結果
| 問題 |
No.749 クエリ全部盛り
|
| コンテスト | |
| ユーザー |
 jell
|
| 提出日時 | 2021-11-17 23:27:59 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
TLE
|
| 実行時間 | - |
| コード長 | 46,214 bytes |
| コンパイル時間 | 3,646 ms |
| コンパイル使用メモリ | 212,600 KB |
| 最終ジャッジ日時 | 2025-01-25 19:06:19 |
|
ジャッジサーバーID （参考情報） |
judge4 / judge5 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| other | AC * 15 TLE * 5 |
ソースコード
#line 1 "other-workspace\\749.cpp"
#include <bits/stdc++.h>
#line 2 "Library\\src\\algebra\\linear\\matrix.hpp"
/**
* @file matrix.hpp
* @brief Matrix
* @date 2021-02-15
*
*
*/
#line 13 "Library\\src\\algebra\\linear\\matrix.hpp"
namespace workspace {
/**
* @brief Fixed size matrix.
*
* @tparam _Scalar
* @tparam _Rows Number of rows
* @tparam _Cols Number of columns
*/
template <class _Scalar, std::size_t _Rows = 0, std::size_t _Cols = _Rows>
class matrix {
public:
_Scalar __data[_Rows][_Cols] = {};
using value_type = _Scalar;
using size_type = std::size_t;
constexpr static matrix eye() {
static_assert(_Rows == _Cols);
matrix __e;
for (size_type __d = 0; __d != _Rows; ++__d) __e.__data[__d][__d] = 1;
return __e;
}
constexpr operator decltype((__data))() { return __data; }
constexpr operator decltype(
std::declval<const matrix>().__data) const&() const {
return __data;
}
constexpr auto begin() { return __data; }
constexpr auto begin() const { return __data; }
constexpr auto end() { return __data + _Rows; }
constexpr auto end() const { return __data + _Rows; }
constexpr size_type rows() const { return _Rows; }
constexpr size_type cols() const { return _Cols; }
constexpr auto transpose() const {
matrix<_Scalar, _Cols, _Rows> __t;
for (size_type __r = 0; __r != _Rows; ++__r)
for (size_type __c = 0; __c != _Cols; ++__c)
__t.__data[__c][__r] = __data[__r][__c];
return __t;
}
constexpr matrix operator+() const { return *this; }
constexpr matrix operator-() const {
matrix __cp = *this;
for (auto& __v : __cp.__data)
for (auto& __e : __v) __e = -__e;
return __cp;
}
template <class _Matrix> constexpr matrix& operator+=(const _Matrix& __x) {
auto __m = std::min(_Rows, __x.rows());
auto __n = std::min(_Cols, __x.cols());
for (size_type __r = 0; __r != __m; ++__r)
for (size_type __c = 0; __c != __n; ++__c)
__data[__r][__c] += __x[__r][__c];
return *this;
}
template <class _Matrix>
constexpr matrix operator+(const _Matrix& __x) const {
return matrix(*this) += __x;
}
template <class _Matrix> constexpr matrix& operator-=(const _Matrix& __x) {
auto __m = std::min(_Rows, __x.rows());
auto __n = std::min(_Cols, __x.cols());
for (size_type __r = 0; __r != __m; ++__r)
for (size_type __c = 0; __c != __n; ++__c)
__data[__r][__c] -= __x[__r][__c];
return *this;
}
template <class _Matrix>
constexpr matrix operator-(const _Matrix& __x) const {
return matrix(*this) -= __x;
}
template <class _Scalar2>
constexpr matrix& operator*=(const matrix<_Scalar2, _Cols, _Cols>& __x) {
if (this == &__x) return operator=(operator*(__x));
for (auto& __r : __data) {
_Scalar __tmp[_Cols] = {};
auto __v = *__x.__data;
for (auto& __w : __tmp) {
auto __i = __v++;
for (const auto& __e : __r) __w += __e * *__i, __i += _Cols;
}
auto __w = __tmp;
for (auto& __e : __r) __e = std::move(*__w++);
}
return *this;
}
template <class _Scalar2, size_type _Rows2, size_type _Cols2>
constexpr auto operator*(const matrix<_Scalar2, _Rows2, _Cols2>& __x) const {
matrix<typename std::common_type<_Scalar, _Scalar2>::type, _Rows, _Cols2>
__m;
auto __w = *__m.__data;
for (const auto& __r : __data)
for (auto __v = *__x.__data, __v_end = __v + _Cols2; __v != __v_end;
++__w) {
auto __i = __v++;
for (auto __e = __r; __e != __r + std::min(_Cols, _Rows2); ++__e)
*__w += *__e * *__i, __i += _Cols2;
}
return __m;
}
// template <class _Matrix>
// constexpr
