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 23:29:41 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 664 ms / 3,000 ms |
| コード長 | 38,525 bytes |
| コンパイル時間 | 4,513 ms |
| コンパイル使用メモリ | 264,896 KB |
| 最終ジャッジ日時 | 2025-01-25 19:06:37 |
|
ジャッジサーバーID （参考情報） |
judge5 / judge4 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| other | AC * 20 |
ソースコード
#line 1 "other/ms.cc"
// #undef _GLIBCXX_DEBUG
// #define NDEBUG
#include <bits/extc++.h>
// #include "lib/alias"
// #include "lib/cxx20"
// #include "lib/direct"
// #include "lib/opt"
// #include "lib/sys"
// #include "lib/utils"
// signed main() {
// using namespace workspace;
// io_setup(15);
// /* given
// case_info.read(); //*/
// /* unspecified
// case_info.total = -1; //*/
// return case_info.iterate();
// }
#line 2 "Library/src/algebra/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 _Cols2>
constexpr matrix<_Scalar, _Rows, _Cols2> operator*(
const matrix<_Scalar2, _Cols, _Cols2>& __x) const {
matrix<_Scalar, _Rows, _Cols2> __m;
auto __w = *__m.__data;
for (const auto& __r : __data)
for (auto __v = *__x.__data, __end = __v + _Cols2; __v != __end; ++__w) {
auto __i = __v++;
for (const auto& __e : __r) *__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 {
assert(_Cols <= __x.rows());
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 != _Cols; ++__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 {
static_assert(_Rows == _Cols);
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 operator=(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 {
assert(cols() <= __x.rows());
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 != cols(); ++__c)
__m[__r] += operator[](__r)[__c] * __x[__c];
else
for (size_type __r = 0; __r != rows(); ++__r)
for (size_type __c = 0; __c != cols(); ++__c)
for (size_type __i = 0; __i != __x.cols(); ++__i)
__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;
}
};
} // 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
*/
#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 16 "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(std::is_assignable<Monoid&, decltype(std::declval<Monoid>() +
std::declval<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;
class iterator {
segment_tree *__p;
size_type __i;
public:
using difference_type = typename std::make_signed<size_type>::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 init
*/
segment_tree(size_type __n, Monoid const &init) : segment_tree(__n) {
for (auto i = begin(); i != end(); ++i) *i = init;
}
/**
* @brief Construct a new segment tree object
*
* @tparam Tp
* @param __n Number of elements.
* @param init
*/
template <class Tp, typename std::enable_if<std::is_convertible<
Tp, Monoid>::value>::type * = nullptr>
segment_tree(size_type __n, Tp &&init) : segment_tree(__n) {
for (auto i = begin(); i != end(); ++i) *i = init;
}
/**
* @brief Construct a new segment tree object
*
* @tparam Iterator
* @param __first
* @param __last
*/
template <class Iterator,
typename std::enable_if<std::is_convertible<
typename std::iterator_traits<Iterator>::value_type,
Monoid>::value> * = nullptr>
segment_tree(Iterator __first, Iterator __last)
: segment_tree(std::distance(__first, __last)) {
for (auto i = begin(); __first != __last; ++i, ++__first) *i = *__first;
}
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(); }
/**
* @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 fold(0, size_orig); }
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;
}
};
} // namespace workspace
#line 2 "Library/src/modular/modint.hpp"
/**
* @file modint.hpp
*
* @brief Modular Arithmetic
*/
#line 12 "Library/src/modular/modint.hpp"
#line 2 "Library/src/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; };
#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;
template <class Container>
using element_type = typename std::decay<decltype(
*std::begin(std::declval<Container&>()))>::type;
template <class T, class = std::nullptr_t>
struct has_begin : std::false_type {};
template <class T>
struct has_begin<T, decltype(std::begin(std::declval<T>()), nullptr)>
: std::true_type {};
template <class T, class = int> struct mapped_of {
using type = element_type<T>;
};
template <class T>
struct mapped_of<T,
typename std::pair<int, typename T::mapped_type>::first_type> {
using type = typename T::mapped_type;
};
template <class T> using mapped_type = typename mapped_of<T>::type;
template <class T, class = void> struct is_integral_ext : std::false_type {};
template <class T>
struct is_integral_ext<
T, typename std::enable_if<std::is_integral<T>::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 T>
constexpr static bool is_integral_ext_v = is_integral_ext<T>::value;
#endif
template <typename T, typename = void> struct multiplicable_uint {
using type = uint_least32_t;
};
template <typename T>
struct multiplicable_uint<
T, typename std::enable_if<(2 < sizeof(T)) &&
(!__INT128_DEFINED__ || sizeof(T) <= 4)>::type> {
using type = uint_least64_t;
};
#if __INT128_DEFINED__
template <typename T>
struct multiplicable_uint<T, typename std::enable_if<(4 < sizeof(T))>::type> {
using type = __uint128_t;
};
#endif
template <typename T> struct multiplicable_int {
using type =
typename std::make_signed<typename multiplicable_uint<T>::type>::type;
};
} // namespace workspace
#line 14 "Library/src/modular/modint.hpp"
namespace workspace {
namespace internal {
/**
* @brief Base of modular arithmetic.
