#line 1 "verify/ds/segtree/dynamic_lazy_segtree.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/range_affine_range_sum"
#line 1 "ds/segtree/dynamic_lazy_segtree.hpp"
#include <cassert>
#include <concepts>
#include <cstddef>
#include <limits>
#include <numeric>
#include <type_traits>
#include <utility>
#include <vector>
#line 1 "acted_monoid/concept.hpp"
#line 5 "acted_monoid/concept.hpp"
namespace m1une {
namespace acted_monoid {
// Concept defining the requirements for an Acted Monoid.
template <typename AM>
concept IsActedMonoid = requires(typename AM::value_type a, typename AM::value_type b, typename AM::operator_type f,
typename AM::operator_type g) {
// 1. Value Monoid
typename AM::value_type;
{ AM::id() } -> std::same_as<typename AM::value_type>;
{ AM::op(a, b) } -> std::same_as<typename AM::value_type>;
// 2. Operator Monoid
typename AM::operator_type;
{ AM::op_id() } -> std::same_as<typename AM::operator_type>;
{ AM::op_comp(f, g) } -> std::same_as<typename AM::operator_type>; // Composition order: f(g(x))
// 3. Mapping: Operator x Value -> Value
{ AM::mapping(f, a) } -> std::same_as<typename AM::value_type>;
};
// Concept for acted monoids whose value monoid is a commutative group.
// The value operation must obey commutativity and inverse laws.
template <typename AM>
concept IsCommutativeActedGroup = IsActedMonoid<AM> && requires(typename AM::value_type a) {
{ AM::inv(a) } -> std::same_as<typename AM::value_type>;
};
} // namespace acted_monoid
} // namespace m1une
#line 1 "ds/segtree/dynamic_segtree_common.hpp"
#line 11 "ds/segtree/dynamic_segtree_common.hpp"
namespace m1une {
namespace ds {
namespace detail {
template <std::integral Index>
using dynamic_size_type = std::make_unsigned_t<Index>;
template <std::integral Index>
constexpr dynamic_size_type<Index> dynamic_distance(Index left, Index right) {
return static_cast<dynamic_size_type<Index>>(right) - static_cast<dynamic_size_type<Index>>(left);
}
template <class Monoid, class Size>
typename Monoid::value_type monoid_repeat(typename Monoid::value_type value, Size count) {
typename Monoid::value_type result = Monoid::id();
while (count != 0) {
if (count & 1) result = Monoid::op(result, value);
count >>= 1;
if (count != 0) value = Monoid::op(value, value);
}
return result;
}
template <class ActedMonoid>
typename ActedMonoid::value_type dynamic_mapping(
const typename ActedMonoid::operator_type& f,
const typename ActedMonoid::value_type& value
) {
using F = typename ActedMonoid::operator_type;
using T = typename ActedMonoid::value_type;
if constexpr (requires(F g, T x, long long ord) { ActedMonoid::mapping(g, x, ord); }) {
return ActedMonoid::mapping(f, value, 0);
} else {
return ActedMonoid::mapping(f, value);
}
}
template <class ActedMonoid, class Size>
typename ActedMonoid::operator_type dynamic_shift(
const typename ActedMonoid::operator_type& f,
Size offset
) {
using F = typename ActedMonoid::operator_type;
if constexpr (requires(F g, long long ord) { ActedMonoid::op_shift(g, ord); }) {
assert(offset <= static_cast<Size>(std::numeric_limits<long long>::max()));
return ActedMonoid::op_shift(f, static_cast<long long>(offset));
} else {
return f;
}
}
template <class Monoid, std::integral Index>
class UniformMonoidDomain {
public:
using T = typename Monoid::value_type;
using size_type = dynamic_size_type<Index>;
private:
struct Level {
size_type small_length;
T small_value;
T large_value;
};
Index _left;
Index _right;
T _initial_value;
std::vector<Level> _levels;
public:
UniformMonoidDomain(Index left, Index right, T initial_value)
: _left(left), _right(right), _initial_value(std::move(initial_value)) {
assert(left <= right);
size_type n = size();
constexpr int digits = std::numeric_limits<size_type>::digits;
_levels.reserve(digits + 1);
for (int depth = 0; depth <= digits; depth++) {
size_type small = depth == digits ? 0 : n >> depth;
size_type large = small;
if (depth != 0) {
bool has_remainder;
if (depth == digits) {
has_remainder = n != 0;
} else {
size_type mask = (size_type(1) << depth) - 1;
has_remainder = (n & mask) != 0;
}
if (has_remainder) large++;
}
_levels.push_back(Level{
small,
monoid_repeat<Monoid>(_initial_value, small),
monoid_repeat<Monoid>(_initial_value, large),
});
}
}
Index left_bound() const {
return _left;
}
Index right_bound() const {
return _right;
}
size_type size() const {
return dynamic_distance(_left, _right);
}
bool empty() const {
return _left == _right;
}
const T& initial_value() const {
return _initial_value;
}
const T& default_product(int depth, Index left, Index right) const {
assert(0 <= depth && depth < int(_levels.size()));
const Level& level = _levels[depth];
size_type length = dynamic_distance(left, right);
if (length == level.small_length) return level.small_value;
assert(length == level.small_length + 1);
return level.large_value;
}
};
} // namespace detail
} // namespace ds
} // namespace m1une
#line 15 "ds/segtree/dynamic_lazy_segtree.hpp"
namespace m1une {
namespace ds {
// A sparse lazy segment tree over an integral half-open interval.