// typename std::enable_if<!std::is_convertible<_Matrix,
// value_type>::value,
// matrix<_Scalar>>::type
// operator*(const _Matrix& __x) const {
// matrix<_Scalar> __m(_Rows, __x.cols());
// for (size_type __r = 0; __r != _Rows; ++__r)
// for (size_type __i = 0; __i != __x.cols(); ++__i)
// for (size_type __c = 0; __c != std::min(_Cols, __x.rows()); ++__c)
// __m[__r][__i] += __data[__r][__c] * __x[__c][__i];
// return __m;
// }
constexpr matrix& operator*=(const value_type& __x) {
for (auto& __v : __data)
for (auto& __e : __v) __e *= __x;
return *this;
}
constexpr matrix operator*(const value_type& __x) const {
return matrix(*this) *= __x;
}
constexpr matrix& operator/=(const value_type& __x) {
assert(__x != value_type(0));
for (auto& __v : __data)
for (auto& __e : __v) __e /= __x;
return *this;
}
constexpr matrix operator/(const value_type& __x) const {
return matrix(*this) /= __x;
}
template <class _Int> constexpr matrix pow(_Int __e) const {
assert(0 <= __e);
matrix __m = eye();
for (matrix __cp = *this; __e; __cp *= __cp, __e >>= 1)
if (__e & 1) __m *= __cp;
return __m;
}
template <class _Os>
constexpr friend _Os& operator<<(_Os& __os, const matrix& __x) {
for (auto __i = __x.begin(); __i != __x.end(); ++__i, __os << '\n')
for (size_type __c = 0; __c != _Cols; ++__c)
__c ? void(__os << ' ') : (void)0, __os << *(*__i + __c);
return __os;
}
}; // namespace workspace
/**
* @brief Dynamic matrix.
*
* @tparam _Scalar
* @tparam _Rows Number of rows
* @tparam _Cols Number of columns
*/
template <class _Scalar>
class matrix<_Scalar, 0, 0> : public std::valarray<std::valarray<_Scalar>> {
using base = std::valarray<std::valarray<_Scalar>>;
using row_type = typename base::value_type;
public:
using value_type = _Scalar;
using size_type = std::size_t;
using base::operator[];
static matrix eye(size_type __n) {
matrix __e(__n, __n);
for (size_type __d = 0; __d != __n; ++__d) __e[__d][__d] = 1;
return __e;
}
matrix() = default;
matrix(size_type __n) : matrix(__n, __n) {}
matrix(size_type __m, size_type __n) : base(row_type(__n), __m) {}
template <class _Tp, typename = typename std::enable_if<
std::is_constructible<base, _Tp>::value &&
!std::is_constructible<size_type, _Tp>::value>::type>
matrix(_Tp&& __x) : base(__x) {}
matrix(std::initializer_list<row_type> __x) : base(__x) {}
size_type rows() const { return base::size(); }
size_type cols() const { return rows() ? operator[](0).size() : 0; }
matrix transpose() const {
matrix __t(cols(), rows());
for (size_type __r = 0; __r != rows(); ++__r)
for (size_type __c = 0; __c != cols(); ++__c)
__t[__c][__r] = operator[](__r)[__c];
return __t;
}
void resize(size_type __m, size_type __n) {
matrix __t(__m, __n);
if (rows() < __m) __m = rows();
if (cols() < __n) __n = cols();
for (size_type __r = 0; __r != __m; ++__r)
for (size_type __c = 0; __c != __n; ++__c)
__t[__r][__c] = std::move(operator[](__r)[__c]);
base::swap(__t);
}
// binary operators {{
template <class _Matrix, typename = void>
struct is_valarray_based : std::false_type {};
template <class _Matrix>
struct is_valarray_based<
_Matrix,
typename std::enable_if<std::is_same<
row_type, typename std::decay<decltype(std::declval<_Matrix>()[0])>::
type>::value>::type> : std::true_type {};
template <class _Matrix>
typename std::enable_if<!std::is_convertible<_Matrix, value_type>::value,
matrix&>::type
operator*=(_Matrix&& __x) {
return *this = operator*(std::forward<_Matrix>(__x));
}
template <class _Matrix>
typename std::enable_if<!std::is_convertible<_Matrix, value_type>::value,
matrix>::type
operator*(const _Matrix& __x) const {
matrix __m(rows(), __x.cols());
if constexpr (is_valarray_based<_Matrix>::value)
for (size_type __r = 0; __r != rows(); ++__r)
for (size_type __c = 0; __c != std::min(cols(), __x.rows()); ++__c)
