workspace { namespace ntt_impl { /** * @see * https://github.com/atcoder/ac-library/blob/master/atcoder/convolution.hpp */ template 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 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 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 constexpr void ntt(_FIter __first, _FIter __last) noexcept { using value_type = typename std::decay::type; constexpr __coef _; 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 constexpr void ntt(_A &a) noexcept { ntt(std::begin(a), std::end(a)); } template constexpr void intt(_FIter __first, _FIter __last) noexcept { using value_type = typename std::decay::type; constexpr __icoef _; 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 __; while (__first != __last) *--__last *= __.__ip2[__h]; } // namespace ntt_impl template constexpr void intt(_A &a) noexcept { intt(std::begin(a), std::end(a)); } } // namespace ntt_impl using ntt_impl::intt; using ntt_impl::ntt; } // namespace workspace #line 15 "Library\\src\\algebra\\polynomial.hpp" namespace workspace { /** * @brief Polynomial. * * @tparam _Tp Ring structure * @tparam _Conv_threshold Threshold for convolution method */ template class polynomial : public std::vector<_Tp> { using vec = std::vector<_Tp>; using poly = polynomial; template friend _Os& operator<<(_Os& __os, const poly& __x) { bool __head = true; for (const auto& __a : __x) { if (!__head) __os << ' '; __head = false; __os << __a; } return __os; } public: using vec::vec; using size_type = typename vec::size_type; protected: void _erase_leading_zeros() noexcept { auto __i = vec::_M_impl._M_finish; while (__i != vec::_M_impl._M_start && *(__i - 1) == _Tp(0)) --__i; vec::_M_erase_at_end(__i); } template void _dft(_Iter __first, _Iter __last) const noexcept { if _CXX17_CONSTEXPR (has_mod<_Tp>::value) ntt(__first, __last); else { // fft(__first, __last); assert(0); // Not implemented! } } template void _idft(_Iter __first, _Iter __last) const noexcept { if _CXX17_CONSTEXPR (has_mod<_Tp>::value) intt(__first, __last); else { // ifft(__first, __last); assert(0); // Not implemented! } } void _conv_naive(const poly& __x) noexcept { if (vec::_M_impl._M_start == vec::_M_impl._M_finish) return; if (__x._M_impl._M_start == __x._M_impl._M_finish) { vec::_M_erase_at_end(vec::_M_impl._M_start); return; } vec::_M_default_append(__x._M_impl._M_finish - __x._M_impl._M_start - 1); for (auto __i = vec::_M_impl._M_finish; __i-- != vec::_M_impl._M_start;) { auto __j = __i, __k = __x._M_impl._M_start; *__i *= *__k++; while (__j != vec::_M_impl._M_start && __k != __x._M_impl._M_finish) *__i += *--__j * *__k++; } } void _conv_dft(poly&& __x) noexcept { if _CXX17_CONSTEXPR (has_mod<_Tp>::value) _conv_ntt(std::move(__x)); else { // _conv_fft(std::move(__x)); assert(0); // Not implemented! } } void _conv_fft(poly&& __x) noexcept; void _conv_ntt(poly&& __x) noexcept { size_type __n = vec::_M_impl._M_finish - vec::_M_impl._M_start, __m = __x._M_impl._M_finish - __x._M_impl._M_start, __len = 1 << (32 - __builtin_clz(__n + __m - 1)); vec::_M_default_append(__len - __n); __x._M_default_append(__len - __m); ntt(vec::_M_impl._M_start, vec::_M_impl._M_finish); ntt(__x._M_impl._M_start, __x._M_impl._M_finish); for (auto __i = vec::_M_impl._M_start, __j = __x._M_impl._M_start; __i != vec::_M_impl._M_finish; ++__i, ++__j) *__i *= std::move(*__j); intt(vec::_M_impl._M_start, vec::_M_impl._M_finish); vec::_M_erase_at_end(vec::_M_impl._M_start + __n + __m - 1); } /** * @brief * * @param __x * @return Degree of __x. */ size_type _divmod_naive(const poly& __x) { auto __xfin = __x._M_impl._M_finish; auto __xlen = __x.size(); while (__xfin != __x._M_impl._M_start && *(__xfin - 1) == _Tp(0)) --__xfin, --__xlen; assert(__xlen != 0); _erase_leading_zeros(); auto __p = vec::_M_impl._M_finish; while (size_type(__p - vec::_M_impl._M_start) >= __xlen) { --__p; auto __src = __xfin; auto __dst = __p; *__dst /= *--__src; while (__src != __x._M_impl._M_start) *--__dst -= *--__src * *__p; } return std::min(__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 > _Iter eval(_Iter __first, _Iter __last) const noexcept { return eval(__first, __last, __first); } /** * @brief Multipoint evaluation. */ template > _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 poly operator+(_T&& __x) const noexcept { return poly(*this).operator+=(std::forward<_T>(__x)); } template poly operator-(_T&& __x) const noexcept { return poly(*this).operator-=(std::forward<_T>(__x)); } template poly operator*(_T&& __x) const noexcept { return poly(*this).operator*=(std::forward<_T>(__x)); } template poly operator/(_T&& __x) const noexcept { return poly(*this).operator/=(std::forward<_T>(__x)); } template poly operator%(_T&& __x) const noexcept { return poly(*this).operator%=(std::forward<_T>(__x)); } std::pair divmod(const poly& __x) const { if (__x.size() > _Conv_threshold) return {operator/(__x), operator%(__x)}; poly __rem(*this); auto __p = __rem._M_impl._M_start + __rem._divmod_naive(__x); poly __quot(__p, __rem._M_impl._M_finish); __rem._M_erase_at_end(__p); return {__quot, __rem}; } /** * @brief Differentiate. * * @return Derivative. */ poly deriv() const noexcept { if (auto __s = vec::_M_impl._M_start, __f = vec::_M_impl._M_finish; __s != __f) { poly __der(++__s, __f); __s = __der._M_impl._M_start, __f = __der._M_impl._M_finish; for (_Tp __i(1); __s != __f; ++__s, __i += 1) *__s *= __i; __der._erase_leading_zeros(); return __der; } return {}; } /** * @brief Differentiate at given point. * * @return Derivative coefficient. */ _Tp deriv(const _Tp& __a) const noexcept { _Tp __der(0); if (auto __s = vec::_M_impl._M_start, __f = vec::_M_impl._M_finish; __s != __f) for (_Tp __i(1), __p(1); ++__s != __f; __i += 1, __p *= __a) __der += *__s * __i * __p; return __der; } /** * @brief Integrate. * * @return Integral indefinite at the degrees divisible by the characteristic * of `_Tp`. Coefficients are set as 0 there. */ poly integ() const noexcept { if (auto __s = vec::_M_impl._M_start, __f = vec::_M_impl._M_finish; __s != __f) { poly __int(__f - __s + 1); __f = std::copy(__s, __f, __int._M_impl._M_start + 1); __s = __int._M_impl._M_start + 1; for (_Tp __i(1); __s != __f; ++__s, __i += 1) __i == _Tp(0) ? assert(*__s == _Tp(0)) : void(*__s /= __i); return __int; } return {}; } /** * @brief Integrate in given range. * * @return Definite integral over [0, __a]. */ _Tp integ(const _Tp& __a) const noexcept { _Tp __int(0); auto __s = vec::_M_impl._M_start, __f = vec::_M_impl._M_finish; for (_Tp __p(__a), __i(1); __s != __f; ++__s, __p *= __a, __i += 1) __int += *__s / __i * __p; return __int; } /** * @brief Integrate in given range. * * @return Definite integral over [__a, __b]. */ _Tp integ(const _Tp& __a, const _Tp& __b) const noexcept { _Tp __int(0); auto __s = vec::_M_impl._M_start, __f = vec::_M_impl._M_finish; for (_Tp __pa(__a), __pb(__b), __i(1); __s != __f; ++__s, __pa *= __a, __pb *= __b, __i += 1) __int += *__s / __i * (__pb - __pa); return __int; } }; /** * @brief Polynomial interpolation in O(n log(n)^2) time. * * @param __first * @param __last * @return */ template > auto interpolate(_InputIter __first, _InputIter __last) { size_t __n = std::distance(__first, __last); auto [__1, __2] = typename std::iterator_traits::value_type{}; using poly = polynomial; if (!__n) return poly{}; struct node { poly __all, __lack; }; auto __tree = new node[__n << 1]; auto __iter = __first; for (size_t __i = 0; __i != __n; ++__i) { auto&& [__a, __b] = *__iter++; __tree[__i + __n].__all = {-__a, 1}, __tree[__i + __n].__lack = {1}; } for (size_t __i = __n; --__i;) __tree[__i].__all = __tree[__i << 1].__all * __tree[__i << 1 | 1].__all, __tree[__i].__lack = __tree[__i << 1].__all * std::move(__tree[__i << 1 | 1].__lack) + __tree[__i << 1 | 1].__all * std::move(__tree[__i << 1].