結果
| 問題 |
No.925 紲星 Extra
|
| コンテスト | |
| ユーザー |
 Pachicobue
|
| 提出日時 | 2019-11-09 08:56:00 |
| 言語 | C++17(gcc12) (gcc 12.3.0 + boost 1.87.0) |
| 結果 |
TLE
(最新)
AC
(最初)
|
| 実行時間 | - |
| コード長 | 56,630 bytes |
| コンパイル時間 | 20,650 ms |
| コンパイル使用メモリ | 331,580 KB |
| 最終ジャッジ日時 | 2025-01-08 03:43:40 |
|
ジャッジサーバーID （参考情報） |
judge1 / judge4 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 16 TLE * 3 |
ソースコード
#include <bits/stdc++.h>
#pragma GCC diagnostic ignored "-Wsign-compare"
#pragma GCC diagnostic ignored "-Wsign-conversion"
using i32 = int32_t;
using i64 = int64_t;
using u32 = uint32_t;
using u64 = uint64_t;
using uint = unsigned int;
using usize = std::size_t;
using ll = long long;
using ull = unsigned long long;
using ld = long double;
template<typename T> constexpr T popcount(const T u) { return u ? static_cast<T>(__builtin_popcountll(static_cast<u64>(u))) : static_cast<T>(0); }
template<typename T> constexpr T log2p1(const T u) { return u ? static_cast<T>(64 - __builtin_clzll(static_cast<u64>(u))) : static_cast<T>(0); }
template<typename T> constexpr T msbp1(const T u) { return log2p1(u); }
template<typename T> constexpr T lsbp1(const T u) { return __builtin_ffsll(u); }
template<typename T> constexpr T clog(const T u) { return u ? log2p1(u - 1) : static_cast<T>(u); }
template<typename T> constexpr bool ispow2(const T u) { return u and (static_cast<u64>(u) & static_cast<u64>(u - 1)) == 0; }
template<typename T> constexpr T ceil2(const T u) { return static_cast<T>(1) << clog(u); }
template<typename T> constexpr T floor2(const T u) { return u == 0 ? static_cast<T>(0) : static_cast<T>(1) << (log2p1(u) - 1); }
template<typename T> constexpr bool btest(const T mask, const usize ind) { return static_cast<bool>((static_cast<u64>(mask) >> ind) & static_cast<u64>(1)); }
template<typename T> void bset(T& mask, const usize ind) { mask |= (static_cast<T>(1) << ind); }
template<typename T> void breset(T& mask, const usize ind) { mask &= ~(static_cast<T>(1) << ind); }
template<typename T> void bflip(T& mask, const usize ind) { mask ^= (static_cast<T>(1) << ind); }
template<typename T> void bset(T& mask, const usize ind, const bool b) { (b ? bset(mask, ind) : breset(mask, ind)); }
template<typename T> constexpr T bcut(const T mask, const usize ind) { return ind == 0 ? static_cast<T>(0) : static_cast<T>((static_cast<u64>(mask) << (64 - ind)) >> (64 - ind)); }
template<typename T> bool chmin(T& a, const T& b) { return (a > b ? a = b, true : false); }
template<typename T> bool chmax(T& a, const T& b) { return (a < b ? a = b, true : false); }
constexpr unsigned int mod = 1000000007;
template<typename T> constexpr T inf_v = std::numeric_limits<T>::max() / 4;
template<typename Real> constexpr Real pi_v = Real{3.141592653589793238462643383279502884};
template<typename T>
T read()
{
T v;
return std::cin >> v, v;
}
template<typename T, typename... Args>
auto read(const usize size, Args... args)
{
std::vector<decltype(read<T>(args...))> ans(size);
for (usize i = 0; i < size; i++) { ans[i] = read<T>(args...); }
return ans;
}
template<typename... Types>
auto reads() { return std::tuple<std::decay_t<Types>...>{read<Types>()...}; }
# define SHOW(...) static_cast<void>(0)
template<typename T>
T make_v(const T v) { return v; }
template<typename... Args>
auto make_v(const std::size_t size, Args... args) { return std::vector<decltype(make_v(args...))>(size, make_v(args...)); }
class stopwatch
{
public:
stopwatch() : start{std::chrono::system_clock::now()}, rap_point{start} {}
template<typename Duration = std::chrono::milliseconds>
int64_t rap()
{
const auto now = std::chrono::system_clock::now();
const auto cnt = std::chrono::duration_cast<Duration>(now - rap_point).count();
return rap_point = now, cnt;
}
template<typename Duration = std::chrono::milliseconds>
int64_t total()
{
const auto now = std::chrono::system_clock::now();
const auto cnt = std::chrono::duration_cast<Duration>(now - start).count();
return cnt;
}
private:
std::chrono::system_clock::time_point start;
std::chrono::system_clock::time_point rap_point;
};
namespace bbst_node {
template<typename Key, typename Node, typename Comp>
struct key_node : Node
