結果
| 問題 | No.1549 [Cherry 2nd Tune] BANning Tuple |
| ユーザー |
 jell
|
| 提出日時 | 2021-06-11 22:07:12 |
| 言語 | C++17 (gcc 13.2.0 + boost 1.83.0) |
| 結果 |
AC
|
| 実行時間 | 477 ms / 4,000 ms |
| コード長 | 60,233 bytes |
| コンパイル時間 | 1,601 ms |
| コンパイル使用メモリ | 114,352 KB |
| 実行使用メモリ | 5,948 KB |
| 最終ジャッジ日時 | 2023-08-21 12:35:16 |
| 合計ジャッジ時間 | 10,142 ms |
|
ジャッジサーバーID （参考情報） |
judge11 / judge15 |
（要ログイン）
テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | AC | 5 ms
4,380 KB |
| testcase_01 | AC | 13 ms
4,380 KB |
| testcase_02 | AC | 219 ms
4,380 KB |
| testcase_03 | AC | 396 ms
4,580 KB |
| testcase_04 | AC | 400 ms
4,476 KB |
| testcase_05 | AC | 387 ms
4,464 KB |
| testcase_06 | AC | 388 ms
4,504 KB |
| testcase_07 | AC | 477 ms
5,816 KB |
| testcase_08 | AC | 474 ms
5,752 KB |
| testcase_09 | AC | 476 ms
5,948 KB |
| testcase_10 | AC | 475 ms
5,776 KB |
| testcase_11 | AC | 476 ms
5,716 KB |
| testcase_12 | AC | 477 ms
5,656 KB |
| testcase_13 | AC | 477 ms
5,660 KB |
| testcase_14 | AC | 477 ms
5,684 KB |
| testcase_15 | AC | 476 ms
5,616 KB |
| testcase_16 | AC | 474 ms
5,624 KB |
| testcase_17 | AC | 476 ms
5,612 KB |
| testcase_18 | AC | 476 ms
5,716 KB |
| testcase_19 | AC | 56 ms
4,376 KB |
ソースコード
#line 2 "Library\\src\\algebra\\polynomial.hpp"
/**
* @file polynomial.hpp
* @brief Polynomial
*/
#include <algorithm>
#include <cassert>
#include <vector>
#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 <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 13 "Library\\src\\algebra\\ntt.hpp"
namespace workspace {
namespace ntt_impl {
/**
* @see
* https://github.com/atcoder/ac-library/blob/master/atcoder/convolution.hpp
*/
template <class _Tp> struct __coef {
_Tp sum_e[30]; // sum_e[i] = ies[0] * ... * ies[i - 1] * es[i]
constexpr __coef() : sum_e{} {
if (_Tp::mod < 2) return;
int cnt2 = __builtin_ctz(_Tp::mod - 1);
_Tp e = 1;
{
auto p = (_Tp::mod - 1) >> cnt2;
_Tp w = primitive_root(_Tp::mod);
while (p) {
if (p & 1) e *= w;
p >>= 1;
w *= w;
}
}
_Tp ie = ext_gcd(decltype(_Tp::mod)(e), _Tp::mod).first;
_Tp es[30] = {}, ies[30] = {}; // es[i]^(2^(2+i)) == 1
for (int i = cnt2; i >= 2; i--) {
// e^(2^i) == 1
es[i - 2] = e;
ies[i - 2] = ie;
e *= e;
ie *= ie;
}
_Tp now = 1;
for (int i = 0; i <= cnt2 - 2; i++) {
sum_e[i] = es[i] * now;
now *= ies[i];
}
}
};
template <class _Tp> struct __icoef {
_Tp sum_ie[30]; // sum_e[i] = ies[0] * ... * ies[i - 1] * es[i]
constexpr __icoef() : sum_ie{} {
if (_Tp::mod < 2) return;
int cnt2 = __builtin_ctz(_Tp::mod - 1);
_Tp e = 1;
{
auto p = (_Tp::mod - 1) >> cnt2;
_Tp w = primitive_root(_Tp::mod);
while (p) {
if (p & 1) e *= w;
p >>= 1;
w *= w;
}
}
_Tp ie = ext_gcd(decltype(_Tp::mod)(e), _Tp::mod).first;
_Tp es[30] = {}, ies[30] = {}; // es[i]^(2^(2+i)) == 1
for (int i = cnt2; i >= 2; i--) {
// e^(2^i) == 1
es[i - 2] = e;
ies[i - 2] = ie;
e *= e;
ie *= ie;
}
_Tp now = 1;
for (int i = 0; i <= cnt2 - 2; i++) {
sum_ie[i] = ies[i] * now;
now *= es[i];
}
}
};
template <class _Tp> struct __ipow2 {
_Tp __ip2[30];
constexpr __ipow2() : __ip2{1, (1 + _Tp::mod) / 2} {
for (size_t __i = 1; __i + 1 != std::size(__ip2); ++__i)
__ip2[__i + 1] = __ip2[__i] * __ip2[1];
}
};
template <class _FIter>
constexpr void ntt(_FIter __first, _FIter __last) noexcept {
using value_type = typename std::decay<decltype(*__first)>::type;