__lack); for (size_t __i = 2; __i != __n << 1; __i += 2) __tree[__i].__lack = __tree[__i >> 1].__lack % __tree[__i].__all, __tree[__i | 1].__lack = std::move(__tree[__i >> 1].__lack %= __tree[__i | 1].__all); for (size_t __i = 0; __i != __n; ++__i) { auto&& [__a, __b] = *__first++; __tree[__i + __n].__lack[0] = std::move(__b) / std::move(__tree[__i + __n].__lack[0]); } for (size_t __i = __n; --__i;) __tree[__i].__lack = std::move(__tree[__i << 1].__all) * std::move(__tree[__i << 1 | 1].__lack) + std::move(__tree[__i << 1 | 1].__all) * std::move(__tree[__i << 1].__lack); auto __result = std::move(__tree[1].__lack); delete[] __tree; return __result; } // /** // * @brief Rising factorial of degree n. // * @return \\prod_{i=0}^{n-1} (x+i) // */ // template auto rising_factorial(_Tp __n) {} // /** // * @brief \\prod_{i=0}^{n-1} (x+i). // */ // template auto rising_factorial(_Tp __n) { // return rising_factorial(__n, __n); // } // /** // * @brief \\prod_{i=0}^{n-1} (x-i) \\bmod x^d. // */ // template 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 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 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\\data_structure\\segment_tree\\basic.hpp" /** * @file basic.hpp * @brief Segment Tree */ #line 10 "Library\\src\\data_structure\\segment_tree\\basic.hpp" #if __cplusplus >= 201703L #include #endif #line 2 "Library\\src\\algebra\\system\\monoid.hpp" /* * @file monoid.hpp * @brief Monoid */ #include namespace workspace { template struct min_monoid { using value_type = T; static T min, max; T value; min_monoid() : value(max) {} min_monoid(const T &value) : value(value) {} operator T() const { return value; } min_monoid operator+(const min_monoid &rhs) const { return value < rhs.value ? *this : rhs; } min_monoid operator*(const E &rhs) const; }; template T min_monoid::min = std::numeric_limits::min() / 2; template T min_monoid::max = std::numeric_limits::max() / 2; template struct max_monoid : min_monoid { using base = min_monoid; using base::min_monoid; max_monoid() : base(base::min) {} max_monoid operator+(const max_monoid &rhs) const { return !(base::value < rhs.value) ? *this : rhs; } max_monoid operator*(const E &rhs) const; }; } // 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 using require_unary_plus = std::enable_if_t< std::is_convertible()), _Tp>::value>; template struct has_unary_plus : std::false_type {}; template struct has_unary_plus<_Tp, require_unary_plus<_Tp>> : std::true_type {}; // Unary `-` template using require_unary_minus = std::enable_if_t< std::is_convertible()), _Tp>::value>; template struct has_unary_minus : std::false_type {}; template struct has_unary_minus<_Tp, require_unary_minus<_Tp>> : std::true_type {}; // Binary `+` template using require_binary_plus = std::enable_if_t() + std::declval()), _Tp1>::value>; template struct has_binary_plus : std::false_type {}; template struct has_binary_plus<_Tp1, _Tp2, require_binary_plus<_Tp1, _Tp2>> : std::true_type {}; // Binary `-` template using require_binary_minus = std::__void_t() - std::declval())>; template struct has_binary_minus : std::false_type {}; template struct has_binary_minus<_Tp1, _Tp2, require_binary_minus<_Tp1, _Tp2>> : std::true_type {}; // Binary `*` template using require_binary_multiplies = std::enable_if_t() * std::declval()), _Tp1>::value>; template struct has_binary_multiplies : std::false_type {}; template struct has_binary_multiplies<_Tp1, _Tp2, require_binary_multiplies<_Tp1, _Tp2>> : std::true_type {}; // Binary `/` template using require_binary_divides = std::enable_if_t() / std::declval()), _Tp1>::value>; template struct has_binary_divides : std::false_type {}; template struct has_binary_divides<_Tp1, _Tp2, require_binary_divides<_Tp1, _Tp2>> : std::true_type {}; // Binary `%` template using require_binary_modulus = std::enable_if_t() % std::declval()), _Tp1>::value>; template struct has_binary_modulus : std::false_type {}; template