{
using ptr = key_node* const;
using const_ptr = const ptr;
using key_type = Key;
using comp_type = Comp;
key_node() : Node{}, key{Key{}} {}
template<typename... Args>
key_node(const Key& key, Args... args) : Node{args...}, key{key} { this->sz = 1; }
void pull_up(const_ptr l, const_ptr r) { Node::pull_up(l, r); }
void push_down(ptr l, ptr r) { Node::push_down(l, r); }
template<typename Value>
void set(const Value& val, const_ptr l, const_ptr r) { Node::set(val, l, r); }
template<typename Op>
void act(const Op& o) { Node::act(o); }
friend std::ostream& operator<<(std::ostream& os, const key_node& n) { return os << "key=" << n.key << ":" << static_cast<Node>(n); }
const key_type key;
};
struct node
{
using ptr = node* const;
using const_ptr = const ptr;
void pull_up(const_ptr l, const_ptr r) { sz = (l ? l->sz : 0UL) + 1UL + (r ? r->sz : 0UL); }
void push_down(ptr, ptr) {}
friend std::ostream& operator<<(std::ostream& os, const node& n) { return os << "size=" << n.sz; }
usize sz = 0;
};
template<typename Value>
struct value_node
{
using ptr = value_node* const;
using const_ptr = const ptr;
using value_type = Value;
value_node() = default;
value_node(const value_type& value) : value{value}, sz{1} {}
void pull_up(const_ptr l, const_ptr r) { sz = (l ? l->sz : 0UL) + 1UL + (r ? r->sz : 0UL); }
void push_down(ptr, ptr) {}
void set(const value_type& val, const_ptr, const_ptr) { value = val; }
friend std::ostream& operator<<(std::ostream& os, const value_node& n) { return os << "value=" << n.value; }
value_type value{};
usize sz = 0;
};
template<typename ValueMonoid>
struct merge_node
{
using ptr = merge_node* const;
using const_ptr = const ptr;
using value_monoid_type = ValueMonoid;
using value_type = typename value_monoid_type::value_type;
merge_node() = default;
merge_node(const value_type& value) : value{value}, merged{value}, sz{1} {}
void pull_up(const_ptr l, const_ptr r) { sz = (l ? l->sz : 0UL) + 1UL + (r ? r->sz : 0UL), merged = value_monoid_type::merge((l ? l->merged : value_monoid_type::id()), value_monoid_type::merge(value, (r ? r->merged : value_monoid_type::id()))); }
void push_down(ptr, ptr) {}
void set(const value_type& val, const_ptr l, const_ptr r) { value = val, pull_up(l, r); }
friend std::ostream& operator<<(std::ostream& os, const merge_node& n) { return os << "value=" << n.value << ",merged=" << n.merged; }
value_type value = value_monoid_type::id(), merged = value_monoid_type::id();
usize sz = 0;
};
template<typename MonoidAct>
struct lazy_node
{
using ptr = lazy_node* const;
using const_ptr = const ptr;
using monoid_act_type = MonoidAct;
using value_monoid_type = typename monoid_act_type::value_monoid_type;
using operator_monoid_type = typename monoid_act_type::operator_monoid_type;
using value_type = typename value_monoid_type::value_type;
using operator_type = typename operator_monoid_type::operator_type;
lazy_node() = default;
lazy_node(const value_type& value) : value{value}, merged{value}, sz{1} {}
void pull_up(const_ptr l, const_ptr r) { sz = (l ? l->sz : 0UL) + 1UL + (r ? r->sz : 0UL), merged = value_monoid_type::merge((l ? l->merged : value_monoid_type::id()), value_monoid_type::merge(value, (r ? r->merged : value_monoid_type::id()))); }
void push_down(ptr l, ptr r)
{
if (op == operator_monoid_type::id()) { return; }
if (l) { l->act(op); }
if (r) { r->act(op); }
op = operator_monoid_type::id();
}
void set(const value_type& val, const_ptr l, const_ptr r) { value = val, pull_up(l, r); }
void act(const operator_type& o) { value = monoid_act_type::apply(o, value, 1), merged = monoid_act_type::apply(o, merged, sz), op = operator_monoid_type::compose(op, o); }
friend std::ostream& operator<<(std::ostream& os, const lazy_node& n) { return os << "value=" << n.value << ",merged=" << n.merged << ",op=" << n.op; }
value_type value = value_monoid_type::id(), merged = value_monoid_type::id();
operator_type op = operator_monoid_type::id();
usize sz = 0;
};
} // namespace bbst_node
/**
* http://xoshiro.di.unimi.it/xoshiro128starstar.c
* http://xoshiro.di.unimi.it/xoshiro256starstar.c
* http://xoshiro.di.unimi.it/splitmix64.c
*/
class xoshiro
{
public:
using result_type = uint32_t;
static constexpr result_type min() { return std::numeric_limits<result_type>::min(); }
static constexpr result_type max() { return std::numeric_limits<result_type>::max(); }
xoshiro() : xoshiro(std::random_device{}()) {}
xoshiro(uint64_t seed)
{
uint64_t z = 0;
for (int i = 0; i < 4; i++) { z = (seed += 0x9e3779b97f4a7c15), z = (z ^ (z >> 33)) * 0x62A9D9ED799705F5, z = (z ^ (z >> 28)) * 0xCB24D0A5C88C35B3, s[i] = static_cast<result_type>(z >> 32); }
}
result_type operator()()
{
const result_type result = rotl(s[1] * 5, 7) * 9, t = s[1] << 9;
return s[2] ^= s[0], s[3] ^= s[1], s[1] ^= s[2], s[0] ^= s[3], s[2] ^= t, s[3] = rotl(s[3], 11), result;
}
void discard(const usize rep)
{
for (usize i = 0; i < rep; i++) { (*this)(); }
}
private:
result_type s[4];
static result_type rotl(const result_type x, const int k) { return (x << k) | (x >> (32 - k)); }
};
class xoshiro_64
{
public:
using result_type = uint64_t;
static constexpr result_type min() { return std::numeric_limits<result_type>::min(); }
static constexpr result_type max() { return std::numeric_limits<result_type>::max(); }
xoshiro_64() : xoshiro_64(std::random_device{}()) {}
xoshiro_64(uint64_t seed)
{
uint64_t z = 0;
for (int i = 0; i < 4; i++) { z = (seed += 0x9e3779b97f4a7c15), z = (z ^ (z >> 30)) * 0xbf58476d1ce4e5b9, z = (z ^ (z >> 27)) * 0x94d049bb133111eb, s[i] = static_cast<result_type>(z ^ (z >> 31)); }
}
result_type operator()()
{
const result_type result = rotl(s[1] * 5, 7) * 9, t = s[1] << 17;
return s[2] ^= s[0], s[3] ^= s[1], s[1] ^= s[2], s[0] ^= s[3], s[2] ^= t, s[3] = rotl(s[3], 45), result;
}
void discard(const usize rep)
{
for (usize i = 0; i < rep; i++) { (*this)(); }
}
private:
result_type s[4];
static result_type rotl(const result_type x, const int k) { return (x << k) | (x >> (64 - k)); }
};
template<typename Rng>
class rng_base
{
public:
using rng_type = Rng;
using result_type = typename rng_type::result_type;
static constexpr result_type min() { return rng_type::min(); }
static constexpr result_type max() { return rng_type::max(); }
rng_base() : rng_base(std::random_device{}()) {}
rng_base(const u64 seed) : rng(seed) {}
~rng_base() = default;
result_type operator()(const result_type max = std::numeric_limits<result_type>::max())
{
if (max == std::numeric_limits<result_type>::max()) { return static_cast<result_type>(rng()); }
if (ispow2(max + 1)) { return static_cast<result_type>(rng() & max); }
const result_type mask = static_cast<result_type>(ceil2(static_cast<u64>(max + 1))) - 1;
while (true) {
const result_type ans = static_cast<result_type>(rng() & mask);
if (ans <= max) { return ans; }
}
}
result_type operator()(const result_type min, const result_type max) { return min + (*this)(max - min); }
operator bool() { return *this(0, 1); }
template<typename Int> std::pair<Int, Int> pair(const Int min, const Int max, const bool sorted = false) { return sorted ? std::minmax(*this(min, max), *this(min, max)) : std::pair<Int, Int>{*this(min, max), *this(min, max)}; }
template<typename Int>
std::vector<Int> vec(const std::size_t size, const Int min, const Int max)
{
std::vector<Int> v(size);
for (std::size_t i = 0; i < size; i++) { v[i] = *this(min, max); }
return v;
}
std::vector<usize> perm(const usize n)
{
std::vector<usize> ans(n);
std::iota(ans.begin(), ans.end(), 0UL);
std::shuffle(ans.begin(), ans.end(), rng);
return ans;
}
private:
Rng rng;
};
using rng_mt = rng_base<std::mt19937>;
using rng_mt64 = rng_base<std::mt19937_64>;
using rng_xoshiro = rng_base<xoshiro>;
using rng_xoshiro64 = rng_base<xoshiro_64>;
rng_mt g_rng_mt;
rng_mt64 g_rng_mt64;
rng_xoshiro g_rng_xo;
rng_xoshiro64 g_rng_xo64;
template<typename NodeData>
class base_rbstree
{
private:
class node
{
using ptr = node*;
using const_ptr = const node* const;
using tree = ptr;
public:
node() : node_data{} {}
template<typename... Args>
node(Args... args) : node_data{args...} {}
usize size() const { return node_data.sz; }
const NodeData& data() const { return node_data; }
template<typename Operator>
void act(const Operator& op) { node_data.act(op); }
template<typename Value>
void set(const Value& value) { node_data.set(value, data_ptr_of(l), data_ptr_of(r)), pull_up(); }