constexpr __coef<value_type> _;
auto __h = __builtin_ctz(std::distance(__first, __last));
for (ptrdiff_t __p = 1 << __h; __p >>= 1;) {
value_type now = -1;
auto __l = __first;
for (size_t __s = 1 << __h; __l != __last;
now *= _.sum_e[__builtin_ctz(--__s)]) {
auto __r = __l + __p;
for (auto __mid = __r; __l != __mid; ++__l, ++__r) {
auto __tmp = *__l;
*__l -= *__r *= now;
*__r += __tmp;
}
__l = __r;
}
}
}
template <class _A> constexpr void ntt(_A &a) noexcept {
ntt(std::begin(a), std::end(a));
}
template <class _FIter>
constexpr void intt(_FIter __first, _FIter __last) noexcept {
using value_type = typename std::decay<decltype(*__first)>::type;
constexpr __icoef<value_type> _;
auto __h = __builtin_ctz(std::distance(__first, __last));
for (ptrdiff_t __p = 1; __p >> __h ^ 1; __p <<= 1) {
value_type inow = 1;
auto __l = __first;
for (size_t __s = 1 << __h; __l != __last;
inow *= _.sum_ie[__builtin_ctz(--__s)]) {
auto __r = __l + __p;
for (auto __mid = __r; __l != __mid; ++__l, ++__r) {
auto __tmp = (*__l - *__r) * inow;
*__l += *__r;
*__r = __tmp;
}
__l = __r;
}
}
constexpr __ipow2<value_type> __;
while (__first != __last) *--__last *= __.__ip2[__h];
} // namespace ntt_impl
template <class _A> constexpr void intt(_A &a) noexcept {
intt(std::begin(a), std::end(a));
}
} // namespace ntt_impl
using ntt_impl::intt;
using ntt_impl::ntt;
} // namespace workspace
#line 15 "Library\\src\\algebra\\polynomial.hpp"
namespace workspace {
/**
* @brief Polynomial.
*
* @tparam _Tp Ring structure
* @tparam _Conv_threshold Threshold for convolution method
*/
template <class _Tp, std::size_t _Conv_threshold = 64>
class polynomial : public std::vector<_Tp> {
using vec = std::vector<_Tp>;
using poly = polynomial;
template <class _Os> friend _Os& operator<<(_Os& __os, const poly& __x) {
bool __head = true;
for (const auto& __a : __x) {
if (!__head) __os << ' ';
__head = false;
__os << __a;
}
return __os;
}
public:
using vec::vec;
using size_type = typename vec::size_type;
protected:
void _erase_leading_zeros() noexcept {
auto __i = vec::_M_impl._M_finish;
while (__i != vec::_M_impl._M_start && *(__i - 1) == _Tp(0)) --__i;
vec::_M_erase_at_end(__i);
}
template <class _Iter> void _dft(_Iter __first, _Iter __last) const noexcept {
if _CXX17_CONSTEXPR (has_mod<_Tp>::value)
ntt(__first, __last);
else {
// fft(__first, __last);
assert(0); // Not implemented!
}
}
template <class _Iter>
void _idft(_Iter __first, _Iter __last) const noexcept {
if _CXX17_CONSTEXPR (has_mod<_Tp>::value)
intt(__first, __last);
else {
// ifft(__first, __last);
assert(0); // Not implemented!
}
}
void _conv_naive(const poly& __x) noexcept {
if (vec::_M_impl._M_start == vec::_M_impl._M_finish) return;
if (__x._M_impl._M_start == __x._M_impl._M_finish) {
vec::_M_erase_at_end(vec::_M_impl._M_start);
return;
}
vec::_M_default_append(__x._M_impl._M_finish - __x._M_impl._M_start - 1);
for (auto __i = vec::_M_impl._M_finish; __i-- != vec::_M_impl._M_start;) {
auto __j = __i, __k = __x._M_impl._M_start;
*__i *= *__k++;
while (__j != vec::_M_impl._M_start && __k != __x._M_impl._M_finish)
*__i += *--__j * *__k++;
}
}
void _conv_dft(poly&& __x) noexcept {
if _CXX17_CONSTEXPR (has_mod<_Tp>::value)
_conv_ntt(std::move(__x));
else {
// _conv_fft(std::move(__x));
assert(0); // Not implemented!