struct has_binary_modulus<_Tp1, _Tp2, require_binary_modulus<_Tp1, _Tp2>> : std::true_type {}; } // namespace workspace #line 17 "Library\\src\\data_structure\\segment_tree\\basic.hpp" namespace workspace { /** * @tparam _Monoid `operator+`, `operator=` * @tparam Container_tmpl `operator[]`, `size_type` */ template class Container_tmpl = std::vector> class segment_tree { static_assert(has_binary_plus<_Monoid>::value, "\'_Monoid\' has no proper binary \'operator+\'."); constexpr static bool __support_lazy = !std::is_void<_Endomorphism>::value; #if __cplusplus < 201703L struct node_base { node_base() = default; node_base(_Monoid const &__x) : __v(__x) {} operator bool() const { return __f; } void operator=(_Monoid const &__x) { __v = __x; __f = true; } _Monoid &operator*() { return __v; } _Monoid const &operator*() const { return __v; } void reset() { __f = false; } private: _Monoid __v{}; bool __f{true}; }; #else struct node_base : std::optional<_Monoid> { using std::optional<_Monoid>::operator=; node_base() : std::optional<_Monoid>(_Monoid{}) {} }; #endif struct node_lazy : node_base { using node_base::operator=; std::optional<_Endomorphism> __z; }; using node = typename std::conditional<__support_lazy, node_lazy, node_base>::type; using container_type = Container_tmpl; public: using size_type = typename container_type::size_type; using difference_type = typename container_type::difference_type; class iterator { segment_tree *__p; size_type __i; public: using difference_type = segment_tree::difference_type; using value_type = _Monoid; using reference = _Monoid &; using pointer = iterator; using iterator_category = std::random_access_iterator_tag; /** * @brief Construct a new iterator object * */ iterator() = default; /** * @brief Construct a new iterator object * * @param __p Pointer to a segment tree object * @param __i Index */ iterator(segment_tree *__p, size_type __i) : __p(__p), __i(__i) {} bool operator==(iterator const &rhs) const { return __p == rhs.__p && __i == rhs.__i; } bool operator!=(iterator const &rhs) const { return !operator==(rhs); } bool operator<(iterator const &rhs) const { return __i < rhs.__i; } bool operator>(iterator const &rhs) const { return __i > rhs.__i; } bool operator<=(iterator const &rhs) const { return __i <= rhs.__i; } bool operator>=(iterator const &rhs) const { return __i >= rhs.__i; } iterator &operator++() { return ++__i, *this; } iterator &operator--() { return --__i, *this; } difference_type operator-(iterator const &rhs) const { return __i - rhs.__i; } /** * @brief * * @return reference */ reference operator*() const { return __p->operator[](__i); } }; using value_type = typename iterator::value_type; using reference = typename iterator::reference; iterator begin() { return {this, 0}; } iterator end() { return {this, size_orig}; } auto rbegin() { return std::make_reverse_iterator(end()); } auto rend() { return std::make_reverse_iterator(begin()); } protected: size_type size_orig, height, size_ext; container_type data; node &pull(size_type __i) noexcept { if (!data[__i]) data[__i] = *pull(__i << 1) + *pull(__i << 1 | 1); return data[__i]; } void push(size_type __i) { if (auto &__lz = data[__i].__z) { apply(data[__i << 1], *__lz); apply(data[__i << 1 | 1], *__lz); __lz.reset(); } } void sync(size_type __i) { if (!data[__i]) data[__i] = *pull(__i << 1) + *pull(__i << 1 | 1); else if (data[__i].__z) { apply(data[__i << 1], *data[__i].__z); apply(data[__i << 1 | 1], *data[__i].__z); data[__i].__z.reset(); } } template void apply(node &__nd, _End const &endo) { *__nd = *__nd * endo; __nd.__z = __nd.__z ? *__nd.__z * endo : endo; } // template // void apply_top(size_t __i, _End const &endo) { // auto &__nd = pull(__i); // *__nd = *__nd * endo; // __nd.__z = __nd.__z ? *__nd.