*
* @tparam Mod identifier, which represents modulus if positive
* @tparam Storage Reserved size for inverse calculation
*/
template <auto Mod, unsigned Storage> struct modint_base {
static_assert(is_integral_ext<decltype(Mod)>::value,
"Mod must be integral type.");
using mod_type = typename std::make_signed<typename std::conditional<
0 < Mod, typename std::add_const<decltype(Mod)>::type,
decltype(Mod)>::type>::type;
using value_type = typename std::decay<mod_type>::type;
using mul_type = typename multiplicable_uint<value_type>::type;
static mod_type mod;
static value_type storage;
constexpr static void reserve(unsigned __n) noexcept { storage = __n; }
protected:
value_type value = 0;
public:
constexpr modint_base() noexcept = default;
template <class int_type,
typename std::enable_if<is_integral_ext<int_type>::value>::type * =
nullptr>
constexpr modint_base(int_type n) noexcept
: value((n %= mod) < 0 ? n += mod : n) {}
constexpr modint_base(bool n) noexcept : value(n) {}
constexpr operator value_type() const noexcept { return value; }
constexpr static modint_base one() noexcept { return 1; }
// unary operators {{
constexpr modint_base operator++(int) noexcept {
modint_base __t{*this};
operator++();
return __t;
}
constexpr modint_base operator--(int) noexcept {
modint_base __t{*this};
operator--();
return __t;
}
constexpr modint_base &operator++() noexcept {
if (++value == mod) value = 0;
return *this;
}
constexpr modint_base &operator--() noexcept {
if (!value) value = mod;
--value;
return *this;
}
constexpr modint_base operator-() const noexcept {
modint_base __t;
__t.value = value ? mod - value : 0;
return __t;
}
// }} unary operators
// operator+= {{
constexpr modint_base &operator+=(modint_base const &rhs) noexcept {
if ((value += rhs.value) >= mod) value -= mod;
return *this;
}
template <class int_type>
constexpr typename std::enable_if<is_integral_ext<int_type>::value,
modint_base>::type &
operator+=(int_type const &rhs) noexcept {
if (((value += rhs) %= mod) < 0) value += mod;
return *this;
}
// }} operator+=
// operator+ {{
template <class int_type>
constexpr typename std::enable_if<is_integral_ext<int_type>::value,
modint_base>::type
operator+(int_type const &rhs) const noexcept {
return modint_base{*this} += rhs;
}
constexpr modint_base operator+(modint_base rhs) const noexcept {
return rhs += *this;
}
template <class int_type>
constexpr friend typename std::enable_if<is_integral_ext<int_type>::value,
modint_base>::type
operator+(int_type const &lhs, modint_base rhs) noexcept {
return rhs += lhs;
}
// }} operator+
// operator-= {{
constexpr modint_base &operator-=(modint_base const &rhs) noexcept {
if ((value -= rhs.value) < 0) value += mod;
return *this;
}
template <class int_type>
constexpr typename std::enable_if<is_integral_ext<int_type>::value,
modint_base>::type &
operator-=(int_type rhs) noexcept {
if (((value -= rhs) %= mod) < 0) value += mod;
return *this;
}
// }} operator-=
// operator- {{
template <class int_type>
constexpr typename std::enable_if<is_integral_ext<int_type>::value,
modint_base>::type
operator-(int_type const &rhs) const noexcept {
return modint_base{*this} -= rhs;