template <m1une::acted_monoid::IsActedMonoid ActedMonoid, std::integral Index = long long>
requires(!std::same_as<std::remove_cv_t<Index>, bool>)
struct DynamicLazySegtree {
using T = typename ActedMonoid::value_type;
using F = typename ActedMonoid::operator_type;
using index_type = Index;
using size_type = detail::dynamic_size_type<Index>;
private:
struct Node {
T val;
F lazy;
int left;
int right;
bool has_lazy;
explicit Node(T value)
: val(std::move(value)),
lazy(ActedMonoid::op_id()),
left(0),
right(0),
has_lazy(false) {}
};
detail::UniformMonoidDomain<ActedMonoid, Index> _domain;
int _root;
std::vector<Node> _nodes;
int new_node(Index left, Index right, int depth) {
assert(_nodes.size() < std::size_t(std::numeric_limits<int>::max()));
_nodes.emplace_back(_domain.default_product(depth, left, right));
return int(_nodes.size()) - 1;
}
const T& value(int t, Index left, Index right, int depth) const {
if (t) return _nodes[t].val;
return _domain.default_product(depth, left, right);
}
void all_apply(int& t, Index left, Index right, int depth, const F& f) {
if (!t) t = new_node(left, right, depth);
Node& node = _nodes[t];
node.val = detail::dynamic_mapping<ActedMonoid>(f, node.val);
if (std::midpoint(left, right) != left) {
node.lazy = ActedMonoid::op_comp(f, node.lazy);
node.has_lazy = true;
}
}
void push(int t, Index left, Index right, int depth) {
if (!_nodes[t].has_lazy) return;
Index middle = std::midpoint(left, right);
if (middle == left) return;
F lazy = _nodes[t].lazy;
int left_child = _nodes[t].left;
int right_child = _nodes[t].right;
all_apply(left_child, left, middle, depth + 1, lazy);
all_apply(
right_child,
middle,
right,
depth + 1,
detail::dynamic_shift<ActedMonoid>(lazy, detail::dynamic_distance(left, middle))
);
Node& node = _nodes[t];
node.left = left_child;
node.right = right_child;
node.lazy = ActedMonoid::op_id();
node.has_lazy = false;
}
void update(int t, Index left, Index right, int depth) {
Index middle = std::midpoint(left, right);
_nodes[t].val = ActedMonoid::op(
value(_nodes[t].left, left, middle, depth + 1),
value(_nodes[t].right, middle, right, depth + 1)
);
}
int set_node(int t, Index left, Index right, int depth, Index p, T x) {
if (!t) t = new_node(left, right, depth);
Index middle = std::midpoint(left, right);
if (middle == left) {
Node& node = _nodes[t];
node.val = std::move(x);
node.lazy = ActedMonoid::op_id();
node.has_lazy = false;
return t;
}
push(t, left, right, depth);
if (p < middle) {
int child = set_node(_nodes[t].left, left, middle, depth + 1, p, std::move(x));
_nodes[t].left = child;
} else {
int child = set_node(_nodes[t].right, middle, right, depth + 1, p, std::move(x));
_nodes[t].right = child;
}
update(t, left, right, depth);
return t;
}
int apply_node(
int t,
Index left,
Index right,
int depth,
Index query_left,
Index query_right,
const F& f
) {
if (query_right <= left || right <= query_left) return t;
if (query_left <= left && right <= query_right) {
all_apply(
t,
left,
right,
depth,
detail::dynamic_shift<ActedMonoid>(f, detail::dynamic_distance(query_left, left))
);
return t;
}
if (!t) t = new_node(left, right, depth);
push(t, left, right, depth);
Index middle = std::midpoint(left, right);
int left_child = apply_node(_nodes[t].left, left, middle, depth + 1, query_left, query_right, f);
int right_child = apply_node(_nodes[t].right, middle, right, depth + 1, query_left, query_right, f);
_nodes[t].left = left_child;
_nodes[t].right = right_child;
update(t, left, right, depth);
return t;
}
F compose_for_child(const F& inherited, int t, size_type offset) const {
F shifted = detail::dynamic_shift<ActedMonoid>(inherited, offset);
if (!t || !_nodes[t].has_lazy) return shifted;
return ActedMonoid::op_comp(
shifted,
detail::dynamic_shift<ActedMonoid>(_nodes[t].lazy, offset)
);
}
T prod_node(
int t,
Index left,
Index right,
int depth,
Index query_left,
Index query_right,
const F& inherited
) const {
if (query_right <= left || right <= query_left) return ActedMonoid::id();
if (query_left <= left && right <= query_right) {
return detail::dynamic_mapping<ActedMonoid>(
inherited,
value(t, left, right, depth)
);
}
Index middle = std::midpoint(left, right);
return ActedMonoid::op(
prod_node(
t ? _nodes[t].left : 0,
left,
middle,
depth + 1,
query_left,
query_right,
compose_for_child(inherited, t, 0)
),
prod_node(
t ? _nodes[t].right : 0,
middle,
right,
depth + 1,
query_left,
query_right,
compose_for_child(inherited, t, detail::dynamic_distance(left, middle))
)
);
}
template <class G>
Index max_right_node(
int t,
Index left,
Index right,
int depth,
Index query_left,
T& product,
const F& inherited,
G& predicate
) const {
if (right <= query_left) return right;
if (query_left <= left) {
T next = ActedMonoid::op(
product,
detail::dynamic_mapping<ActedMonoid>(
inherited,
value(t, left, right, depth)
)
);
if (predicate(next)) {
product = std::move(next);
return right;
}
Index middle = std::midpoint(left, right);
if (middle == left) return left;
}
Index middle = std::midpoint(left, right);
Index result = max_right_node(
t ? _nodes[t].left : 0,
left,
middle,
depth + 1,
query_left,
product,
compose_for_child(inherited, t, 0),
predicate
);
if (result < middle) return result;
return max_right_node(
t ? _nodes[t].right : 0,
middle,
right,
depth + 1,
query_left,
product,
compose_for_child(inherited, t, detail::dynamic_distance(left, middle)),
predicate
);
}
template <class G>
Index min_left_node(
int t,
Index left,
Index right,
int depth,
Index query_right,
T& product,
const F& inherited,
G& predicate
) const {
if (query_right <= left) return left;
if (right <= query_right) {
T next = ActedMonoid::op(
detail::dynamic_mapping<ActedMonoid>(
inherited,
value(t, left, right, depth)
),
product
);
if (predicate(next)) {
product = std::move(next);
return left;
}
Index middle = std::midpoint(left, right);
if (middle == left) return right;
}
Index middle = std::midpoint(left, right);
Index result = min_left_node(
t ? _nodes[t].right : 0,
middle,
right,
depth + 1,
query_right,
product,
compose_for_child(inherited, t, detail::dynamic_distance(left, middle)),
predicate
);