__z * endo : endo; // } template constexpr decltype(std::declval()(_Monoid{})) pass_args( Pred pred, _Monoid const &_1, [[maybe_unused]] size_type _2) { return pred(_1); } template constexpr decltype(std::declval()(_Monoid{}, size_type{})) pass_args( Pred pred, _Monoid const &_1, size_type _2) { return pred(_1, _2); } template size_type left_partition_subtree(size_type __i, _Monoid mono, size_type step, Pred pred) { assert(__i); while (__i < size_ext) { if constexpr (__support_lazy) push(__i); const _Monoid tmp = *pull((__i <<= 1) | 1) + mono; if (pass_args(pred, tmp, ((__i | 1) << --step) ^ size_ext)) mono = tmp; else ++__i; } return ++__i -= size_ext; } template size_type right_partition_subtree(size_type __i, _Monoid mono, size_type step, Pred pred) { assert(__i); while (__i < size_ext) { if constexpr (__support_lazy) push(__i); const _Monoid tmp = mono + *pull(__i <<= 1); if (pass_args(pred, tmp, ((__i | 1) << --step) ^ size_ext)) ++__i, mono = tmp; } return (__i -= size_ext) < size_orig ? __i : size_orig; } public: /** * @brief Construct a new segment tree object. * * @param __n Number of elements. */ segment_tree(size_type __n = 0) : size_orig{__n}, height(__n > 1 ? 64 - __builtin_clzll(__n - 1) : 0), size_ext{size_type{1} << height} { if constexpr (std::is_constructible::value) data = container_type(size_ext << 1); data[0].reset(); } /** * @brief Construct a new segment tree object. * * @param __n Number of elements. * @param __x */ segment_tree(size_type __n, const value_type &__x) : segment_tree(__n) { for (auto __i = begin(); __i != end(); ++__i) *__i = __x; } /** * @brief Construct a new segment tree object. * * @param __n Number of elements. * @param __x */ template segment_tree(size_type __n, _Tp &&__x) : segment_tree(__n) { for (auto __i = begin(); __i != end(); ++__i) *__i = __x; } /** * @brief Construct a new segment tree object. * * @param __first * @param __last */ template > segment_tree(_Iterator __first, _Iterator __last) : segment_tree(std::distance(__first, __last)) { for (auto __i = begin(); __first != __last; ++__i, ++__first) *__i = *__first; } /** * @brief Conversion to container_type. */ operator Container_tmpl() const { Container_tmpl __c(size()); for (size_type __i = 0; __i != size(); ++__i) __c[__i] = *data[__i | size_ext]; return __c; } /** * @return Number of elements. */ size_type size() const { return size_orig; } /** * @return Whether %segment_tree is empty. */ bool empty() const { return !size(); } /** * @brief Subscripting ( @c [] ) access. * * @param __i Index of the element * @return Reference to the element. */ reference operator[](size_type __i) { assert(__i < size_orig); reference __ref = *data[__i |= size_ext]; if constexpr (__support_lazy) { for (size_t __h{height}; __h; --__h) { push(__i >> __h); data[__i >> __h].reset(); } } else { while (data[__i >>= 1]) data[__i].reset(); } return __ref; } /** * @param first Left end, inclusive * @param last Right end, exclusive * @return Sum of elements in the interval. */ value_type fold(size_type first, size_type last) { assert(last <= size_orig); if (!(first < last)) return {}; first += size_ext, last += size_ext; value_type left{}, right{}; for (size_t l = first, r = last--; l != r; l >>= 1, r >>= 1) { if (l & 1) left = left + *pull(l++); if (r & 1) right = *pull(--r) + right; if constexpr (__support_lazy) { if (data[first >>= 1].__z) left = left * *data[first].__z; if (data[last >>= 1].__z) right = right * *data[last].__z; } } if constexpr (__support_lazy) { while (first >>= 1, last >>= 1) { if (data[first].__z) left = left * *data[first].__z; if (data[last].__z) right = right * *data[last].__z; } } // if (first >= last) return _Monoid{}; // first += size_ext, last += size_ext - 1; // _Monoid left{}, right{}; // for (size_t l = first, r = last + 1; last; l >>= 1, r >>= 1) { // if (l < r) { // if (l & 1) left = left + data[l++]; // if (r & 1) right = data[--r] + right; // } // if (first >>= 1, last >>= 1) { // left = left * lazy[first]; // right = right * lazy[last]; // } // } // return left + right; return left + right; } /** * @return The whole sum. */ value_type fold() { return *pull(1); } template void update(size_type first, size_type last, _End const &endo) { static_assert(__support_lazy); assert(last <= size_orig); if (!