friend std::ostream& operator<<(std::ostream& os, const node& n) { return os << "[" << n.node_data << "]"; }
bool has_left() const { return l; }
bool has_right() const { return r; }
const node& left() const { return deptr(l); }
const node& right() const { return deptr(r); }
static node& deptr(ptr x) { return x ? (*x) : empty_node; }
static ptr merge(tree tp1, tree tp2)
{
if (not tp1) { return tp2; }
if (not tp2) { return tp1; }
if (g_rng_xo(static_cast<uint>(size_of(tp1) + size_of(tp2) - 1)) < static_cast<uint>(size_of(tp1))) {
return tp1->push_down(), tp1->r = merge(tp1->r, tp2), tp1->pull_up(), tp1;
} else {
return tp2->push_down(), tp2->l = merge(tp1, tp2->l), tp2->pull_up(), tp2;
}
}
static std::pair<ptr, ptr> split_at(tree tp, const usize pos)
{
if (not tp) { return {nullptr, nullptr}; }
tp->push_down();
if (pos == 0) { return std::make_pair(nullptr, tp); }
if (pos == size_of(tp)) { return std::make_pair(tp, nullptr); }
if (pos <= size_of(tp->l)) {
auto ls = split_at(tp->l, pos);
return tp->l = ls.second, tp->pull_up(), std::make_pair(ls.first, tp);
} else {
auto rs = split_at(tp->r, pos - size_of(tp->l) - 1);
return tp->r = rs.first, tp->pull_up(), std::make_pair(tp, rs.second);
}
}
static std::tuple<ptr, ptr, ptr> split_range(tree tp, const usize pos_min, const usize pos_sup)
{
auto ts = split_at(tp, pos_min), trs = split_at(ts.second, pos_sup - pos_min);
return std::make_tuple(ts.first, trs.first, trs.second);
}
template<typename Key>
static std::pair<ptr, ptr> split_lower(tree tp, const Key& key)
{
if (not tp) { return {nullptr, nullptr}; }
const typename NodeData::comp_type& comp{};
if (comp(tp->data().key, key)) {
auto rs = split_lower(tp->r, key);
return tp->r = rs.first, tp->pull_up(), std::make_pair(tp, rs.second);
} else {
auto ls = split_lower(tp->l, key);
return tp->l = ls.second, tp->pull_up(), std::make_pair(ls.first, tp);
}
}
template<typename Key>
static std::pair<ptr, ptr> split_upper(tree tp, const Key& key)
{
if (not tp) { return {nullptr, nullptr}; }
const typename NodeData::comp_type& comp{};
if (comp(key, tp->data().key)) {
auto ls = split_upper(tp->l, key);
return tp->l = ls.second, tp->pull_up(), std::make_pair(ls.first, tp);
} else {
auto rs = split_upper(tp->r, key);
return tp->r = rs.first, tp->pull_up(), std::make_pair(tp, rs.second);
}
}
template<typename Key>
static std::tuple<ptr, ptr, ptr> split_key_range(tree tp, const Key& key_min, const Key& key_max)
{
auto ts = split_lower(tp, key_min), trs = split_upper(ts.second, key_max);
return std::make_tuple(ts.first, trs.first, trs.second);
}
private:
static NodeData* data_ptr_of(ptr x) { return x ? &(x->node_data) : nullptr; }
static usize size_of(const_ptr x) { return x ? x->size() : 0UL; }
void pull_up() { node_data.pull_up(data_ptr_of(l), data_ptr_of(r)); }
void push_down() { node_data.push_down(data_ptr_of(l), data_ptr_of(r)); }
static node empty_node; // inline変数を使いたいでござる
NodeData node_data;
ptr l = nullptr, r = nullptr;
};
using ptr = node*;
ptr root = nullptr;
public:
base_rbstree() = default;
base_rbstree(const ptr r) : root{r} {}
template<typename... Args>
base_rbstree(Args... args) : root{new node{args...}} {}
bool empty() const { return not root; }
usize size() const { return node::size(root); }
const node& top() const { return node::deptr(root); }
node at(const usize pos) { return fold_range(pos, pos + 1); }
node fold_range(const usize pos_min, const usize pos_sup)
{
auto ts = node::split_range(root, pos_min, pos_sup);
const node ans = node::deptr(std::get<1>(ts));
return root = node::merge(std::get<0>(ts), node::merge(std::get<1>(ts), std::get<2>(ts))), ans;
}
template<typename Key>
node fold_key_range(const Key& key_min, const Key& key_max)
{
auto ts = node::split_key_range(root, key_min, key_max);
const node ans = node::deptr(std::get<1>(ts));
return root = node::merge(std::get<0>(ts), node::merge(std::get<1>(ts), std::get<2>(ts))), ans;
}
template<typename Key>
node fold_lower(const Key& key)
{
auto ts = node::split_lower(root, key);
const node ans = node::deptr(ts.first);
return root = node::merge(ts.first, ts.second), ans;
}
template<typename Key>