}
}
void _conv_fft(poly&& __x) noexcept;
void _conv_ntt(poly&& __x) noexcept {
size_type __n = vec::_M_impl._M_finish - vec::_M_impl._M_start,
__m = __x._M_impl._M_finish - __x._M_impl._M_start,
__len = 1 << (32 - __builtin_clz(__n + __m - 1));
vec::_M_default_append(__len - __n);
__x._M_default_append(__len - __m);
ntt(vec::_M_impl._M_start, vec::_M_impl._M_finish);
ntt(__x._M_impl._M_start, __x._M_impl._M_finish);
for (auto __i = vec::_M_impl._M_start, __j = __x._M_impl._M_start;
__i != vec::_M_impl._M_finish; ++__i, ++__j)
*__i *= std::move(*__j);
intt(vec::_M_impl._M_start, vec::_M_impl._M_finish);
vec::_M_erase_at_end(vec::_M_impl._M_start + __n + __m - 1);
}
/**
* @brief
*
* @param __x
* @return Degree of __x.
*/
size_type _divmod_naive(const poly& __x) {
auto __xfin = __x._M_impl._M_finish;
auto __xlen = __x.size();
while (__xfin != __x._M_impl._M_start && *(__xfin - 1) == _Tp(0))
--__xfin, --__xlen;
assert(__xlen != 0);
_erase_leading_zeros();
auto __p = vec::_M_impl._M_finish;
while (size_type(__p - vec::_M_impl._M_start) >= __xlen) {
--__p;
auto __src = __xfin;
auto __dst = __p;
*__dst /= *--__src;
while (__src != __x._M_impl._M_start) *--__dst -= *--__src * *__p;
}
return std::min<size_type>(__xlen - 1, __p - vec::_M_impl._M_start);
}
void _div_naive(const poly& __x) { operator>>=(_divmod_naive(__x)); }
void _div_doubling(poly&& __x) noexcept {
_erase_leading_zeros();
__x._erase_leading_zeros();
auto __n = vec::_M_impl._M_finish - vec::_M_impl._M_start;
auto __m = __x._M_impl._M_finish - __x._M_impl._M_start;
if (__n < __m)
vec::clear();
else {
assert(__m != 0);
std::reverse(__x._M_impl._M_start, __x._M_impl._M_finish);
__x = __x.inv(__n - __m + 1);
std::reverse(vec::_M_impl._M_start, vec::_M_impl._M_finish);
vec::_M_erase_at_end(vec::_M_impl._M_finish - (__m - 1));
operator*=(__x).resize(__n - __m + 1);
std::reverse(vec::_M_impl._M_start, vec::_M_impl._M_finish);
}
}
public:
/**
* @return Degree of %polynomial. Return -1 if it equals zero.
*/
size_type deg() const noexcept { return vec::size() - 1; }
/**
* @param __i Not exceeding the degree.
* @return Coefficient of x^i.
*/
typename vec::reference operator[](size_type __i) noexcept {
assert(__i < vec::size());
return *(vec::_M_impl._M_start + __i);
}
/**
* @param __i Not exceeding the degree.
* @return Coefficient of x^i.
*/
typename vec::const_reference operator[](size_type __i) const noexcept {
assert(__i < vec::size());
return *(vec::_M_impl._M_start + __i);
}
/**
* @brief Evaluate at given point.
*/
_Tp eval(const _Tp& __a) const noexcept {
_Tp __v(0), __p(1);
for (auto __i = vec::_M_impl._M_start; __i != vec::_M_impl._M_finish;
++__i, __p *= __a)
__v += *__i * __p;
return __v;
}
/**
* @brief In-place multipoint evaluation.
*/
template <class _Iter, typename = std::_RequireInputIter<_Iter>>
_Iter eval(_Iter __first, _Iter __last) const noexcept {
return eval(__first, __last, __first);
}
/**
* @brief Multipoint evaluation.
*/
template <class _InputIter, class _OutputIter,
typename = std::_RequireInputIter<_InputIter>>
_OutputIter eval(_InputIter __first, _InputIter __last,
_OutputIter __result) const noexcept {
size_type __n = std::distance(__first, __last);
if (!__n) return __result;
auto __tree = new poly[__n << 1];
for (auto __p = __tree + __n; __first != __last; ++__p, ++__first)
*__p = {-*__first, 1};
for (size_type __i = __n; --__i;)
__tree[__i] = __tree[__i << 1] * __tree[__i << 1 | 1];
__tree[1] = operator%(std::move(__tree[1]));
for (size_type __i = 2; __i != __n << 1; __i += 2)
__tree[__i] = __tree[__i >> 1] % std::move(__tree[__i]),
__tree[__i | 1] =
std::move(__tree[__i >> 1] %= std::move(__tree[__i | 1]));
for (size_type __i = 0; __i != __n; ++__i)
*__result++ = std::move(*__tree[__n + __i]._M_impl._M_start);
delete[] __tree;
return __result;
}
/**
* @brief Conversion to bool.