}
constexpr modint_base operator-(modint_base const &rhs) const noexcept {
modint_base __t;
if (((__t.value = value) -= rhs.value) < 0) __t.value += mod;
return __t;
}
template <class int_type>
constexpr friend typename std::enable_if<is_integral_ext<int_type>::value,
modint_base>::type
operator-(int_type lhs, modint_base const &rhs) noexcept {
if (((lhs -= rhs.value) %= mod) < 0) lhs += mod;
modint_base __t;
__t.value = lhs;
return __t;
}
// }} operator-
// operator*= {{
constexpr modint_base &operator*=(modint_base const &rhs) noexcept {
if (!rhs.value)
value = 0;
else if (value) {
mul_type __r(value);
value = static_cast<value_type &&>((__r *= rhs.value) %= mod);
}
return *this;
}
template <class int_type>
constexpr typename std::enable_if<is_integral_ext<int_type>::value,
modint_base>::type &
operator*=(int_type rhs) noexcept {
if (!rhs)
value = 0;
else if (value) {
if ((rhs %= mod) < 0) rhs += mod;
mul_type __r(value);
value = static_cast<value_type &&>((__r *= rhs) %= mod);
}
return *this;
}
// }} operator*=
// operator* {{
constexpr modint_base operator*(modint_base const &rhs) const noexcept {
if (!value or !rhs.value) return {};
mul_type __r(value);
modint_base __t;
__t.value = static_cast<value_type &&>((__r *= rhs.value) %= mod);
return __t;
}
template <class int_type>
constexpr typename std::enable_if<is_integral_ext<int_type>::value,
modint_base>::type
operator*(int_type rhs) const noexcept {
if (!value or !rhs) return {};
if ((rhs %= mod) < 0) rhs += mod;
mul_type __r(value);
modint_base __t;
__t.value = static_cast<value_type &&>((__r *= rhs) %= mod);
return __t;
}
template <class int_type>
constexpr friend typename std::enable_if<is_integral_ext<int_type>::value,
modint_base>::type
operator*(int_type lhs, modint_base const &rhs) noexcept {
if (!lhs or !rhs.value) return {};
if ((lhs %= mod) < 0) lhs += mod;
mul_type __r(lhs);
modint_base __t;
__t.value = static_cast<value_type &&>((__r *= rhs.value) %= mod);
return __t;
}
// }} 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];
}
template <class int_type>
constexpr static typename std::enable_if<is_integral_ext<int_type>::value,
value_type>::type
_div(mul_type __r, int_type __x) noexcept {
assert(__x);
if (!__r) return 0;
int_type __v{};
bool __neg = __x < 0 ? __x = -__x, true : false;
if (__x < storage)
__v = _mem(__x);
else {
int_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;
if (__r == 1) return static_cast<value_type>(__v);
return static_cast<value_type>((__r *= __v) %= mod);
}
public:
// operator/= {{
constexpr modint_base &operator/=(modint_base const &rhs) noexcept {
if (value) value = _div(value, rhs.value);
return *this;
}
template <class int_type>
constexpr typename std::enable_if<is_integral_ext<int_type>::value,
modint_base>::type &
operator/=(int_type rhs) noexcept {
if (value) value = _div(value, rhs %= mod);
return *this;
}
// }} operator/=
// operator/ {{
constexpr modint_base operator/(modint_base const &rhs) const noexcept {
if (!value) return {};
modint_base __t;
__t.value = _div(value, rhs.value);
return __t;
}
template <class int_type>
constexpr typename std::enable_if<is_integral_ext<int_type>::value,