node fold_upper(const Key& key)
{
auto ts = node::split_upper(root, key);
const node ans = node::deptr(ts.first);
return root = node::merge(ts.first, ts.second), ans;
}
template<typename Value>
base_rbstree& set_at(const usize pos, const Value& value)
{
auto ts = node::split_range(root, pos, pos + 1);
std::get<1>(ts)->set(value);
return root = node::merge(std::get<0>(ts), node::merge(std::get<1>(ts), std::get<2>(ts))), *this;
}
template<typename Key, typename Value>
base_rbstree& set(const Key& key, const Value& value)
{
auto ts = node::split_key_range(root, key, key);
std::get<1>(ts)->set(value);
return root = node::merge(std::get<0>(ts), node::merge(std::get<1>(ts), std::get<2>(ts))), *this;
}
template<typename Op>
base_rbstree& act_range(const usize pos_min, const usize pos_sup, const Op& op)
{
auto ts = node::split_range(root, pos_min, pos_sup);
std::get<1>(ts)->act(op);
return root = node::merge(std::get<0>(ts), node::merge(std::get<1>(ts), std::get<2>(ts))), *this;
}
template<typename Key, typename Op>
base_rbstree& act_key_range(const Key& key_min, const Key& key_max, const Op& op)
{
auto ts = node::split_key_range(root, key_min, key_max);
std::get<1>(ts)->act(op);
return root = node::merge(std::get<0>(ts), node::merge(std::get<1>(ts), std::get<2>(ts))), *this;
}
base_rbstree& merge(base_rbstree&& t) { return root = node::merge(root, t.root), *this; }
base_rbstree split_at(const usize pos)
{
auto ts = node::split_at(root, pos);
return root = ts.first, base_rbstree(ts.second);
}
std::pair<base_rbstree, base_rbstree> split_range(const usize pos_min, const usize pos_sup)
{
auto ts = node::split_range(root, pos_min, pos_sup);
return root = std::get<0>(ts), std::make_pair(base_rbstree(std::get<1>(ts)), base_rbstree(std::get<2>(ts)));
}
base_rbstree& erase_at(const usize pos)
{
auto ts = node::split_at(root, pos), trs = node::split_at(ts.second, 1);
return root = node::merge(ts.first, trs.second), *this;
}
base_rbstree& insert_at(const usize pos, base_rbstree&& t)
{
auto ts = node::split_at(root, pos);
return root = node::merge(node::merge(ts.first, t.root), ts.second), *this;
}
template<typename Key>
base_rbstree split_lower(const Key& key)
{
auto ts = node::split_lower(root, key);
return root = ts.first, base_rbstree(ts.second);
}
template<typename Key>
base_rbstree split_upper(const Key& key)
{
auto ts = node::split_upper(root, key);
return root = ts.first, base_rbstree(ts.second);
}
template<typename Key>
std::pair<base_rbstree, base_rbstree> split_key_range(const Key& key_min, const Key& key_max)
{
auto ts = node::split_key_range(root, key_min, key_max);
return root = std::get<0>(ts), std::make_pair(base_rbstree(std::get<1>(ts)), base_rbstree(std::get<2>(ts)));
}
base_rbstree& insert(const node& n)
{
auto ts = node::split_lower(root, n.data().key);
return root = node::merge(node::merge(ts.first, new node{n}), ts.second), *this;
}
std::vector<node> data()
{
if (empty()) { return std::vector<node>{}; }
auto dfs = [&](auto&& self, const node& n) -> std::vector<node> {
std::vector<node> ans;
if (n.has_left()) {
for (auto&& e : self(self, n.left())) { ans.emplace_back(e); }
}
ans.push_back(n);
if (n.has_right()) {
for (auto&& e : self(self, n.right())) { ans.emplace_back(e); }
}
return ans;
};
return dfs(dfs, *root);
}
};
template<typename NodeData>
typename base_rbstree<NodeData>::node base_rbstree<NodeData>::node::empty_node = node{};
template<typename Value>
using rbstree = base_rbstree<bbst_node::value_node<Value>>;
template<typename Key, typename Comp = std::less<Key>>
using mset_rbstree = base_rbstree<bbst_node::key_node<Key, bbst_node::node, Comp>>;
template<typename Key, typename Value, typename Comp = std::less<Key>>
using mmap_rbstree = base_rbstree<bbst_node::key_node<Key, bbst_node::value_node<Value>, Comp>>;
template<typename ValueMonoid>
using merge_rbstree = base_rbstree<bbst_node::merge_node<ValueMonoid>>;
template<typename MonoidAct>
using lazy_rbstree = base_rbstree<bbst_node::lazy_node<MonoidAct>>;
class segments
{
private:
using P = std::pair<usize, usize>;
const usize ceil;
std::vector<P> rs;
const usize num; // 区間0は存在しないので、実際は区間1,2,...,num-1
public:
segments(const usize sz) : ceil{ceil2(sz)}, rs(ceil << 1, P{0, 0}), num{ceil << 1}
{
for (usize sz = 1; sz <= ceil; sz <<= 1) {
const usize len = ceil / sz;
for (usize j = sz; j < (sz << 1); j++) { rs[j] = {len * (j - sz), len * (j - sz + 1)}; }
}
}
std::vector<usize> under(usize l, usize r) const
{
assert(l < r), assert(r <= ceil);
std::vector<usize> lind, rind;
for (l += ceil, r += ceil; l < r; l >>= 1, r >>= 1) {
if (l & 1) { lind.push_back(l++); }
if (r & 1) { rind.push_back(--r); }
}
for (; not rind.empty(); rind.pop_back()) { lind.push_back(rind.back()); }
return lind;
}
std::vector<usize> over(const usize a) const
{
assert(a < ceil);
std::vector<usize> ans;
for (usize i = a + ceil; i >= 1; i >>= 1) { ans.push_back(i); }
std::reverse(ans.begin(), ans.end());
return ans;
}
usize max_index() const { return num; }
const P& operator[](const usize i) const
{
assert(i >= 1), assert(i < 2 * ceil);
return rs[i];
}
};
template<typename Element>
struct plus
{
using element_type = Element;
using operator_type = element_type;
plus() = delete;
static operator_type compose(const operator_type& a, const operator_type& b) { return a + b; }
static constexpr operator_type id() { return operator_type{}; }
};
template<typename Element>
struct sum
{
using element_type = Element;
using value_type = element_type;
sum() = delete;
static value_type merge(const value_type& a, const value_type& b) { return a + b; }
static constexpr value_type id() { return value_type{}; }
};
template<typename ValueElement, typename OperatorElement>
struct sum_plus
{
using value_element_type = ValueElement;
using operator_element_type = OperatorElement;
using value_monoid_type = sum<value_element_type>;
using operator_monoid_type = plus<operator_element_type>;
using value_type = typename value_monoid_type::value_type;
using operator_type = typename operator_monoid_type::operator_type;
sum_plus() = delete;
template<typename Ind>
static value_type apply(const operator_type& f, const value_type& x, const Ind l) { return x + static_cast<value_type>(l) * static_cast<value_type>(f); }
};
enum {
NOTFOUND = 0xFFFFFFFFFFFFFFFFLLU
};
uint64_t NODE_NO = 0;
class Node
{
public:
uint64_t no; // node番号
// internal nodeのときに使用
uint64_t num; // 左の子の部分木のもつbitの数
uint64_t ones; // 左の子の部分木のもつ1の数
Node* left;
Node* right;
int64_t balance; // 右の子の高さ - 左の子の高さ．+なら右の子の方が高い，-なら左の子の方が高い
// leafのときに使用
uint64_t bits; // bit
uint64_t bits_size; // bitのサイズ(debug用)
bool is_leaf;
Node(uint64_t bits, uint64_t bits_size, bool is_leaf) : no(NODE_NO++), num(0), ones(0), bits(bits), bits_size(bits_size), is_leaf(is_leaf), left(nullptr), right(nullptr), balance(0) {}
};
class DynamicBitVector
{
public:
Node* root;
uint64_t size; // 全体のbitの数
uint64_t num_one; // 全体の1の数
const uint64_t bits_size_limit = 32; // 各ノードが管理するbitの長さ制限．2 * bits_size_limit以上になったらノードを分割し， 1/2*bits_size_limit以下になったらノードを結合する
DynamicBitVector() : root(nullptr), size(0), num_one(0) {}
DynamicBitVector(std::vector<uint64_t>& v) : root(nullptr), size(0), num_one(0)
{
if (v.size() == 0) {
return;
}
std::deque<std::pair<Node*, uint64_t>> leaves;
for (int i = 0; i < v.size(); i += this->bits_size_limit) {
uint64_t bits = 0;
const uint64_t bits_size = std::min(this->bits_size_limit, (uint64_t)v.size() - i);
for (int j = 0; j < bits_size; ++j) {
assert(v[i + j] == 0 or v[i + j] == 1);
if (v[i + j] == 1) {
bits |= (uint64_t)1 << j;
}
}
leaves.emplace_back(std::make_pair(new Node(bits, bits_size, true), bits_size));
}
std::deque<std::tuple<Node*, uint64_t, uint64_t, uint64_t>> nodes; // (node, 全体のbit数, 全体の1の数, 高さ)
while (not leaves.empty()) {
const auto node = leaves.front().first;
const auto bits_size = leaves.front().second;
leaves.pop_front();
nodes.emplace_back(std::make_tuple(node, bits_size, popCount(node->bits), 0));
}
while (nodes.size() > 1) {
std::deque<std::tuple<Node*, uint64_t, uint64_t, uint64_t>> next_nodes;
while (not nodes.empty()) {
// あまりがでたときは，最後に作った中間ノードと結合させるためにnodesに戻す
if (nodes.size() == 1) {
nodes.push_front(next_nodes.back());
next_nodes.pop_back();
}
Node* left_node;
uint64_t left_num, left_ones, left_height;
std::tie(left_node, left_num, left_ones, left_height) = nodes.front();