*
* @return Whether the %polynomial is not zero.
*/
operator bool() const noexcept {
auto __first = vec::_M_impl._M_start, __last = vec::_M_impl._M_finish;
while (__first != __last)
if (*__first++ != _Tp(0)) return true;
return false;
}
bool operator==(const poly& __x) const noexcept {
auto __first1 = vec::_M_impl._M_start, __last1 = vec::_M_impl._M_finish;
auto __first2 = __x._M_impl._M_start, __last2 = __x._M_impl._M_finish;
if (__last1 - __first1 < __last2 - __first2) {
while (__first1 != __last1)
if (*__first1++ != *__first2++) return false;
while (__first2 != __last2)
if (*__first2++ != _Tp(0)) return false;
}
else {
while (__first2 != __last2)
if (*__first1++ != *__first2++) return false;
while (__first1 != __last1)
if (*__first1++ != _Tp(0)) return false;
}
return true;
}
bool operator!=(const poly& __x) const noexcept { return !operator==(__x); }
/**
* @brief Multiply by x^i.
*/
poly& operator<<=(size_type __i) noexcept {
vec::insert(vec::begin(), __i, _Tp(0));
return *this;
}
/**
* @brief Divide by x^i.
*/
poly& operator>>=(size_type __i) noexcept {
vec::_M_erase_at_end(
std::move(vec::_M_impl._M_start + std::min(__i, vec::size()),
vec::_M_impl._M_finish, vec::_M_impl._M_start));
return *this;
}
/**
* @brief Multiply by x^i.
*/
poly operator<<(size_type __i) const noexcept {
return poly(*this).operator<<=(__i);
}
/**
* @brief Divide by x^i.
*/
poly operator>>(size_type __i) const noexcept {
return poly(*this).operator>>=(__i);
}
poly operator+() const noexcept { return *this; }
poly operator-() const noexcept {
poly __x = *this;
for (auto __i = __x._M_impl._M_start; __i != __x._M_impl._M_finish; ++__i)
*__i = -*__i;
return __x;
}
poly& operator+=(const poly& __x) noexcept {
if (vec::size() < __x.size())
vec::_M_default_append(__x.size() - vec::size());
for (auto __i = vec::_M_impl._M_start, __j = __x._M_impl._M_start;
__j != __x._M_impl._M_finish; ++__i, ++__j)
*__i += *__j;
_erase_leading_zeros();
return *this;
}
poly& operator+=(const _Tp& __c) noexcept {
if (__c != static_cast<_Tp>(0)) {
if (vec::_M_impl._M_start == vec::_M_impl._M_finish)
vec::emplace_back(__c);
else
*vec::_M_impl._M_start += __c, _erase_leading_zeros();
}
return *this;
}
poly& operator-=(const poly& __x) noexcept {
if (vec::size() < __x.size())
vec::_M_default_append(__x.size() - vec::size());
for (auto __i = vec::_M_impl._M_start, __j = __x._M_impl._M_start;
__j != __x._M_impl._M_finish; ++__i, ++__j)
*__i -= *__j;
_erase_leading_zeros();
return *this;
}
poly& operator-=(const _Tp& __c) noexcept {
if (__c != static_cast<_Tp>(0)) {
if (vec::_M_impl._M_start == vec::_M_impl._M_finish)
vec::emplace_back(-__c);
else
*vec::_M_impl._M_start -= __c, _erase_leading_zeros();
}
return *this;
}
poly& operator*=(const poly& __x) noexcept {
std::min(vec::size(), __x.size()) > _Conv_threshold
? _conv_dft(poly(__x))
: _conv_naive(this == std::addressof(__x) ? poly(__x) : __x);
return *this;
}
poly& operator*=(poly&& __x) noexcept {
std::min(vec::size(), __x.size()) > _Conv_threshold
? _conv_dft(std::move(__x))
: _conv_naive(__x);
return *this;
}
poly& operator*=(const _Tp& __c) noexcept {
if (__c == static_cast<_Tp>(0))
vec::_M_erase_at_end(vec::_M_impl._M_start);
else
for (auto __i = vec::_M_impl._M_start; __i != vec::_M_impl._M_finish;
++__i)
*__i *= __c;
return *this;
}
poly& operator/=(const _Tp& __c) noexcept {
assert(__c != static_cast<_Tp>(0));
for (auto __i = vec::_M_impl._M_start; __i != vec::_M_impl._M_finish; ++__i)
*__i /= __c;
return *this;
}
poly rev() const noexcept { return rev(vec::size()); }
poly rev(size_type __n) const noexcept {
poly __r(__n);
auto __src = vec::_M_impl._M_start;
auto __dst = __r._M_impl._M_finish;
for (size_type __i = std::min(__n, vec::size()); __i; --__i)
*--__dst = *__src++;
return __r;
}
poly inv() const noexcept { return inv(vec::size()); }
/**
* @brief Multiplicative inverse modulo x^n.