if (middle < result) return result;
return min_left_node(
t ? _nodes[t].left : 0,
left,
middle,
depth + 1,
query_right,
product,
compose_for_child(inherited, t, 0),
predicate
);
}
public:
DynamicLazySegtree()
: DynamicLazySegtree(Index(0), Index(0), ActedMonoid::id()) {}
explicit DynamicLazySegtree(Index n)
: DynamicLazySegtree(Index(0), n, ActedMonoid::id()) {
if constexpr (std::signed_integral<Index>) assert(Index(0) <= n);
}
DynamicLazySegtree(Index left, Index right)
: DynamicLazySegtree(left, right, ActedMonoid::id()) {}
DynamicLazySegtree(Index left, Index right, T initial_value)
: _domain(left, right, std::move(initial_value)), _root(0) {
_nodes.emplace_back(ActedMonoid::id());
}
size_type size() const {
return _domain.size();
}
bool empty() const {
return _domain.empty();
}
Index left_bound() const {
return _domain.left_bound();
}
Index right_bound() const {
return _domain.right_bound();
}
const T& initial_value() const {
return _domain.initial_value();
}
void reserve(std::size_t node_capacity) {
assert(node_capacity < std::numeric_limits<std::size_t>::max());
_nodes.reserve(node_capacity + 1);
}
std::size_t node_count() const {
return _nodes.size() - 1;
}
void clear() {
_root = 0;
_nodes.erase(_nodes.begin() + 1, _nodes.end());
}
void set(Index p, T x) {
assert(left_bound() <= p && p < right_bound());
_root = set_node(_root, left_bound(), right_bound(), 0, p, std::move(x));
}
T get(Index p) const {
assert(left_bound() <= p && p < right_bound());
return prod(p, p + 1);
}
T operator[](Index p) const {
return get(p);
}
T prod(Index left, Index right) const {
assert(left_bound() <= left && left <= right && right <= right_bound());
if (left == right) return ActedMonoid::id();
return prod_node(
_root,
left_bound(),
right_bound(),
0,
left,
right,
ActedMonoid::op_id()
);
}
T all_prod() const {
return value(_root, left_bound(), right_bound(), 0);
}
void apply(Index p, const F& f) {
assert(left_bound() <= p && p < right_bound());
apply(p, p + 1, f);
}
void apply(Index left, Index right, const F& f) {
assert(left_bound() <= left && left <= right && right <= right_bound());
if (left == right) return;
_root = apply_node(
_root,
left_bound(),
right_bound(),
0,
left,
right,
f
);
}
template <class G>
Index max_right(Index left, G predicate) const {
assert(left_bound() <= left && left <= right_bound());
assert(predicate(ActedMonoid::id()));
if (left == right_bound()) return right_bound();
T product = ActedMonoid::id();
return max_right_node(
_root,
left_bound(),
right_bound(),
0,
left,
product,
ActedMonoid::op_id(),
predicate
);
}
template <class G>
Index min_left(Index right, G predicate) const {
assert(left_bound() <= right && right <= right_bound());
assert(predicate(ActedMonoid::id()));
if (right == left_bound()) return left_bound();
T product = ActedMonoid::id();
return min_left_node(
_root,
left_bound(),
right_bound(),
0,
right,
product,
ActedMonoid::op_id(),
predicate
);
}
};
} // namespace ds
} // namespace m1une
#line 4 "verify/ds/segtree/dynamic_lazy_segtree.test.cpp"
#include <algorithm>
#line 7 "verify/ds/segtree/dynamic_lazy_segtree.test.cpp"
#include <cstdint>
#line 1 "utilities/fast_io.hpp"
#line 5 "utilities/fast_io.hpp"
#include <array>
#include <cerrno>
#include <charconv>
#line 9 "utilities/fast_io.hpp"
#include <cstdio>
#include <cstdlib>
#line 12 "utilities/fast_io.hpp"
#include <cstring>
#include <iterator>
#include <string>
#include <sys/stat.h>
#line 18 "utilities/fast_io.hpp"
#include <unistd.h>
#line 20 "utilities/fast_io.hpp"
namespace m1une {
namespace utilities {
struct FastOutput;
namespace internal {
// Shared with the convenience helpers in template.hpp.
inline FastOutput* standard_output_instance = nullptr;
// Detect std::begin(x), std::end(x).
template <class T, class = void>
struct is_range : std::false_type {};
template <class T>
struct is_range<T, std::void_t<
decltype(std::begin(std::declval<T&>())),
decltype(std::end(std::declval<T&>()))
>> : std::true_type {};
template <class T>
inline constexpr bool is_range_v = is_range<T>::value;
template <class T>
using range_reference_t = decltype(*std::begin(std::declval<T&>()));
template <class T>
using range_value_t = std::remove_cv_t<std::remove_reference_t<range_reference_t<T>>>;
template <class T, class = void>
struct range_stored_value {
using type = range_value_t<T>;
};
template <class T>
struct range_stored_value<T, std::void_t<typename std::remove_cv_t<std::remove_reference_t<T>>::value_type>> {
using type = typename std::remove_cv_t<std::remove_reference_t<T>>::value_type;
};
template <class T>
using range_stored_value_t = typename range_stored_value<T>::type;
// Treat strings and C strings as scalar output objects, not as ranges.
template <class T>
struct is_char_array : std::false_type {};
template <class T, std::size_t N>
struct is_char_array<T[N]>
: std::bool_constant<std::is_same_v<std::remove_cv_t<T>, char>> {};
template <class T>
struct is_string_like
: std::bool_constant<
std::is_same_v<std::decay_t<T>, std::string>
|| std::is_same_v<std::decay_t<T>, const char*>
|| std::is_same_v<std::decay_t<T>, char*>
|| is_char_array<std::remove_reference_t<T>>::value
> {};
template <class T>
inline constexpr bool is_string_like_v = is_string_like<T>::value;
// ModInt-like type: x.val() is printable, and x can be assigned from long long.
template <class T, class = void>
struct has_val_method : std::false_type {};
template <class T>
struct has_val_method<T, std::void_t<decltype(std::declval<const T&>().val())>>
: std::true_type {};
template <class T>
inline constexpr bool has_val_method_v = has_val_method<T>::value;
template <class T, class = void>
struct has_static_mod_raw : std::false_type {};
template <class T>
struct has_static_mod_raw<
T, std::void_t<decltype(T::mod()), decltype(T::raw(std::declval<uint32_t>()))>>
: std::true_type {};
template <class T>
inline constexpr bool has_static_mod_raw_v = has_static_mod_raw<T>::value;
// libstdc++ before GCC 16 does not classify __int128 as an integral type in
// strict ISO modes such as -std=c++23. Keep the fast-I/O interface independent
// of that implementation detail.