nodes.pop_front();
Node* right_node;
uint64_t right_num, right_ones, right_height;
std::tie(right_node, right_num, right_ones, right_height) = nodes.front();
nodes.pop_front();
const auto internal_node = new Node(0, 0, false);
internal_node->num = left_num;
internal_node->ones = left_ones;
internal_node->left = left_node;
internal_node->right = right_node;
internal_node->balance = right_height - left_height;
next_nodes.emplace_back(std::make_tuple(internal_node, left_num + right_num, left_ones + right_ones, std::max(left_height, right_height) + 1));
}
nodes = next_nodes;
}
uint64_t height;
std::tie(this->root, this->size, this->num_one, height) = nodes.front();
nodes.pop_front();
assert(this->size == v.size());
}
// B[pos]
uint64_t access(uint64_t pos)
{
assert(pos < this->size);
return access(this->root, pos);
}
// B[0, pos)にある指定されたbitの数
uint64_t rank(uint64_t bit, uint64_t pos)
{
assert(bit == 0 or bit == 1);
assert(pos <= this->size);
if (bit) {
return rank1(this->root, pos, 0);
} else {
return pos - rank1(this->root, pos, 0);
}
}
// rank番目の指定されたbitの位置 + 1(rankは1-origin)
uint64_t select(uint64_t bit, uint64_t rank)
{
assert(bit == 0 or bit == 1);
assert(rank > 0);
if (bit == 0 and rank > this->size - this->num_one) { return NOTFOUND; }
if (bit == 1 and rank > this->num_one) { return NOTFOUND; }
if (bit) {
return select1(this->root, 0, rank);
} else {
return select0(this->root, 0, rank);
}
}
// posにbitを挿入する
void insert(uint64_t pos, uint64_t bit)
{
assert(bit == 0 or bit == 1);
assert(pos <= this->size); // 現在もってるbitsの末尾には挿入できる
if (root == nullptr) {
root = new Node(bit, 1, true);
} else {
insert(this->root, nullptr, bit, pos, this->size);
}
this->size++;
this->num_one += (bit == 1);
}
// posを削除する
void erase(uint64_t pos)
{
assert(pos < this->size);
uint64_t bit = this->remove(this->root, nullptr, pos, this->size, 0, true).first;
this->size--;
this->num_one -= (bit == 1);
}
private:
uint64_t access(const Node* node, uint64_t pos)
{
if (node->is_leaf) {
assert(pos <= 2 * this->bits_size_limit);
return (node->bits >> pos) & (uint64_t)1;
}
if (pos < node->num) {
return this->access(node->left, pos);
} else {
return this->access(node->right, pos - node->num);
}
}
uint64_t rank1(const Node* node, uint64_t pos, uint64_t ones)
{
if (node->is_leaf) {
assert(node->bits_size >= pos);
const uint64_t mask = ((uint64_t)1 << pos) - 1;
return ones + popCount(node->bits & mask);
}
if (pos < node->num) {
return this->rank1(node->left, pos, ones);
} else {
return this->rank1(node->right, pos - node->num, ones + node->ones);
}
}
uint64_t select1(const Node* node, uint64_t pos, uint64_t rank)
{
if (node->is_leaf) {
return pos + this->selectInBlock(node->bits, rank) + 1;
}
if (rank <= node->ones) {
return this->select1(node->left, pos, rank);
} else {
return this->select1(node->right, pos + node->num, rank - node->ones);
}
}
uint64_t select0(const Node* node, uint64_t pos, uint64_t rank)
{
if (node->is_leaf) {
return pos + this->selectInBlock(~node->bits, rank) + 1;
}
if (rank <= (node->num - node->ones)) {
return this->select0(node->left, pos, rank);
} else {
return this->select0(node->right, pos + node->num, rank - (node->num - node->ones));
}
}
// bits(64bit)のrank番目(0-index)の1の数
uint64_t selectInBlock(uint64_t bits, uint64_t rank)
{
const uint64_t x1 = bits - ((bits & 0xAAAAAAAAAAAAAAAALLU) >> (uint64_t)1);
const uint64_t x2 = (x1 & 0x3333333333333333LLU) + ((x1 >> (uint64_t)2) & 0x3333333333333333LLU);
const uint64_t x3 = (x2 + (x2 >> (uint64_t)4)) & 0x0F0F0F0F0F0F0F0FLLU;
uint64_t pos = 0;
for (;; pos += 8) {
const uint64_t rank_next = (x3 >> pos) & 0xFFLLU;
if (rank <= rank_next) break;
rank -= rank_next;
}
const uint64_t v2 = (x2 >> pos) & 0xFLLU;
if (rank > v2) {
rank -= v2;
pos += 4;
}
const uint64_t v1 = (x1 >> pos) & 0x3LLU;
if (rank > v1) {
rank -= v1;
pos += 2;
}
const uint64_t v0 = (bits >> pos) & 0x1LLU;
if (v0 < rank) {
pos += 1;
}
return pos;
}
// nodeから辿れる葉のpos番目にbitをいれる(葉のbitの長さはlen)
// 高さの変化を返す
int64_t insert(Node* node, Node* parent, uint64_t bit, uint64_t pos, uint64_t len)
{
assert(bit == 0 or bit == 1);
if (node->is_leaf) {
assert(pos <= 2 * this->bits_size_limit);