*
* @param __n Degree of modulus
* @return
*/
poly inv(size_type __n) const noexcept {
if (!__n) return {};
assert(*vec::_M_impl._M_start != _Tp(0));
size_type __len = 1;
while (__len < __n) __len <<= 1;
poly __y(__len);
auto __xp = new _Tp[__len], __yp = __y._M_impl._M_start,
__zp = new _Tp[__len];
*__yp = _Tp(1) / *vec::_M_impl._M_start;
for (size_type __i = 1; __i != __len; __i <<= 1) {
std::fill(std::copy_n(__yp, __i, __zp), __zp + (__i << 1), _Tp(0));
_dft(__zp, __zp + (__i << 1));
std::fill(std::copy_n(vec::_M_impl._M_start,
std::min(__i << 1, vec::size()), __xp),
__xp + (__i << 1), _Tp(0));
_dft(__xp, __xp + (__i << 1));
for (size_type __j = 0; __j != (__i << 1); ++__j) __xp[__j] *= -__zp[__j];
_idft(__xp, __xp + (__i << 1));
std::fill(std::move(__xp + __i, __xp + (__i << 1), __xp),
__xp + (__i << 1), _Tp(0));
_dft(__xp, __xp + (__i << 1));
for (size_type __j = 0; __j != (__i << 1); ++__j)
__xp[__j] *= static_cast<_Tp&&>(__zp[__j]);
_idft(__xp, __xp + (__i << 1));
std::move(__xp, __xp + __i, __yp + __i);
}
delete[] __xp;
delete[] __zp;
__y._M_erase_at_end(__yp + __n);
return __y;
}
poly& operator/=(const poly& __x) noexcept {
if (__x.size() > _Conv_threshold)
_div_doubling(poly(__x));
else
_div_naive(__x);
return *this;
}
poly& operator/=(poly&& __x) noexcept {
if (__x.size() > _Conv_threshold)
_div_doubling(std::move(__x));
else
_div_naive(__x);
return *this;
}
poly& operator%=(const poly& __x) noexcept {
if (__x.size() > _Conv_threshold)
return operator-=(__x.operator*(operator/(__x)));
vec::_M_erase_at_end(vec::_M_impl._M_start + _divmod_naive(__x));
return *this;
}
template <class _T> poly operator+(_T&& __x) const noexcept {
return poly(*this).operator+=(std::forward<_T>(__x));
}
template <class _T> poly operator-(_T&& __x) const noexcept {
return poly(*this).operator-=(std::forward<_T>(__x));
}
template <class _T> poly operator*(_T&& __x) const noexcept {
return poly(*this).operator*=(std::forward<_T>(__x));
}
template <class _T> poly operator/(_T&& __x) const noexcept {
return poly(*this).operator/=(std::forward<_T>(__x));
}
template <class _T> poly operator%(_T&& __x) const noexcept {
return poly(*this).operator%=(std::forward<_T>(__x));
}
std::pair<poly, poly> divmod(const poly& __x) const {
if (__x.size() > _Conv_threshold) return {operator/(__x), operator%(__x)};
poly __rem(*this);
auto __p = __rem._M_impl._M_start + __rem._divmod_naive(__x);
poly __quot(__p, __rem._M_impl._M_finish);
__rem._M_erase_at_end(__p);
return {__quot, __rem};
}
/**
* @brief Differentiate.
*
* @return Derivative.
*/
poly deriv() const noexcept {
if (auto __s = vec::_M_impl._M_start, __f = vec::_M_impl._M_finish;
__s != __f) {
poly __der(++__s, __f);
__s = __der._M_impl._M_start, __f = __der._M_impl._M_finish;
for (_Tp __i(1); __s != __f; ++__s, __i += 1) *__s *= __i;
__der._erase_leading_zeros();
return __der;
}
return {};
}
/**
* @brief Differentiate at given point.
*
* @return Derivative coefficient.
*/
_Tp deriv(const _Tp& __a) const noexcept {
_Tp __der(0);
if (auto __s = vec::_M_impl._M_start, __f = vec::_M_impl._M_finish;
__s != __f)
for (_Tp __i(1), __p(1); ++__s != __f; __i += 1, __p *= __a)
__der += *__s * __i * __p;
return __der;
}
/**
* @brief Integrate.
*
* @return Integral indefinite at the degrees divisible by the characteristic
* of `_Tp`. Coefficients are set as 0 there.