template <class T>
inline constexpr bool is_integral_v =
std::is_integral_v<T>
|| std::is_same_v<std::remove_cv_t<T>, __int128_t>
|| std::is_same_v<std::remove_cv_t<T>, __uint128_t>;
template <class T>
inline constexpr bool is_signed_v =
std::is_signed_v<T>
|| std::is_same_v<std::remove_cv_t<T>, __int128_t>;
template <class T>
struct make_unsigned {
using type = std::make_unsigned_t<T>;
};
template <>
struct make_unsigned<__int128_t> {
using type = __uint128_t;
};
template <>
struct make_unsigned<__uint128_t> {
using type = __uint128_t;
};
template <class T>
using make_unsigned_t = typename make_unsigned<std::remove_cv_t<T>>::type;
} // namespace internal
struct FastInput {
static constexpr int buffer_size = 1 << 20;
private:
std::FILE* _stream;
char _buffer[buffer_size];
int _position;
int _length;
int _file_descriptor;
bool _streaming;
bool refill() {
_position = 0;
if (_streaming) {
ssize_t length;
do {
length = ::read(_file_descriptor, _buffer, buffer_size);
} while (length < 0 && errno == EINTR);
if (length <= 0) {
_length = 0;
return false;
}
_length = int(length);
} else {
_length = int(std::fread(_buffer, 1, buffer_size, _stream));
}
return _length != 0;
}
template <class T>
bool read_integer_from_stream(T& value) {
if (!skip_spaces()) return false;
int c = read_char_raw();
bool negative = false;
if (c == '-') {
negative = true;
c = read_char_raw();
}
if constexpr (internal::is_signed_v<T>) {
T result = 0;
while ('0' <= c && c <= '9') {
result = negative ? result * 10 - (c - '0')
: result * 10 + (c - '0');
c = read_char_raw();
}
value = result;
} else {
T result = 0;
while ('0' <= c && c <= '9') {
result = result * 10 + T(c - '0');
c = read_char_raw();
}
value = negative ? T(0) - result : result;
}
return true;
}
bool prepare_number() {
if (_length - _position >= 64) return true;
const int remaining = _length - _position;
if (remaining > 0) std::memmove(_buffer, _buffer + _position, remaining);
const int added = int(std::fread(_buffer + remaining, 1, buffer_size - remaining, _stream));
_position = 0;
_length = remaining + added;
if (_length < buffer_size) _buffer[_length] = '\0';
return _length != 0;
}
public:
explicit FastInput(std::FILE* stream = stdin)
: _stream(stream),
_position(0),
_length(0),
_file_descriptor(::fileno(stream)),
_streaming([&] {
struct stat status;
return _file_descriptor >= 0
&& ::fstat(_file_descriptor, &status) == 0
&& !S_ISREG(status.st_mode);
}()) {}
FastInput(const FastInput&) = delete;
FastInput& operator=(const FastInput&) = delete;
int read_char_raw() {
if (_position == _length && !refill()) return EOF;
return _buffer[_position++];
}
bool skip_spaces() {
int c = read_char_raw();
while (c != EOF && c <= ' ') c = read_char_raw();
if (c == EOF) return false;
--_position;
return true;
}
bool read(char& value) {
if (!skip_spaces()) return false;
value = char(read_char_raw());
return true;
}
bool read(std::string& value) {
if (!skip_spaces()) return false;
value.clear();
while (true) {
const int begin = _position;
while (_position < _length &&
static_cast<unsigned char>(_buffer[_position]) > ' ') {
++_position;
}
value.append(_buffer + begin, _position - begin);
if (_position < _length) {
++_position;
return true;
}
if (!refill()) return true;
}
}
bool read(bool& value) {
int x;
if (!read(x)) return false;
value = x != 0;
return true;
}
template <class T>
std::enable_if_t<
internal::is_integral_v<T>
&& !std::is_same_v<std::remove_cv_t<T>, bool>
&& !std::is_same_v<std::remove_cv_t<T>, char>,
bool
>
read(T& value) {
if (_streaming) return read_integer_from_stream(value);
if (!prepare_number()) return false;
int c = static_cast<unsigned char>(_buffer[_position++]);
while (c <= ' ') c = static_cast<unsigned char>(_buffer[_position++]);
bool negative = false;
if (c == '-') {
negative = true;
c = static_cast<unsigned char>(_buffer[_position++]);
}
if constexpr (internal::is_signed_v<T>) {
T result = 0;
while ('0' <= c && c <= '9') {
const int first = c - '0';
const int second = static_cast<unsigned char>(_buffer[_position]) - '0';
if (0 <= second && second <= 9) {
result = negative ? result * 100 - (first * 10 + second)
: result * 100 + (first * 10 + second);
++_position;
} else {
result = negative ? result * 10 - first : result * 10 + first;
}
c = static_cast<unsigned char>(_buffer[_position++]);
}
value = result;
} else {
T result = 0;
while ('0' <= c && c <= '9') {
const unsigned first = unsigned(c - '0');
const int second = static_cast<unsigned char>(_buffer[_position]) - '0';
if (0 <= second && second <= 9) {
result = result * 100 + T(first * 10 + unsigned(second));
++_position;
} else {
result = result * 10 + T(first);
}
c = static_cast<unsigned char>(_buffer[_position++]);
}
value = negative ? T(0) - result : result;
}
if (_position > _length) _position = _length;
return true;
}
template <class T>
std::enable_if_t<std::is_floating_point_v<T>, bool>
read(T& value) {
if (!skip_spaces()) return false;
int c = read_char_raw();
bool negative = false;
if (c == '-' || c == '+') {
negative = c == '-';
c = read_char_raw();
}
long double result = 0;
while ('0' <= c && c <= '9') {
result = result * 10 + (c - '0');
c = read_char_raw();
}
if (c == '.') {
long double place = 0.1L;
c = read_char_raw();
while ('0' <= c && c <= '9') {
result += (c - '0') * place;
place *= 0.1L;
c = read_char_raw();
}
}
if (c == 'e' || c == 'E') {
c = read_char_raw();
bool exponent_negative = false;
if (c == '-' || c == '+') {
exponent_negative = c == '-';
c = read_char_raw();
}
int exponent = 0;
while ('0' <= c && c <= '9') {
exponent = exponent * 10 + (c - '0');
c = read_char_raw();
}
long double scale = 1;
long double power = 10;
while (exponent > 0) {
if (exponent & 1) scale *= power;
power *= power;
exponent >>= 1;
}
result = exponent_negative ? result / scale : result * scale;
}
value = static_cast<T>(negative ? -result : result);
return true;
}
template <class T>
std::enable_if_t<
internal::has_val_method_v<T>
&& !internal::is_integral_v<T>