__m[__r] += operator[](__r)[__c] * __x[__c];
else
for (size_type __r = 0; __r != rows(); ++__r)
for (size_type __i = 0; __i != __x.cols(); ++__i)
for (size_type __c = 0; __c != std::min(cols(), __x.rows()); ++__c)
__m[__r][__i] += operator[](__r)[__c] * __x[__c][__i];
return __m;
}
matrix& operator*=(const value_type& __x) {
for (size_type __r = 0; __r != rows(); ++__r)
operator[](__r).operator*=(__x);
return *this;
}
matrix operator*(const value_type& __x) const { return matrix(*this) *= __x; }
friend matrix operator*(const value_type& __x, matrix __i) {
for (size_type __r = 0; __r != __i.rows(); ++__r)
__i.operator[](__r) = __x * __i.operator[](__r);
return __i;
}
matrix& operator/=(const value_type& __x) {
assert(__x != value_type(0));
for (size_type __r = 0; __r != rows(); ++__r)
operator[](__r).operator/=(__x);
return *this;
}
matrix operator/(const value_type& __x) const { return matrix(*this) /= __x; }
// }} binary operators
template <class _Int> matrix pow(_Int __e) const {
assert(0 <= __e);
matrix __m = eye(rows());
for (matrix __cp = *this; __e; __cp *= __cp, __e >>= 1)
if (__e & 1) __m *= __cp;
return __m;
}
// template <class _Is> friend _Is& operator>>(_Is& __is, matrix& __x) {
// for (size_type __r = 0; __r != __x.rows(); ++__r)
// for (size_type __c = 0; __c != __x.cols(); ++__c)
// __is >> __x.operator[](__r).operator[](__c);
// return __is;
// }
template <class _Os> friend _Os& operator<<(_Os& __os, const matrix& __x) {
for (size_type __r = 0; __r != __x.rows(); ++__r, __os << '\n')
for (size_type __c = 0; __c != __x.cols(); ++__c)
__c ? void(__os << ' ') : (void)0,
__os << __x.operator[](__r).operator[](__c);
return __os;
}
};
template <class _Scalar, std::size_t _Rows, std::size_t _Cols = _Rows>
class matrix_operator : public matrix<_Scalar, _Rows, _Cols> {
using _Base = matrix<_Scalar, _Rows, _Cols>;
public:
constexpr operator _Base&() { return *this; }
constexpr operator _Base const &() const { return *this; }
constexpr matrix_operator() : _Base(_Base::eye()) {}
constexpr matrix_operator(const _Base& __x) : _Base(__x) {}
};
} // namespace workspace
#line 2 "Library\\src\\algebra\\modint.hpp"
/**
* @file modint.hpp
* @brief Modular Arithmetic
*/
#line 11 "Library\\src\\algebra\\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 2 "Library\\src\\utils\\sfinae.hpp"
/**
* @file sfinae.hpp
* @brief SFINAE
*/
#line 10 "Library\\src\\utils\\sfinae.hpp"
#include <type_traits>
#ifndef __INT128_DEFINED__
#ifdef __SIZEOF_INT128__
#define __INT128_DEFINED__ 1
#else
#define __INT128_DEFINED__ 0
#endif
#endif
namespace std {
#if __INT128_DEFINED__
template <> struct make_signed<__uint128_t> { using type = __int128_t; };
template <> struct make_signed<__int128_t> { using type = __int128_t; };
template <> struct make_unsigned<__uint128_t> { using type = __uint128_t; };
template <> struct make_unsigned<__int128_t> { using type = __uint128_t; };
template <> struct is_signed<__uint128_t> : std::false_type {};
template <> struct is_signed<__int128_t> : std::true_type {};
template <> struct is_unsigned<__uint128_t> : std::true_type {};
template <> struct is_unsigned<__int128_t> : std::false_type {};
#endif
} // namespace std
namespace workspace {
template <class Tp, class... Args> struct variadic_front { using type = Tp; };
template <class... Args> struct variadic_back;
template <class Tp> struct variadic_back<Tp> { using type = Tp; };
template <class Tp, class... Args> struct variadic_back<Tp, Args...> {
using type = typename variadic_back<Args...>::type;
};
template <class type, template <class> class trait>
using enable_if_trait_type = typename std::enable_if<trait<type>::value>::type;
/**
* @brief Return type of subscripting ( @c [] ) access.