modint_base>::type
operator/(int_type rhs) const noexcept {
if (!value) return {};
modint_base __t;
__t.value = _div(value, rhs %= mod);
return __t;
}
template <class int_type>
constexpr friend typename std::enable_if<is_integral_ext<int_type>::value,
modint_base>::type
operator/(int_type lhs, modint_base const &rhs) noexcept {
if (!lhs) return {};
if ((lhs %= mod) < 0) lhs += mod;
modint_base __t;
__t.value = _div(lhs, rhs.value);
return __t;
}
// }} operator/
constexpr modint_base inv() const noexcept { return _div(1, value); }
template <class int_type>
friend constexpr typename std::enable_if<is_integral_ext<int_type>::value,
modint_base>::type
pow(modint_base b, int_type e) noexcept {
if (e < 0) {
e = -e;
b.value = _div(1, b.value);
}
modint_base __r;
for (__r.value = 1; e; e >>= 1, b *= b)
if (e & 1) __r *= b;
return __r;
}
template <class int_type>
constexpr typename std::enable_if<is_integral_ext<int_type>::value,
modint_base>::type
pow(int_type e) const noexcept {
modint_base __r, b;
__r.value = 1;
for (b.value = e < 0 ? e = -e, _div(1, value) : value; e; e >>= 1, b *= b)
if (e & 1) __r *= b;
return __r;
}
friend std::ostream &operator<<(std::ostream &os,
const modint_base &rhs) noexcept {
return os << rhs.value;
}
friend std::istream &operator>>(std::istream &is, modint_base &rhs) noexcept {
intmax_t value;
rhs = (is >> value, value);
return is;
}
};
template <auto Mod, unsigned Storage>
typename modint_base<Mod, Storage>::mod_type modint_base<Mod, Storage>::mod =
Mod > 0 ? Mod : 0;
template <auto Mod, unsigned Storage>
typename modint_base<Mod, Storage>::value_type
modint_base<Mod, Storage>::storage = Storage;
} // namespace internal
/**
* @brief Modular arithmetic.
*
* @tparam Mod modulus
* @tparam Storage Reserved size for inverse calculation
*/
template <auto Mod, unsigned Storage = 0,
typename std::enable_if<(Mod > 0)>::type * = nullptr>
using modint = internal::modint_base<Mod, Storage>;
/**
* @brief Runtime modular arithmetic.
*
* @tparam type_id uniquely assigned
* @tparam Storage Reserved size for inverse calculation
*/
template <unsigned type_id = 0, unsigned Storage = 0>
using modint_runtime = internal::modint_base<-(signed)type_id, Storage>;
// #define modint_newtype modint_runtime<__COUNTER__>
} // namespace workspace
#line 29 "other/ms.cc"
namespace workspace {
using mint = modint<(int)1e9 + 7>;
using mat = matrix<mint, 3>;
using vec = matrix<mint, 1, 3>;
void main() {
// start here!
using std::cin;
using std::cout;
int n, q;
cin >> n >> q;
segment_tree<vec, mat> sgt(n);
// init
{
mint a = 0, b = 1;
for (auto &&x : sgt) {
x = {{0, 1, a}};
std::swap(b, a += b);
}
}
while (q--) {
int tp, l, r, k;
cin >> tp >> l >> r >> k;
++r;
mat op = mat::eye();
switch (tp) {
case 0: {
cout << sgt.fold(l, r)[0][0] * k << "\n";
} break;
case 1: {
op[0][0] = 0;
op[1][0] = k;
sgt.update(l, r, op);
} break;
case 2: {
op[1][0] = k;
sgt.update(l, r, op);
} break;
case 3: {
op[0][0] = k;
sgt.update(l, r, op);
} break;
case 4: {
op[2][0] = k;
sgt.update(l, r, op);
} break;
}
}
}
} // namespace workspace
int main() {
std::ios::sync_with_stdio(false);
std::cin.tie(0);
workspace::main();
}