&& !internal::is_range_v<T>,
bool
>
read(T& value) {
long long x;
if (!read(x)) return false;
if constexpr (internal::has_static_mod_raw_v<T>) {
if (x >= 0 && uint64_t(x) < uint64_t(T::mod())) {
value = T::raw(uint32_t(x));
} else {
value = T(x);
}
} else {
value = T(x);
}
return true;
}
template <class First, class Second>
bool read(std::pair<First, Second>& value) {
if (!read(value.first)) return false;
return read(value.second);
}
template <class Range>
std::enable_if_t<
internal::is_range_v<Range>
&& !internal::is_string_like_v<Range>,
bool
>
read(Range& range) {
using StoredValue = internal::range_stored_value_t<Range>;
constexpr bool nested = internal::is_range_v<StoredValue>
&& !internal::is_string_like_v<StoredValue>;
for (auto&& value : range) {
if constexpr (std::is_same_v<StoredValue, bool> && !nested) {
bool x;
if (!read(x)) return false;
value = x;
} else {
if (!read(value)) return false;
}
}
return true;
}
template <class First, class Second, class... Rest>
bool read(First& first, Second& second, Rest&... rest) {
if (!read(first)) return false;
return read(second, rest...);
}
template <class T>
FastInput& operator>>(T& value) {
if (!read(value)) std::abort();
return *this;
}
};
struct FastOutput {
static constexpr int buffer_size = 1 << 20;
private:
inline static const auto digit_quads = [] {
std::array<char, 40000> result{};
for (int i = 0; i < 10000; i++) {
int value = i;
for (int j = 3; j >= 0; j--) {
result[4 * i + j] = char('0' + value % 10);
value /= 10;
}
}
return result;
}();
std::FILE* _stream;
char _buffer[buffer_size];
int _position;
int _precision;
std::chars_format _float_format;
char _range_separator;
std::string* _capture = nullptr;
template <class T>
std::string format_cell(const T& value) {
std::string result;
struct CaptureGuard {
std::string*& target;
std::string* previous;
~CaptureGuard() { target = previous; }
} guard{_capture, _capture};
_capture = &result;
write(value);
return result;
}
template <class Matrix>
void write_aligned_matrix(const Matrix& matrix) {
std::vector<std::vector<std::string>> rows;
std::vector<std::size_t> widths;
for (const auto& row : matrix) {
auto& cells = rows.emplace_back();
std::size_t column = 0;
for (const auto& value : row) {
cells.push_back(format_cell(value));
if (column == widths.size()) widths.push_back(0);
widths[column] = std::max(widths[column], cells.back().size());
++column;
}
}
bool first = true;
for (const auto& row : rows) {
if (!first) write_char('\n');
first = false;
for (std::size_t column = 0; column < row.size(); ++column) {
if (column != 0) write_char(_range_separator);
for (std::size_t padding = row[column].size();
padding < widths[column]; ++padding) {
write_char(' ');
}
write(row[column]);
}
}
}
public:
explicit FastOutput(std::FILE* stream = stdout)
: _stream(stream),
_position(0),
_precision(6),
_float_format(std::chars_format::general),
_range_separator(' ') {
if (_stream == stdout
&& internal::standard_output_instance == nullptr) {
internal::standard_output_instance = this;
}
}
FastOutput(const FastOutput&) = delete;
FastOutput& operator=(const FastOutput&) = delete;
~FastOutput() {
flush();
if (internal::standard_output_instance == this) {
internal::standard_output_instance = nullptr;
}
}
void flush() {
if (_position != 0) {
std::fwrite(_buffer, 1, _position, _stream);
_position = 0;
}
std::fflush(_stream);
}
void write_char(char c) {
if (_capture != nullptr) {
_capture->push_back(c);
return;
}
if (_position == buffer_size) flush();
_buffer[_position++] = c;
}
void write(const char* s) {
while (*s != '\0') write_char(*s++);
}
void write(const std::string& s) {
if (_capture != nullptr) {
_capture->append(s);
return;
}
std::size_t position = 0;
while (position < s.size()) {
if (_position == buffer_size) flush();
const std::size_t copied =
std::min<std::size_t>(buffer_size - _position, s.size() - position);
std::memcpy(_buffer + _position, s.data() + position, copied);
_position += int(copied);
position += copied;
}
}
void write(char c) {
write_char(c);
}
void write(bool value) {
write_char(value ? '1' : '0');
}
template <class T>
std::enable_if_t<std::is_floating_point_v<T>>
write(T value) {
char digits[128];
auto [end, error] = std::to_chars(
digits,
digits + sizeof(digits),
value,
_float_format,
_precision
);
if (error != std::errc()) std::abort();
for (const char* pointer = digits; pointer != end; pointer++) {
write_char(*pointer);
}
}
template <class T>
std::enable_if_t<
internal::is_integral_v<T>
&& !std::is_same_v<std::remove_cv_t<T>, bool>
&& !std::is_same_v<std::remove_cv_t<T>, char>
>
write(T value) {
using Raw = std::remove_cv_t<T>;
using Unsigned = internal::make_unsigned_t<Raw>;
Unsigned magnitude;
if constexpr (internal::is_signed_v<Raw>) {
if (value < 0) {
write_char('-');
magnitude = Unsigned(0) - Unsigned(value);
} else {
magnitude = Unsigned(value);
}
} else {
magnitude = value;
}
if (magnitude == 0) {
write_char('0');
return;
}
unsigned chunks[16];
int count = 0;
while (magnitude >= 10000) {
const Unsigned quotient = magnitude / 10000;
chunks[count++] = unsigned(magnitude - quotient * 10000);
magnitude = quotient;
}
if (_capture == nullptr && _position > buffer_size - 64) flush();
char captured[64];
char* const begin = _capture != nullptr ? captured : _buffer + _position;
char* destination = begin;
const unsigned leading = unsigned(magnitude);
const char* first = digit_quads.data() + 4 * leading;
int skip = leading < 10 ? 3 : leading < 100 ? 2 : leading < 1000 ? 1 : 0;
for (; skip < 4; skip++) *destination++ = first[skip];
while (count--) {
const char* digits = digit_quads.data() + 4 * chunks[count];
std::memcpy(destination, digits, 4);
destination += 4;
}
if (_capture != nullptr) {
_capture->append(begin, destination - begin);
} else {
_position += int(destination - begin);
}
}
template <class T>
std::enable_if_t<
internal::has_val_method_v<T>
&& !internal::is_integral_v<T>
&& !internal::is_range_v<T>
>
write(const T& value) {
write(value.val());