*/
template <class _Tp>
using subscripted_type =
typename std::decay<decltype(std::declval<_Tp&>()[0])>::type;
template <class Container>
using element_type = typename std::decay<decltype(*std::begin(
std::declval<Container&>()))>::type;
template <class _Tp, class = void> struct has_begin : std::false_type {};
template <class _Tp>
struct has_begin<
_Tp, std::__void_t<decltype(std::begin(std::declval<const _Tp&>()))>>
: std::true_type {
using type = decltype(std::begin(std::declval<const _Tp&>()));
};
template <class _Tp, class = void> struct has_size : std::false_type {};
template <class _Tp>
struct has_size<_Tp, std::__void_t<decltype(std::size(std::declval<_Tp>()))>>
: std::true_type {};
template <class _Tp, class = void> struct has_resize : std::false_type {};
template <class _Tp>
struct has_resize<_Tp, std::__void_t<decltype(std::declval<_Tp>().resize(
std::declval<size_t>()))>> : 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())> {};
template <class _Container, class = void> struct get_dimension {
static constexpr size_t value = 0;
};
template <class _Container>
struct get_dimension<_Container,
std::enable_if_t<has_begin<_Container>::value>> {
static constexpr size_t value =
1 + get_dimension<typename std::iterator_traits<
typename has_begin<_Container>::type>::value_type>::value;
};
} // namespace workspace
#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 14 "Library\\src\\algebra\\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 reference = value_type &;
using const_reference = value_type const &;
using mul_type = typename multiplicable_uint<value_type>::type;
static mod_type mod; // Modulus.
static unsigned storage;
private:
template <class _Tp>
using modint_if = std::enable_if_t<is_integral_ext<_Tp>::value, modint>;
value_type value = 0; // within [0, mod).
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, class = std::enable_if_t<
std::is_convertible<_Tp, value_type>::value>>
constexpr modint(_Tp __n) noexcept
: value((__n %= mod) < _Tp(0) ? static_cast<value_type>(__n) + mod
: static_cast<value_type>(__n)) {}
constexpr modint(bool __n) noexcept : value(__n) {}
constexpr operator reference() noexcept { return value; }
constexpr operator const_reference() 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 modint_if<_Tp> &operator+=(_Tp __x) noexcept {
__x %= mod, value += __x;
if (value < 0)
value += mod;
else if (value >= mod)
value -= mod;
return *this;
}
// }} operator+=
// operator+ {{
template <class _Tp>
constexpr modint_if<_Tp> 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 modint_if<_Tp> 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 modint_if<_Tp> &operator-=(_Tp __x) noexcept {
__x %= mod, value -= __x;
if (value < 0)
value += mod;
else if (value >= mod)
value -= mod;
return *this;
}
// }} operator-=
// operator- {{
template <class _Tp>
constexpr modint_if<_Tp> 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 modint_if<_Tp> 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 modint_if<_Tp> &operator*=(_Tp __x) noexcept {
value = static_cast<value_type>(
value * ((__x %= mod) < 0 ? mul_type(__x + mod) : mul_type(__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 modint_if<_Tp> 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 modint_if<_Tp> 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:
static void reserve(unsigned __n) noexcept {
if (storage < __n) storage = __n;
}
// operator/= {{
constexpr modint &operator/=(const modint &__x) noexcept {
if (value) value = _div(value, __x.value);
return *this;
}
template <class _Tp> constexpr modint_if<_Tp> &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 modint_if<_Tp> operator/(_Tp __x) const noexcept {
if (!value) return {};
return {_div(value, __x %= mod), direct_ctor_tag};
}
template <class _Tp>