*/
poly integ() const noexcept {
if (auto __s = vec::_M_impl._M_start, __f = vec::_M_impl._M_finish;
__s != __f) {
poly __int(__f - __s + 1);
__f = std::copy(__s, __f, __int._M_impl._M_start + 1);
__s = __int._M_impl._M_start + 1;
for (_Tp __i(1); __s != __f; ++__s, __i += 1)
__i == _Tp(0) ? assert(*__s == _Tp(0)) : void(*__s /= __i);
return __int;
}
return {};
}
/**
* @brief Integrate in given range.
*
* @return Definite integral over [0, __a].
*/
_Tp integ(const _Tp& __a) const noexcept {
_Tp __int(0);
auto __s = vec::_M_impl._M_start, __f = vec::_M_impl._M_finish;
for (_Tp __p(__a), __i(1); __s != __f; ++__s, __p *= __a, __i += 1)
__int += *__s / __i * __p;
return __int;
}
/**
* @brief Integrate in given range.
*
* @return Definite integral over [__a, __b].
*/
_Tp integ(const _Tp& __a, const _Tp& __b) const noexcept {
_Tp __int(0);
auto __s = vec::_M_impl._M_start, __f = vec::_M_impl._M_finish;
for (_Tp __pa(__a), __pb(__b), __i(1); __s != __f;
++__s, __pa *= __a, __pb *= __b, __i += 1)
__int += *__s / __i * (__pb - __pa);
return __int;
}
};
/**
* @brief Polynomial interpolation in O(n log(n)^2) time.
*
* @param __first
* @param __last
* @return
*/
template <class _InputIter, typename = std::_RequireInputIter<_InputIter>>
auto interpolate(_InputIter __first, _InputIter __last) {
size_t __n = std::distance(__first, __last);
auto [__1, __2] =
typename std::iterator_traits<decltype(__first)>::value_type{};
using poly = polynomial<decltype(__1)>;
if (!__n) return poly{};
struct node {
poly __all, __lack;
};
auto __tree = new node[__n << 1];
auto __iter = __first;
for (size_t __i = 0; __i != __n; ++__i) {
auto&& [__a, __b] = *__iter++;
__tree[__i + __n].__all = {-__a, 1}, __tree[__i + __n].__lack = {1};
}
for (size_t __i = __n; --__i;)
__tree[__i].__all = __tree[__i << 1].__all * __tree[__i << 1 | 1].__all,
__tree[__i].__lack =
__tree[__i << 1].__all * std::move(__tree[__i << 1 | 1].__lack) +
__tree[__i << 1 | 1].__all * std::move(__tree[__i << 1].__lack);
for (size_t __i = 2; __i != __n << 1; __i += 2)
__tree[__i].__lack = __tree[__i >> 1].__lack % __tree[__i].__all,
__tree[__i | 1].__lack =
std::move(__tree[__i >> 1].__lack %= __tree[__i | 1].__all);
for (size_t __i = 0; __i != __n; ++__i) {
auto&& [__a, __b] = *__first++;
__tree[__i + __n].__lack[0] =
std::move(__b) / std::move(__tree[__i + __n].__lack[0]);
}
for (size_t __i = __n; --__i;)
__tree[__i].__lack = std::move(__tree[__i << 1].__all) *
std::move(__tree[__i << 1 | 1].__lack) +
std::move(__tree[__i << 1 | 1].__all) *
std::move(__tree[__i << 1].__lack);
auto __result = std::move(__tree[1].__lack);
delete[] __tree;
return __result;
}
// /**
// * @brief 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\\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 <optional>
#endif
#line 2 "Library\\src\\algebra\\system\\monoid.hpp"
/*
* @file monoid.hpp
* @brief Monoid
*/
#include <limits>
namespace workspace {
template <class T, class E = T> 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 <class T, class E>
T min_monoid<T, E>::min = std::numeric_limits<T>::min() / 2;
template <class T, class E>
T min_monoid<T, E>::max = std::numeric_limits<T>::max() / 2;
template <class T, class E = T> struct max_monoid : min_monoid<T, E> {
using base = min_monoid<T, E>;
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 <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 {};
} // 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 _Monoid, class _Endomorphism = void,
template <class...> 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<node>;
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 <class _End = _Endomorphism>
void apply(node &__nd, _End const &endo) {
*__nd = *__nd * endo;
__nd.__z = __nd.__z ? *__nd.__z * endo : endo;
}
// template <class _End = _Endomorphism>
// 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 <class Pred>
constexpr decltype(std::declval<Pred>()(_Monoid{})) pass_args(
Pred pred, _Monoid const &_1, [[maybe_unused]] size_type _2) {
return pred(_1);
}
template <class Pred>
constexpr decltype(std::declval<Pred>()(_Monoid{}, size_type{})) pass_args(
Pred pred, _Monoid const &_1, size_type _2) {
return pred(_1, _2);
}
template <class Pred>
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 <class Pred>