}
template <class First, class Second>
void write(const std::pair<First, Second>& value) {
write(value.first);
write_char(' ');
write(value.second);
}
template <class Range>
std::enable_if_t<
internal::is_range_v<Range>
&& !internal::is_string_like_v<Range>
>
write(const Range& range) {
using StoredValue = internal::range_stored_value_t<const Range>;
constexpr bool nested = internal::is_range_v<StoredValue>
&& !internal::is_string_like_v<StoredValue>;
bool first = true;
for (const auto& value : range) {
if (!first) write_char(nested ? '\n' : _range_separator);
first = false;
if constexpr (std::is_same_v<StoredValue, bool> && !nested) {
write(static_cast<bool>(value));
} else {
write(value);
}
}
}
template <class First, class... Rest>
void print(const First& first, const Rest&... rest) {
write(first);
((write_char(' '), write(rest)), ...);
}
void println() {
write_char('\n');
}
void set_precision(int precision) {
_precision = precision;
}
void set_fixed(int precision = 6) {
_float_format = std::chars_format::fixed;
_precision = precision;
}
void set_general(int precision = 6) {
_float_format = std::chars_format::general;
_precision = precision;
}
void set_range_separator(char separator) {
_range_separator = separator;
}
template <class Matrix>
void write_aligned(const Matrix& matrix) {
using Row = internal::range_stored_value_t<const Matrix>;
using Cell = internal::range_stored_value_t<const Row>;
static_assert(internal::is_range_v<Row> && !internal::is_string_like_v<Row>,
"write_aligned requires a two-dimensional range");
static_assert(!internal::is_range_v<Cell> || internal::is_string_like_v<Cell>,
"write_aligned requires scalar cells");
write_aligned_matrix(matrix);
}
template <class Matrix>
void println_aligned(const Matrix& matrix) {
write_aligned(matrix);
write_char('\n');
}
template <class... Args>
void println(const Args&... args) {
print(args...);
write_char('\n');
}
template <class T>
FastOutput& operator<<(const T& value) {
write(value);
return *this;
}
};
} // namespace utilities
} // namespace m1une
#line 10 "verify/ds/segtree/dynamic_lazy_segtree.test.cpp"
#line 1 "acted_monoid/range_add_range_sum.hpp"
namespace m1une {
namespace acted_monoid {
template <typename T>
struct RangeAddRangeSumNode {
T sum;
long long size;
};
template <typename T>
struct RangeAddRangeSum {
using value_type = RangeAddRangeSumNode<T>;
using operator_type = T;
static constexpr bool commutative = true;
static constexpr bool operator_commutative = true;
// Value Monoid (Sum)
static constexpr value_type id() {
return {T(0), 0};
}
static constexpr value_type op(const value_type& a, const value_type& b) {
return {a.sum + b.sum, a.size + b.size};
}
static constexpr value_type inv(const value_type& x) {
return {-x.sum, -x.size};
}
// Operator Monoid (Add)
static constexpr operator_type op_id() {
return 0;
}
static constexpr operator_type op_comp(const operator_type& f, const operator_type& g) {
return f + g;
}
// Mapping (sum + f * size)
static constexpr value_type mapping(const operator_type& f, const value_type& x) {
return {x.sum + f * x.size, x.size};
}
// Helper for initializing a leaf node
static constexpr value_type make(const T& val) {
return {val, 1};
}
};
} // namespace acted_monoid
} // namespace m1une
#line 1 "acted_monoid/range_affine_range_sum.hpp"
#line 5 "acted_monoid/range_affine_range_sum.hpp"
namespace m1une {
namespace acted_monoid {
template <typename T>
struct RangeAffineRangeSumNode {
T sum;
int size;
};
// Designed to accept Modint or similar types as T
template <typename T>
struct RangeAffineRangeSum {
using value_type = RangeAffineRangeSumNode<T>;
using operator_type = std::pair<T, T>; // {a, b} for ax + b
static constexpr bool commutative = true;
static constexpr bool operator_commutative = false;
// Value Monoid
static constexpr value_type id() {
return {T(0), 0};
}
static constexpr value_type op(const value_type& a, const value_type& b) {
return {a.sum + b.sum, a.size + b.size};
}
static constexpr int size(const value_type& value) {
return value.size;
}
// Operator Monoid (Affine Composition)
// f(x) = a1*x + b1, g(x) = a2*x + b2
// f(g(x)) = a1*(a2*x + b2) + b1 = (a1*a2)*x + (a1*b2 + b1)
static constexpr operator_type op_id() {
return {T(1), T(0)};
}
static constexpr operator_type op_comp(const operator_type& f, const operator_type& g) {
return {f.first * g.first, f.first * g.second + f.second};
}
// Mapping
// \sum (a*x_i + b) = a * \sum x_i + b * size
static constexpr value_type mapping(const operator_type& f, const value_type& x) {
return {f.first * x.sum + f.second * T(x.size), x.size};
}
// Helper for initializing a leaf node
static constexpr value_type make(const T& val) {
return {val, 1};
}
};
} // namespace acted_monoid
} // namespace m1une
#line 1 "acted_monoid/range_ap_add_range_sum.hpp"
#line 5 "acted_monoid/range_ap_add_range_sum.hpp"
namespace m1une {
namespace acted_monoid {
template <typename T>
struct RangeApAddRangeSumNode {
T sum;
long long size;
T ord_sum;
};
template <typename T>
struct RangeApAddRangeSum {
using value_type = RangeApAddRangeSumNode<T>;
using operator_type = std::pair<T, T>; // {a, b} for adding a * i + b
static constexpr bool commutative = false;
static constexpr bool operator_commutative = true;
// Value Monoid (Sum)
static constexpr value_type id() {
return {T(0), 0, T(0)};
}
static constexpr value_type op(const value_type& a, const value_type& b) {
return {a.sum + b.sum, a.size + b.size, a.ord_sum + b.ord_sum + T(a.size) * T(b.size)};
}
// Operator Monoid (Add)
static constexpr operator_type op_id() {
return {T(0), T(0)};
}
static constexpr operator_type op_comp(const operator_type& f, const operator_type& g) {
return {f.first + g.first, f.second + g.second};
}
static constexpr value_type mapping(const operator_type& f, const value_type& x) {
return mapping(f, x, 0);
}
static constexpr value_type mapping(const operator_type& f, const value_type& x, long long ord) {