constexpr friend modint_if<_Tp> 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 modint pow(_Tp __e) const noexcept {
static_assert(not std::is_floating_point<_Tp>::value);
modint __r{mod != 1, direct_ctor_tag};
for (modint __b{__e < _Tp(0) ? __e = -__e, _div(1, value) : value,
direct_ctor_tag};
__e; __e /= 2, __b *= __b)
if (__e % 2) __r *= __b;
return __r;
}
template <class _Tp>
constexpr friend modint pow(modint __b, _Tp __e) noexcept {
static_assert(not std::is_floating_point<_Tp>::value);
if (__e < _Tp(0)) {
__e = -__e;
__b.value = _div(1, __b.value);
}
modint __r{mod != 1, direct_ctor_tag};
for (; __e; __e /= 2, __b *= __b)
if (__e % 2) __r *= __b;
return __r;
}
constexpr modint sqrt() const noexcept {
return {sqrt_mod(value, mod), direct_ctor_tag};
}
friend constexpr modint sqrt(const modint &__x) noexcept {
return {sqrt_mod(__x.value, mod), direct_ctor_tag};
}
friend std::istream &operator>>(std::istream &__is, modint &__x) noexcept {
std::string __s;
__is >> __s;
bool __neg = false;
if (__s.front() == '-') {
__neg = true;
__s.erase(__s.begin());
}
__x = 0;
for (char __c : __s) __x = __x * 10 + (__c - '0');
if (__neg) __x = -__x;
return __is;
}
};
template <auto _Mod, unsigned _Storage>
typename modint<_Mod, _Storage>::mod_type modint<_Mod, _Storage>::mod =
_Mod > 0 ? _Mod : 0;
template <auto _Mod, unsigned _Storage>
unsigned modint<_Mod, _Storage>::storage = _Storage;
} // namespace _modint_impl
constexpr unsigned _modint_default_storage = 1 << 24;
template <auto _Mod, unsigned _Storage = _modint_default_storage,
typename = std::enable_if_t<(_Mod > 0)>>
using modint = _modint_impl::modint<_Mod, _Storage>;
template <unsigned _Id = 0, unsigned _Storage = _modint_default_storage>
using runtime_modint = _modint_impl::modint<-(signed)_Id, _Storage>;
template <unsigned _Id = 0, unsigned _Storage = _modint_default_storage>
using runtime_modint64 = _modint_impl::modint<-(int_least64_t)_Id, _Storage>;
} // namespace workspace
#line 2 "Library\\src\\data_structure\\segment_tree\\lazy.hpp"
/**
* @file lazy.hpp
* @brief Lazy Segment Tree
*/
#line 11 "Library\\src\\data_structure\\segment_tree\\lazy.hpp"
#line 2 "Library\\src\\algebra\\system\\monoid.hpp"
/*
* @file monoid.hpp
* @brief Monoid
*/
#line 9 "Library\\src\\algebra\\system\\monoid.hpp"
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 10 "Library\\src\\algebra\\system\\operation.hpp"
#line 2 "Library\\lib\\cxx17"
#line 2 "Library\\lib\\cxx14"
#ifndef _CXX14_CONSTEXPR
#if __cplusplus >= 201402L
#define _CXX14_CONSTEXPR constexpr
#else
#define _CXX14_CONSTEXPR
#endif
#endif
#line 4 "Library\\lib\\cxx17"
#ifndef _CXX17_CONSTEXPR
#if __cplusplus >= 201703L
#define _CXX17_CONSTEXPR constexpr
#else
#define _CXX17_CONSTEXPR
#endif
#endif
#ifndef _CXX17_STATIC_ASSERT
#if __cplusplus >= 201703L
#define _CXX17_STATIC_ASSERT static_assert
#else
#define _CXX17_STATIC_ASSERT assert
#endif
#endif
#line 22 "Library\\lib\\cxx17"
#if __cplusplus < 201703L
namespace std {
/**
* @brief Return the size of a container.
* @param __cont Container.
*/
template <typename _Container>
constexpr auto size(const _Container& __cont) noexcept(noexcept(__cont.size()))
-> decltype(__cont.size()) {
return __cont.size();
}
/**
* @brief Return the size of an array.
*/
template <typename _Tp, size_t _Nm>
constexpr size_t size(const _Tp (&)[_Nm]) noexcept {
return _Nm;
}
/**
* @brief Return whether a container is empty.
* @param __cont Container.
*/
template <typename _Container>
[[nodiscard]] constexpr auto empty(const _Container& __cont) noexcept(
noexcept(__cont.empty())) -> decltype(__cont.empty()) {
return __cont.empty();
}
/**
* @brief Return whether an array is empty (always false).
*/
template <typename _Tp, size_t _Nm>
[[nodiscard]] constexpr bool empty(const _Tp (&)[_Nm]) noexcept {
return false;
}
/**
* @brief Return whether an initializer_list is empty.
* @param __il Initializer list.