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<container_type, size_t>::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 <class _Tp>
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 <class _Iterator, typename = std::_RequireInputIter<_Iterator>>
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<value_type>() const {
Container_tmpl<value_type> __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 <class _End = _Endomorphism>
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 <class Pred> 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 <class Pred> 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 <class _Iterator, typename = std::_RequireInputIter<_Iterator>>
segment_tree(_Iterator, _Iterator)
-> segment_tree<typename std::iterator_traits<_Iterator>::value_type>;
template <class _Tp, typename = require_binary_plus<_Tp>>
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 <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, typename = std::enable_if_t<is_integral_ext<_Tp>::value>>
constexpr modint(_Tp __n) noexcept
: value((__n %= mod) < 0 ? __n += mod : __n) {}
constexpr modint(bool __n) noexcept : value(__n) {}
constexpr operator value_type() const noexcept { return value; }
// unary operators {{
constexpr modint operator++(int) noexcept {
modint __t{*this};
operator++();
return __t;
}
constexpr modint operator--(int) noexcept {
modint __t{*this};
operator--();
return __t;
}
constexpr modint &operator++() noexcept {
if (++value == mod) value = 0;
return *this;
}
constexpr modint &operator--() noexcept {
if (!value)
value = mod - 1;
else
--value;
return *this;
}
constexpr modint operator+() const noexcept { return *this; }
constexpr modint operator-() const noexcept {
return {value ? mod - value : 0, direct_ctor_tag};
}
// }} unary operators
// operator+= {{
constexpr modint &operator+=(const modint &__x) noexcept {
if ((value += __x.value) >= mod) value -= mod;
return *this;
}
template <class _Tp>
constexpr std::enable_if_t<is_integral_ext<_Tp>::value, modint> &operator+=(
_Tp const &__x) noexcept {
if (((value += __x) %= mod) < 0) value += mod;
return *this;
}
// }} operator+=
// operator+ {{
template <class _Tp>
constexpr std::enable_if_t<is_integral_ext<_Tp>::value, modint> operator+(
_Tp const &__x) const noexcept {
return modint{*this} += __x;
}
constexpr modint operator+(modint __x) const noexcept { return __x += *this; }
template <class _Tp>
constexpr friend std::enable_if_t<is_integral_ext<_Tp>::value, modint>
operator+(_Tp const &__x, modint __y) noexcept {
return __y += __x;
}
// }} operator+
// operator-= {{
constexpr modint &operator-=(const modint &__x) noexcept {
if ((value -= __x.value) < 0) value += mod;
return *this;
}
template <class _Tp>
constexpr std::enable_if_t<is_integral_ext<_Tp>::value, modint> &operator-=(
_Tp __x) noexcept {
if (((value -= __x) %= mod) < 0) value += mod;
return *this;
}
// }} operator-=
// operator- {{
template <class _Tp>
constexpr std::enable_if_t<is_integral_ext<_Tp>::value, modint> operator-(
_Tp const &__x) const noexcept {
return modint{*this} -= __x;
}
constexpr modint operator-(const modint &__x) const noexcept {
return modint{*this} -= __x;
}
template <class _Tp>
constexpr friend std::enable_if_t<is_integral_ext<_Tp>::value, modint>
operator-(_Tp __x, const modint &__y) noexcept {
if (((__x -= __y.value) %= mod) < 0) __x += mod;
return {__x, direct_ctor_tag};
}
// }} operator-
// operator*= {{
constexpr modint &operator*=(const modint &__x) noexcept {
value =
static_cast<value_type>(value * static_cast<mul_type>(__x.value) % mod);
return *this;
}
template <class _Tp>
constexpr std::enable_if_t<is_integral_ext<_Tp>::value, modint> &operator*=(
_Tp __x) noexcept {
value = static_cast<value_type>(
value * mul_type((__x %= mod) < 0 ? __x + mod : __x) % mod);
return *this;
}
// }} operator*=
// operator* {{
constexpr modint operator*(const modint &__x) const noexcept {
return {static_cast<mul_type>(value) * __x.value % mod, direct_ctor_tag};
}
template <class _Tp>
constexpr std::enable_if_t<is_integral_ext<_Tp>::value, modint> operator*(
_Tp __x) const noexcept {
__x %= mod;
if (__x < 0) __x += mod;
return {static_cast<mul_type>(value) * __x % mod, direct_ctor_tag};
}
template <class _Tp>