return {x.sum + f.first * (x.ord_sum + T(ord) * T(x.size)) + f.second * T(x.size), x.size, x.ord_sum};
}
static constexpr operator_type op_shift(const operator_type& f, long long ord) {
return {f.first, f.second + f.first * T(ord)};
}
static constexpr operator_type op_reverse(const operator_type& f, long long size) {
return {-f.first, f.second + f.first * T(size - 1)};
}
static constexpr value_type make(const T& val) {
return {val, 1, T(0)};
}
};
} // namespace acted_monoid
} // namespace m1une
#line 1 "math/modint.hpp"
#line 6 "math/modint.hpp"
#include <iostream>
#line 9 "math/modint.hpp"
namespace m1une {
namespace math {
template <uint32_t Modulus>
struct ModInt {
static_assert(0 < Modulus, "Modulus must be positive");
private:
uint32_t _v;
public:
static constexpr uint32_t mod() {
return Modulus;
}
static constexpr ModInt raw(uint32_t v) noexcept {
ModInt x;
x._v = v;
return x;
}
constexpr ModInt() noexcept : _v(0) {}
template <class Integer, std::enable_if_t<std::is_integral_v<Integer>, int> = 0>
constexpr ModInt(Integer v) noexcept {
if constexpr (std::is_signed_v<Integer>) {
int64_t x = static_cast<int64_t>(v) % static_cast<int64_t>(Modulus);
if (x < 0) x += Modulus;
_v = static_cast<uint32_t>(x);
} else {
_v = static_cast<uint32_t>(static_cast<uint64_t>(v) % Modulus);
}
}
constexpr uint32_t val() const noexcept {
return _v;
}
constexpr ModInt& operator++() noexcept {
_v++;
if (_v == Modulus) _v = 0;
return *this;
}
constexpr ModInt& operator--() noexcept {
if (_v == 0) _v = Modulus;
_v--;
return *this;
}
constexpr ModInt operator++(int) noexcept {
ModInt res = *this;
++*this;
return res;
}
constexpr ModInt operator--(int) noexcept {
ModInt res = *this;
--*this;
return res;
}
constexpr ModInt& operator+=(const ModInt& rhs) noexcept {
_v += rhs._v;
if (_v >= Modulus) _v -= Modulus;
return *this;
}
constexpr ModInt& operator-=(const ModInt& rhs) noexcept {
_v -= rhs._v;
if (_v >= Modulus) _v += Modulus;
return *this;
}
constexpr ModInt& operator*=(const ModInt& rhs) noexcept {
uint64_t z = _v;
z *= rhs._v;
_v = static_cast<uint32_t>(z % Modulus);
return *this;
}
constexpr ModInt& operator/=(const ModInt& rhs) noexcept {
return *this *= rhs.inv();
}
constexpr ModInt operator+(const ModInt& rhs) const noexcept {
return ModInt(*this) += rhs;
}
constexpr ModInt operator-(const ModInt& rhs) const noexcept {
return ModInt(*this) -= rhs;
}
constexpr ModInt operator*(const ModInt& rhs) const noexcept {
return ModInt(*this) *= rhs;
}
constexpr ModInt operator/(const ModInt& rhs) const noexcept {
return ModInt(*this) /= rhs;
}
constexpr bool operator==(const ModInt& rhs) const noexcept {
return _v == rhs._v;
}
constexpr bool operator!=(const ModInt& rhs) const noexcept {
return _v != rhs._v;
}
constexpr ModInt pow(long long n) const noexcept {
ModInt res = raw(1 % Modulus);
ModInt x = n < 0 ? inv() : *this;
uint64_t exponent = n < 0 ? uint64_t(-(n + 1)) + 1 : uint64_t(n);
while (exponent > 0) {
if (exponent & 1) res *= x;
x *= x;
exponent >>= 1;
}
return res;
}
constexpr ModInt inv() const noexcept {
int64_t a = _v, b = Modulus, u = 1, v = 0;
while (b) {
int64_t t = a / b;
a -= t * b;
std::swap(a, b);
u -= t * v;
std::swap(u, v);
}
assert(a == 1);
u %= Modulus;
if (u < 0) u += Modulus;
return raw(static_cast<uint32_t>(u));
}
friend std::ostream& operator<<(std::ostream& os, const ModInt& rhs) {
return os << rhs._v;
}
friend std::istream& operator>>(std::istream& is, ModInt& rhs) {
long long v;
is >> v;
rhs = ModInt(v);
return is;
}
};
using modint998244353 = ModInt<998244353>;
using modint1000000007 = ModInt<1000000007>;
template <int Id = 0>
struct DynamicModInt {
private:
uint32_t _v;
inline static uint32_t _mod = 1;
public:
static uint32_t mod() noexcept {
return _mod;
}
static void set_mod(uint32_t modulus) noexcept {
assert(modulus > 0);
assert(modulus <= uint32_t(1) << 31);
_mod = modulus;
}
static DynamicModInt raw(uint32_t v) noexcept {
assert(v < _mod);
DynamicModInt x;
x._v = v;
return x;
}
DynamicModInt() noexcept : _v(0) {}
template <class Integer, std::enable_if_t<std::is_integral_v<Integer>, int> = 0>
DynamicModInt(Integer v) noexcept {
if constexpr (std::is_signed_v<Integer>) {
int64_t x = static_cast<int64_t>(v) % static_cast<int64_t>(_mod);
if (x < 0) x += _mod;
_v = static_cast<uint32_t>(x);
} else {
_v = static_cast<uint32_t>(static_cast<uint64_t>(v) % _mod);
}
}
uint32_t val() const noexcept {
return _v;
}
DynamicModInt& operator++() noexcept {
_v++;
if (_v == _mod) _v = 0;
return *this;
}
DynamicModInt& operator--() noexcept {
if (_v == 0) _v = _mod;
_v--;
return *this;
}
DynamicModInt operator++(int) noexcept {
DynamicModInt result = *this;
++*this;
return result;
}
DynamicModInt operator--(int) noexcept {
DynamicModInt result = *this;
--*this;
return result;
}
DynamicModInt& operator+=(const DynamicModInt& rhs) noexcept {
_v += rhs._v;
if (_v >= _mod) _v -= _mod;
return *this;
}
DynamicModInt& operator-=(const DynamicModInt& rhs) noexcept {
_v -= rhs._v;
if (_v >= _mod) _v += _mod;
return *this;
}
DynamicModInt& operator*=(const DynamicModInt& rhs) noexcept {
_v = static_cast<uint32_t>(uint64_t(_v) * rhs._v % _mod);
return *this;
}
DynamicModInt& operator/=(const DynamicModInt& rhs) noexcept {
return *this *= rhs.inv();
}
DynamicModInt operator+(const DynamicModInt& rhs) const noexcept {
return DynamicModInt(*this) += rhs;
}
DynamicModInt operator-(const DynamicModInt& rhs) const noexcept {
return DynamicModInt(*this) -= rhs;
}
DynamicModInt operator*(const DynamicModInt& rhs) const noexcept {
return DynamicModInt(*this) *= rhs;
}
DynamicModInt operator/(const DynamicModInt& rhs) const noexcept {
return DynamicModInt(*this) /= rhs;
}
bool operator==(const DynamicModInt& rhs) const noexcept {
return _v == rhs._v;
}
bool operator!=(const DynamicModInt& rhs) const noexcept {
return _v != rhs._v;
}
DynamicModInt pow(long long exponent) const noexcept {
DynamicModInt result = raw(1 % _mod);
DynamicModInt base = exponent < 0 ? inv() : *this;
uint64_t magnitude =