*/
template <typename _Tp>
[[nodiscard]] constexpr bool empty(initializer_list<_Tp> __il) noexcept {
return __il.size() == 0;
}
struct monostate {};
} // namespace std
#else
#include <variant>
#endif
#line 12 "Library\\src\\algebra\\system\\operation.hpp"
namespace workspace {
// Unary `+`
template <class _Tp>
using require_unary_plus = std::enable_if_t<
std::is_convertible<decltype(+std::declval<const _Tp &>()), _Tp>::value>;
template <class _Tp, class = void> struct has_unary_plus : std::false_type {};
template <class _Tp>
struct has_unary_plus<_Tp, require_unary_plus<_Tp>> : std::true_type {};
// Unary `-`
template <class _Tp>
using require_unary_minus = std::enable_if_t<
std::is_convertible<decltype(-std::declval<const _Tp &>()), _Tp>::value>;
template <class _Tp, class = void> struct has_unary_minus : std::false_type {};
template <class _Tp>
struct has_unary_minus<_Tp, require_unary_minus<_Tp>> : std::true_type {};
// Binary `+`
template <class _Tp1, class _Tp2 = _Tp1>
using require_binary_plus =
std::enable_if_t<std::is_convertible<decltype(std::declval<const _Tp1 &>() +
std::declval<const _Tp2 &>()),
_Tp1>::value>;
template <class _Tp1, class _Tp2 = _Tp1, class = void>
struct has_binary_plus : std::false_type {};
template <class _Tp1, class _Tp2>
struct has_binary_plus<_Tp1, _Tp2, require_binary_plus<_Tp1, _Tp2>>
: std::true_type {};
// Binary `-`
template <class _Tp1, class _Tp2 = _Tp1>
using require_binary_minus =
std::__void_t<decltype(std::declval<const _Tp1 &>() -
std::declval<const _Tp2 &>())>;
template <class _Tp1, class _Tp2 = _Tp1, class = void>
struct has_binary_minus : std::false_type {};
template <class _Tp1, class _Tp2>
struct has_binary_minus<_Tp1, _Tp2, require_binary_minus<_Tp1, _Tp2>>
: std::true_type {};
// Binary `*`
template <class _Tp1, class _Tp2 = _Tp1>
using require_binary_multiplies =
std::enable_if_t<std::is_convertible<decltype(std::declval<const _Tp1 &>() *
std::declval<const _Tp2 &>()),
_Tp1>::value>;
template <class _Tp1, class _Tp2 = _Tp1, class = void>
struct has_binary_multiplies : std::false_type {};
template <class _Tp1, class _Tp2>
struct has_binary_multiplies<_Tp1, _Tp2, require_binary_multiplies<_Tp1, _Tp2>>
: std::true_type {};
// Binary `/`
template <class _Tp1, class _Tp2 = _Tp1>
using require_binary_divides =
std::enable_if_t<std::is_convertible<decltype(std::declval<const _Tp1 &>() /
std::declval<const _Tp2 &>()),
_Tp1>::value>;
template <class _Tp1, class _Tp2 = _Tp1, class = void>
struct has_binary_divides : std::false_type {};
template <class _Tp1, class _Tp2>
struct has_binary_divides<_Tp1, _Tp2, require_binary_divides<_Tp1, _Tp2>>
: std::true_type {};
// Binary `%`
template <class _Tp1, class _Tp2 = _Tp1>
using require_binary_modulus =
std::enable_if_t<std::is_convertible<decltype(std::declval<const _Tp1 &>() %
std::declval<const _Tp2 &>()),
_Tp1>::value>;
template <class _Tp1, class _Tp2 = _Tp1, class = void>
struct has_binary_modulus : std::false_type {};
template <class _Tp1, class _Tp2>
struct has_binary_modulus<_Tp1, _Tp2, require_binary_modulus<_Tp1, _Tp2>>
: std::true_type {};
template <class _Tp1, class _Tp2 = _Tp1, class = void, class = void,
class = void, class = void>
struct has_arithmetic : std::false_type {};
template <class _Tp1, class _Tp2>
struct has_arithmetic<_Tp1, _Tp2, require_binary_plus<_Tp1, _Tp2>,
require_binary_minus<_Tp1, _Tp2>,
require_binary_multiplies<_Tp1, _Tp2>,
require_binary_divides<_Tp1, _Tp2>> : std::true_type {};
template <class _Tp1, class _Tp2 = _Tp1>
using require_arithmetic = std::enable_if_t<has_arithmetic<_Tp1, _Tp2>::value>;
// Binary `<`
template <class _Tp, class = void> struct is_comparable : std::false_type {};
template <class _Tp>
struct is_comparable<_Tp, std::__void_t<decltype(std::declval<const _Tp &>() <
std::declval<const _Tp &>())>>
: std::true_type {};
template <class _Tp, bool _Default = false> struct try_less : std::less<_Tp> {
constexpr bool operator()(const _Tp &__x, const _Tp &__y) noexcept {
if _CXX17_CONSTEXPR (is_comparable<_Tp>::value)
return std::less<_Tp>::operator()(__x, __y);
else
return _Default;
}
};
} // namespace workspace