constexpr friend std::enable_if_t<is_integral_ext<_Tp>::value, modint>
operator*(_Tp __x, const modint &__y) noexcept {
__x %= mod;
if (__x < 0) __x += mod;
return {static_cast<mul_type>(__x) * __y.value % mod, direct_ctor_tag};
}
// }} operator*
protected:
static value_type _mem(value_type __x) {
static std::vector<value_type> __m{0, 1};
static value_type __i = (__m.reserve(storage), 1);
while (__i < __x) {
++__i;
__m.emplace_back(mod - mul_type(mod / __i) * __m[mod % __i] % mod);
}
return __m[__x];
}
static value_type _div(mul_type __r, value_type __x) noexcept {
assert(__x != value_type(0));
if (!__r) return 0;
std::make_signed_t<value_type> __v{};
bool __neg = __x < 0 ? __x = -__x, true : false;
if (static_cast<decltype(storage)>(__x) < storage)
__v = _mem(__x);
else {
value_type __y{mod}, __u{1}, __t;
while (__x)
__t = __y / __x, __y ^= __x ^= (__y -= __t * __x) ^= __x,
__v ^= __u ^= (__v -= __t * __u) ^= __u;
if (__y < 0) __neg ^= 1;
}
if (__neg)
__v = 0 < __v ? mod - __v : -__v;
else if (__v < 0)
__v += mod;
return __r == mul_type(1) ? static_cast<value_type>(__v)
: static_cast<value_type>(__r * __v % mod);
}
public:
// operator/= {{
constexpr modint &operator/=(const modint &__x) noexcept {
if (value) value = _div(value, __x.value);
return *this;
}
template <class _Tp>
constexpr std::enable_if_t<is_integral_ext<_Tp>::value, modint> &operator/=(
_Tp __x) noexcept {
if (value) value = _div(value, __x %= mod);
return *this;
}
// }} operator/=
// operator/ {{
constexpr modint operator/(const modint &__x) const noexcept {
if (!value) return {};
return {_div(value, __x.value), direct_ctor_tag};
}
template <class _Tp>
constexpr std::enable_if_t<is_integral_ext<_Tp>::value, modint> operator/(
_Tp __x) const noexcept {
if (!value) return {};
return {_div(value, __x %= mod), direct_ctor_tag};
}
template <class _Tp>
constexpr friend std::enable_if_t<is_integral_ext<_Tp>::value, modint>
operator/(_Tp __x, const modint &__y) noexcept {
if (!__x) return {};
if ((__x %= mod) < 0) __x += mod;
return {_div(__x, __y.value), direct_ctor_tag};
}
// }} operator/
constexpr modint inv() const noexcept { return _div(1, value); }
template <class _Tp>
constexpr std::enable_if_t<is_integral_ext<_Tp>::value, modint> pow(
_Tp __e) const noexcept {
modint __r{1, direct_ctor_tag};
for (modint __b{__e < 0 ? __e = -__e, _div(1, value) : value,
direct_ctor_tag};
__e; __e >>= 1, __b *= __b)
if (__e & 1) __r *= __b;
return __r;
}
template <class _Tp>
constexpr friend std::enable_if_t<is_integral_ext<_Tp>::value, modint> pow(
modint __b, _Tp __e) noexcept {
if (__e < 0) {
__e = -__e;
__b.value = _div(1, __b.value);
}
modint __r{1, direct_ctor_tag};
for (; __e; __e >>= 1, __b *= __b)
if (__e & 1) __r *= __b;
return __r;
}
constexpr modint sqrt() const noexcept {
return {sqrt_mod(value, mod), direct_ctor_tag};
}
friend constexpr modint sqrt(const modint &__x) noexcept {
return {sqrt_mod(__x.value, mod), direct_ctor_tag};
}
template <class _Os>
friend _Os &operator<<(_Os &__os, const modint &__x) noexcept {
return __os << __x.value;
}
friend std::istream &operator>>(std::istream &__is, modint &__x) noexcept {
std::string __s;
__is >> __s;
bool __neg = false;
if (__s.front() == '-') {
__neg = true;
__s.erase(__s.begin());
}
__x = 0;
for (char __c : __s) __x = __x * 10 + (__c - '0');
if (__neg) __x = -__x;
return __is;
}
};
template <auto _Mod, unsigned _Storage>
typename modint<_Mod, _Storage>::mod_type modint<_Mod, _Storage>::mod =
_Mod > 0 ? _Mod : 0;
template <auto _Mod, unsigned _Storage>
unsigned modint<_Mod, _Storage>::storage = _Storage;
} // namespace _modint_impl
template <auto _Mod, unsigned _Storage = 0,
typename = std::enable_if_t<(_Mod > 0)>>
using modint = _modint_impl::modint<_Mod, _Storage>;
template <unsigned _Id = 0>
using modint_runtime = _modint_impl::modint<-(signed)_Id, 0>;
} // namespace workspace
#line 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<mint>;
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<tuple<int, int, int>> updates;
vector<pair<int, int>> queries;
vector<i64> 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 {
id.emplace_back(k);
k = id.size() - 1;
}
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<mono> 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(); }