(first < last)) return; first += size_ext, last += size_ext; --last; for (auto i = height; i; --i) push(first >> i), push(last >> i); ++last; for (auto l = first, r = last; l < r; l >>= 1, r >>= 1) { if (l & 1) apply(pull(l++), endo); if (r & 1) apply(pull(--r), endo); } for (first >>= __builtin_ffs(first); data[first]; first >>= 1) data[first].reset(); for (last >>= __builtin_ffs(last); data[last]; last >>= 1) data[last].reset(); } /** * @brief Binary search for the partition point. * @param right Right fixed end of the interval, exclusive * @param pred Predicate in the form of either 'bool(_Monoid)' or * 'bool(_Monoid, size_type)' * @return Left end of the extremal interval satisfying the condition, * inclusive. */ template size_type left_partition(size_type right, Pred pred) { assert(right <= size_orig); right += size_ext; if constexpr (__support_lazy) for (size_t i{height}; i; --i) push(right >> i); _Monoid mono{}; for (size_type left{size_ext}, step{}; left != right; left >>= 1, right >>= 1, ++step) { if ((left & 1) != (right & 1)) { _Monoid tmp = *pull(--right) + mono; if (!pass_args(pred, tmp, (right << step) ^ size_ext)) return left_partition_subtree(right, mono, step, pred); mono = tmp; } } return 0; } /** * @brief Binary search for the partition point. * @param left Left fixed end of the interval, inclusive * @param pred Predicate in the form of either 'bool(_Monoid)' or * 'bool(_Monoid, size_type)' * @return Right end of the extremal interval satisfying the condition, * exclusive. */ template size_type right_partition(size_type left, Pred pred) { assert(left <= size_orig); left += size_ext; if constexpr (__support_lazy) for (size_t i{height}; i; --i) push(left >> i); _Monoid mono{}; for (size_type right{size_ext << 1}, step{}; left != right; left >>= 1, right >>= 1, ++step) { if ((left & 1) != (right & 1)) { _Monoid tmp = mono + *pull(left); if (!pass_args(pred, tmp, ((left + 1) << step) ^ size_ext)) return right_partition_subtree(left, mono, step, pred); mono = tmp; ++left; } } return size_orig; } }; template > segment_tree(_Iterator, _Iterator) -> segment_tree::value_type>; template > segment_tree(typename segment_tree<_Tp>::size_type, _Tp &&) -> segment_tree<_Tp>; } // namespace workspace #line 2 "Library\\src\\modular\\modint.hpp" /** * @file modint.hpp * * @brief Modular Arithmetic */ #line 10 "Library\\src\\modular\\modint.hpp" #include #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 4 "other-workspace\\y2.cc" // #include "src/utils/py-like/enumerate.hpp" // #include "src/utils/py-like/range.hpp" namespace workspace { using mint = modint<998244353>; using poly = polynomial; constexpr auto max_value = 3000; struct mono { poly v{1}; mono operator+(mono x) const { auto t = v; t *= x.v; t.resize(max_value + 1); return {t}; } }; using namespace std; using i64 = int_least64_t; void main() { // start here! i64 N; int Q; cin >> N >> Q; vector> updates; vector> queries; vector id; for (int i = 0; i < Q; ++i) { i64 k; int a, b, s, t; cin >> k >> a >> b >> s >> t; if (auto f = find(begin(id), end(id), k); f != id.end()) { k = f - id.begin(); } else { k = id.size(); id.emplace_back(k); } updates.emplace_back(k, a, b); queries.emplace_back(s, t); } poly f(max_value + 1); { mint c = 1; for (int i = 0; i <= max_value; ++i) { f[i] = c; c *= N - id.size() + i; c /= i + 1; } } segment_tree sgt(id.size(), {poly(max_value + 1, 1)}); for (int i = 0; i < Q; ++i) { auto [k, a, b] = updates[i]; { auto &v = sgt[k].v; for (int i = a; i <= b; ++i) { v[i] = 0; } } auto [s, t] = queries[i]; auto v = sgt.fold().v * f; mint ans; for (int i = s; i <= t; ++i) { ans += v[i]; } cout << ans << "\n"; } } } // namespace workspace int main() { workspace::main(); }