#line 2 "Library\\src\\data_structure\\segment_tree\\waitings.hpp"
#line 5 "Library\\src\\data_structure\\segment_tree\\waitings.hpp"
namespace workspace {
namespace internal {
struct waitings : std::queue<size_t> {
waitings(size_t n) : in(n) {}
bool push(size_t index) {
// assert(index < in.size());
if (in[index]) return false;
emplace(index);
return (in[index] = true);
}
size_t pop() {
// assert(!empty());
auto index = front();
std::queue<size_t>::pop();
in[index] = false;
return index;
}
private:
std::vector<int_least8_t> in;
};
} // namespace internal
} // namespace workspace
#line 16 "Library\\src\\data_structure\\segment_tree\\lazy.hpp"
namespace workspace {
template <class _Monoid, class _End,
class Monoid_container = std::vector<_Monoid>,
class Endomorphism_container = std::vector<_End>>
class lazy_segment_tree {
static_assert(
std::is_same<_Monoid, typename Monoid_container::value_type>::value);
static_assert(
std::is_same<_End, typename Endomorphism_container::value_type>::value);
static_assert(has_binary_plus<_Monoid>::value,
"\'_Monoid\' has no proper binary \'operator+\'.");
static_assert(has_binary_multiplies<_End>::value,
"\'_End\' has no proper binary \'operator*\'.");
static_assert(has_binary_multiplies<_Monoid, _End>::value,
"\'_End\' is not applicable to \'_Monoid\'.");
size_t size_orig, height, size_ext;
Monoid_container data;
Endomorphism_container lazy;
internal::waitings wait;
void repair() {
while (!wait.empty()) {
const size_t index = wait.pop() >> 1;
if (index && wait.push(index)) pull(index);
}
}
void apply(size_t node, const _End &endo) {
data[node] = data[node] * endo;
if (node < size_ext) lazy[node] = lazy[node] * endo;
}
void push(size_t node) {
apply(node << 1, lazy[node]);
apply(node << 1 | 1, lazy[node]);
lazy[node] = _End{};
}
void pull(size_t node) { data[node] = data[node << 1] + data[node << 1 | 1]; }
template <class Pred>
static constexpr decltype(std::declval<Pred>()(_Monoid{})) pass_args(
Pred pred, _Monoid const &_1, [[maybe_unused]] size_t _2) {
return pred(_1);
}
template <class Pred>
static constexpr decltype(std::declval<Pred>()(_Monoid{}, size_t{}))
pass_args(Pred pred, _Monoid const &_1, size_t _2) {
return pred(_1, _2);
}
template <class Pred>
size_t left_partition_subtree(size_t node, _Monoid mono, size_t step,
Pred pred) {
assert(node);
while (node < size_ext) {
push(node);
const _Monoid tmp = data[(node <<= 1) | 1] + mono;
if (pass_args(pred, tmp, ((node | 1) << --step) ^ size_ext))
mono = tmp;
else
++node;
}
return ++node -= size_ext;
}
template <class Pred>
size_t right_partition_subtree(size_t node, _Monoid mono, size_t step,
Pred pred) {
assert(node);
while (node < size_ext) {
push(node);
const _Monoid tmp = mono + data[node <<= 1];
if (pass_args(pred, tmp, ((node | 1) << --step) ^ size_ext))
++node, mono = tmp;
}
return (node -= size_ext) < size_orig ? node : size_orig;
}
public:
class iterator {
lazy_segment_tree *__p;
size_t __i;
public:
using difference_type = typename std::make_signed<size_t>::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(lazy_segment_tree *__p, size_t __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()); }
lazy_segment_tree(size_t n = 0)
: size_orig{n},
height(n > 1 ? 32 - __builtin_clz(n - 1) : 0),
size_ext{1u << height},
data(size_ext << 1),
lazy(size_ext),
wait(size_ext << 1) {}
lazy_segment_tree(size_t n, const _Monoid &init) : lazy_segment_tree(n) {
std::fill_n(std::next(std::begin(data), size_ext), n, init);
for (size_t i{size_ext}; --i;) pull(i);
}
template <class iter_type, class value_type = typename std::iterator_traits<
iter_type>::value_type>
lazy_segment_tree(iter_type first, iter_type last)
: size_orig(std::distance(first, last)),
height(size_orig > 1 ? 32 - __builtin_clz(size_orig - 1) : 0),
size_ext{1u << height},
data(size_ext << 1),
lazy(size_ext),
wait(size_ext << 1) {
static_assert(std::is_constructible<_Monoid, value_type>::value,
"_Monoid(iter_type::value_type) is not constructible.");
for (auto iter{std::next(std::begin(data), size_ext)};
iter != std::end(data) && first != last; ++iter, ++first)
*iter = _Monoid(*first);
for (size_t i{size_ext}; --i;) pull(i);
}
/**
* @return Number of elements.