exponent < 0 ? uint64_t(-(exponent + 1)) + 1 : uint64_t(exponent);
while (magnitude > 0) {
if (magnitude & 1) result *= base;
base *= base;
magnitude >>= 1;
}
return result;
}
DynamicModInt inv() const noexcept {
int64_t a = _v, b = _mod, u = 1, v = 0;
while (b) {
int64_t quotient = a / b;
a -= quotient * b;
std::swap(a, b);
u -= quotient * v;
std::swap(u, v);
}
assert(a == 1);
u %= _mod;
if (u < 0) u += _mod;
return raw(static_cast<uint32_t>(u));
}
friend std::ostream& operator<<(std::ostream& os, const DynamicModInt& rhs) {
return os << rhs._v;
}
friend std::istream& operator>>(std::istream& is, DynamicModInt& rhs) {
long long value;
is >> value;
rhs = DynamicModInt(value);
return is;
}
};
} // namespace math
} // namespace m1une
#line 15 "verify/ds/segtree/dynamic_lazy_segtree.test.cpp"
namespace {
void test_range_add() {
using AM = m1une::acted_monoid::RangeAddRangeSum<long long>;
using Seg = m1une::ds::DynamicLazySegtree<AM>;
Seg seg(-1'000'000'000'000'000'000LL, 1'000'000'000'000'000'000LL, AM::make(0));
assert(seg.size() == 2'000'000'000'000'000'000ULL);
assert(seg.node_count() == 0);
assert(seg.all_prod().size == 2'000'000'000'000'000'000LL);
seg.reserve(1024);
seg.apply(-3, 5, 2);
assert(seg.prod(-10, 10).sum == 16);
assert(seg.get(-3).sum == 2);
assert(seg.get(5).sum == 0);
[[maybe_unused]] std::size_t nodes = seg.node_count();
seg.set(0, AM::make(10));
assert(seg.all_prod().sum == 24);
assert(seg.max_right(-10, [](const AM::value_type& x) { return x.sum <= 5; }) == -1);
assert(seg.min_left(10, [](const AM::value_type& x) { return x.sum <= 5; }) == 3);
assert(seg.node_count() >= nodes);
seg.clear();
assert(seg.node_count() == 0);
assert(seg.all_prod().sum == 0);
assert(seg.all_prod().size == 2'000'000'000'000'000'000LL);
}
void test_arithmetic_progression() {
using AM = m1une::acted_monoid::RangeApAddRangeSum<long long>;
m1une::ds::DynamicLazySegtree<AM, int> seg(-20, 21, AM::make(0));
AM::operator_type first;
first.first = 2;
first.second = 3;
seg.apply(-5, 6, first);
for (int p = -5; p < 6; p++) {
assert(seg.get(p).sum == 2LL * (p + 5) + 3);
}
AM::operator_type second;
second.first = -1;
second.second = 4;
seg.apply(-2, 4, second);
[[maybe_unused]] long long expected = 0;
for (int p = -20; p < 21; p++) {
long long value = 0;
if (-5 <= p && p < 6) value += 2LL * (p + 5) + 3;
if (-2 <= p && p < 4) value += -(p + 2) + 4;
expected += value;
}
assert(seg.all_prod().sum == expected);
}
void test_randomized() {
using AM = m1une::acted_monoid::RangeAddRangeSum<long long>;
constexpr int left = -31;
constexpr int right = 38;
m1une::ds::DynamicLazySegtree<AM, int> seg(left, right, AM::make(0));
std::vector<long long> a(right - left);
std::uint64_t state = 1;
auto random = [&state]() {
state ^= state << 7;
state ^= state >> 9;
return state;
};
auto value_at = [&a](int p) -> long long& {
return a[std::size_t(p - left)];
};
for (int step = 0; step < 3000; step++) {
int type = int(random() % 4);
int l = left + int(random() % (a.size() + 1));
int r = left + int(random() % (a.size() + 1));
if (r < l) std::swap(l, r);
if (type == 0) {
long long x = static_cast<long long>(random() % 11);
seg.apply(l, r, x);
for (int p = l; p < r; p++) value_at(p) += x;
} else if (type == 1) {
int p = left + int(random() % a.size());
long long x = static_cast<long long>(random() % 30);
seg.set(p, AM::make(x));
value_at(p) = x;
} else {
[[maybe_unused]] long long expected = 0;
for (int p = l; p < r; p++) expected += value_at(p);
assert(seg.prod(l, r).sum == expected);
}
long long limit = static_cast<long long>(random() % 150);
int start = left + int(random() % (a.size() + 1));
int max_right = start;
long long sum = 0;
while (max_right < right && sum + value_at(max_right) <= limit) {
sum += value_at(max_right);
max_right++;
}
assert(seg.max_right(start, [limit](const AM::value_type& x) {
return x.sum <= limit;
}) == max_right);
int finish = left + int(random() % (a.size() + 1));
int min_left = finish;
sum = 0;
while (left < min_left && value_at(min_left - 1) + sum <= limit) {
min_left--;
sum += value_at(min_left);
}
assert(seg.min_left(finish, [limit](const AM::value_type& x) {
return x.sum <= limit;
}) == min_left);
}
}
void test_affine_order() {
using mint = m1une::math::modint998244353;
using AM = m1une::acted_monoid::RangeAffineRangeSum<mint>;
constexpr int n = 37;
m1une::ds::DynamicLazySegtree<AM, int> seg(0, n, AM::make(1));
std::vector<mint> a(n, 1);
std::uint64_t state = 11;
auto random = [&state]() {
state ^= state << 7;
state ^= state >> 9;
return state;
};
for (int step = 0; step < 1200; step++) {
int l = int(random() % (n + 1));
int r = int(random() % (n + 1));
if (r < l) std::swap(l, r);
mint b = mint(int(random() % 7));
mint c = mint(int(random() % 7));
AM::operator_type f;
f.first = b;
f.second = c;
seg.apply(l, r, f);
for (int p = l; p < r; p++) a[p] = b * a[p] + c;
int ql = int(random() % (n + 1));
int qr = int(random() % (n + 1));
if (qr < ql) std::swap(ql, qr);
mint expected = 0;
for (int p = ql; p < qr; p++) expected += a[p];
assert(seg.prod(ql, qr).sum == expected);
}
}
} // namespace
int main() {
m1une::utilities::FastInput fast_input;
m1une::utilities::FastOutput fast_output;
test_range_add();
test_arithmetic_progression();
test_randomized();
test_affine_order();
using mint = m1une::math::modint998244353;
using AM = m1une::acted_monoid::RangeAffineRangeSum<mint>;
int n, q;
fast_input >> n >> q;
m1une::ds::DynamicLazySegtree<AM, int> seg(0, n, AM::make(0));
seg.reserve(std::size_t(4) * std::size_t(n + q));
for (int i = 0; i < n; i++) {
long long x;
fast_input >> x;
seg.set(i, AM::make(mint(x)));
}
for (int query = 0; query < q; query++) {
int type;
fast_input >> type;
if (type == 0) {
int l, r;
long long b, c;
fast_input >> l >> r >> b >> c;
AM::operator_type f;
f.first = mint(b);
f.second = mint(c);
seg.apply(l, r, f);
} else {
int l, r;
fast_input >> l >> r;
fast_output << seg.prod(l, r).sum << '\n';
}
}
}
verify/ds/segtree/dynamic_lazy_segtree.test.cpp