*/
size_t size() const { return size_orig; }
/**
* @param index Index of the element
* @return Reference to the element.
*/
_Monoid &operator[](size_t index) {
assert(index < size_orig);
index |= size_ext;
wait.push(index);
for (size_t i = height; i; --i) push(index >> i);
return data[index];
}
void update(const _End &endo) { update(0, size_orig, endo); }
void update(size_t index, const _End &endo) {
update(index, index + 1, endo);
}
void update(size_t first, size_t last, const _End &endo) {
assert(last <= size_orig);
repair();
if (first >= last) return;
first += size_ext, last += size_ext;
--last;
for (size_t i = height; i; --i) push(first >> i), push(last >> i);
++last;
for (size_t l = first, r = last; l != r; l >>= 1, r >>= 1) {
if (l & 1) apply(l++, endo);
if (r & 1) apply(--r, endo);
}
for (first >>= __builtin_ffs(first); first; first >>= 1) pull(first);
for (last >>= __builtin_ffs(last); last; last >>= 1) pull(last);
}
/**
* @param first Left end, inclusive
* @param last Right end, exclusive
* @return Sum of elements in the interval.
*/
_Monoid fold(size_t first, size_t last) {
assert(last <= size_orig);
repair();
if (first >= last) return _Monoid{};
first += size_ext, last += size_ext - 1;
_Monoid left_val{}, right_val{};
for (size_t l = first, r = last + 1; l != r; l >>= 1, r >>= 1) {
if (l & 1) left_val = left_val + data[l++];
if (r & 1) right_val = data[--r] + right_val;
left_val = left_val * lazy[first >>= 1];
right_val = right_val * lazy[last >>= 1];
}
while (first >>= 1, last >>= 1) {
left_val = left_val * lazy[first];
right_val = right_val * lazy[last];
}
return left_val + right_val;
}
/**
* @return Sum of all elements.
*/
_Monoid fold() {
repair();
return data[1];
}
/**
* @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_t)'
* @return Left end of the extremal interval satisfying the condition,
* inclusive.
*/
template <class Pred> size_t left_partition(size_t right, Pred pred) {
assert(right <= size_orig);
repair();
right += size_ext - 1;
for (size_t i{height}; i; --i) push(right >> i);
++right;
_Monoid mono{};
for (size_t left{size_ext}, step{}; left != right;
left >>= 1, right >>= 1, ++step) {
if ((left & 1) != (right & 1)) {
const _Monoid tmp = data[--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_t)'
* @return Right end of the extremal interval satisfying the condition,
* exclusive.
*/
template <class Pred> size_t right_partition(size_t left, Pred pred) {
assert(left <= size_orig);
repair();
left += size_ext;
for (size_t i{height}; i; --i) push(left >> i);
_Monoid mono{};
for (size_t right{size_ext << 1}, step{}; left != right;
left >>= 1, right >>= 1, ++step) {
if ((left & 1) != (right & 1)) {
const _Monoid tmp = mono + data[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;
}
};
} // namespace workspace
#line 6 "other-workspace\\749.cpp"
namespace workspace {
using mint = modint<1000000007>;
}
namespace workspace {
void main() {
// start here!
using mono = matrix<mint, 1, 3>;
using endo = matrix_operator<mint, 3, 3>;
int n, q;
std::cin >> n >> q;
lazy_segment_tree<mono, endo> sgt(n);
{
mint x, y{1};
for (auto &e : sgt) {
e[0][1] = x;
e[0][2] = 1;
x += y;
std::swap(x, y);
}
}
while (q--) {
int t, l, r, k;
std::cin >> t >> l >> r >> k;
++r;
if (!t) {
std::cout << sgt.fold(l, r)[0][0] * k << "\n";
continue;
}
endo e;
switch (t) {
case 1: {
e[0][0] = 0;
e[2][0] = k;
} break;
case 2: {
e[2][0] = k;
} break;
case 3: {
e[0][0] = k;
} break;
case 4: {
e[1][0] = k;
} break;
}
sgt.update(l, r, e);
}
}
} // namespace workspace
int main() {
std::ios::sync_with_stdio(0);
std::cin.tie(0);
workspace::main();
}