// posより左をとりだす
const uint64_t up_mask = (((uint64_t)1 << (len - pos)) - 1) << pos;
const uint64_t up = (node->bits & up_mask);
// posより右をとりだす
const uint64_t down_mask = ((uint64_t)1 << pos) - 1;
const uint64_t down = node->bits & down_mask;
node->bits = (up << (uint64_t)1) | (bit << pos) | down;
node->bits_size++;
assert(node->bits_size == len + 1);
// bitsのサイズが大きくなったので分割する
if (len + 1 >= 2 * bits_size_limit) {
this->splitNode(node, len + 1); // 引数のlenはinsert後の長さなので+1する
return 1;
}
return 0;
}
if (pos < node->num) {
const int64_t diff = this->insert(node->left, node, bit, pos, node->num);
node->num += 1;
node->ones += (bit == 1);
return achieveBalance(parent, node, diff, 0);
} else {
const int64_t diff = this->insert(node->right, node, bit, pos - node->num, len - node->num);
return achieveBalance(parent, node, 0, diff);
}
}
// nodeのpos番目のbitを削除する
// 消したbitと高さの変化のpairを返す
std::pair<uint64_t, int64_t> remove(Node* node, Node* parent, uint64_t pos, uint64_t len, uint64_t ones, bool allow_under_flow)
{
if (node->is_leaf) {
// 消すとunder flowになるので消さない
if (node != this->root and len <= bits_size_limit / 2 and not allow_under_flow) {
return std::make_pair(NOTFOUND, 0);
}
assert(pos <= 2 * this->bits_size_limit);
assert(pos < len);
const uint64_t bit = (node->bits >> pos) & (uint64_t)1;
// posより左をとりだす(posを含まないようにする)
const uint64_t up_mask = (((uint64_t)1 << (len - pos - 1)) - 1) << (pos + 1);
const uint64_t up = (node->bits & up_mask);
// posより右をとりだす
const uint64_t down_mask = ((uint64_t)1 << pos) - 1;
const uint64_t down = node->bits & down_mask;
node->bits = (up >> (uint64_t)1) | down;
node->bits_size--;
assert(node->bits_size == len - 1);
return std::make_pair(bit, 0);
}
if (pos < node->num) {
const auto bit_diff = this->remove(node->left, node, pos, node->num, node->ones, allow_under_flow);
if (bit_diff.first == NOTFOUND) {
return bit_diff;
}
node->ones -= (bit_diff.first == 1);
// 左の子の葉のbitを1つ消したのでunder flowが発生している
if (node->num == bits_size_limit / 2) {
const auto b_d = remove(node->right, node, 0, len - bits_size_limit / 2, 0, false); // 右の葉の先頭bitを削る
// 右の葉もunder flowになって消せない場合は2つの葉を統合する
if (b_d.first == NOTFOUND) {
assert(node->left->is_leaf);
assert(node->left->bits_size == bits_size_limit / 2 - 1);
// 右の子から辿れる一番左の葉の先頭にleftのbitsを追加する
mergeNodes(node->right, 0, len - bits_size_limit / 2, node->left->bits, bits_size_limit / 2 - 1, node->ones, true);
this->replace(parent, node, node->right); // parentの子のnodeをnode->rightに置き換える
return std::make_pair(bit_diff.first, -1);
}
// 右の葉からとった先頭bitを左の葉の末尾にいれる
assert(node->left->bits_size == bits_size_limit / 2 - 1);
insert(node->left, node, b_d.first, bits_size_limit / 2 - 1, bits_size_limit / 2 - 1);
node->ones += (b_d.first == 1);
} else {
node->num -= 1;
}
const int64_t diff = achieveBalance(parent, node, bit_diff.second, 0);
return std::make_pair(bit_diff.first, diff);
} else {
const auto bit_diff = this->remove(node->right, node, pos - node->num, len - node->num, ones - node->ones, allow_under_flow);
if (bit_diff.first == NOTFOUND) {
return bit_diff;
}
ones -= (bit_diff.first == 1);
// 右の子の葉のbitを1つ消したのでunder flowが発生する
if ((len - node->num) == bits_size_limit / 2) {
const auto b_d = remove(node->left, node, node->num - 1, node->num, 0, false); // 左の葉の末尾をbitを削る
// 左の葉もunder flowになって消せない場合は2つの葉を統合する
if (b_d.first == NOTFOUND) {
assert(node->right->is_leaf);
assert(node->right->bits_size == bits_size_limit / 2 - 1);
// 左の子から辿れる一番右の葉の末尾にleftのbitsを追加する
mergeNodes(node->left, node->num, node->num, node->right->bits, bits_size_limit / 2 - 1, ones - node->ones, false);
this->replace(parent, node, node->left); // parentの子のnodeをnode->leftに置き換える
return std::make_pair(bit_diff.first, -1);
}
// 左の葉からとった最後尾bitを右の葉の先頭にいれる
insert(node->right, node, b_d.first, 0, bits_size_limit / 2 - 1);
node->num -= 1;
node->ones -= (b_d.first == 1);
}
const int64_t diff = achieveBalance(parent, node, 0, bit_diff.second);
return std::make_pair(bit_diff.first, diff);
}
}
// nodeを2つの葉に分割する
void splitNode(Node* node, uint64_t len)
{
assert(node->is_leaf);
assert(node->bits_size == len);
// 左の葉
const uint64_t left_size = len / 2;
const uint64_t left_bits = node->bits & (((uint64_t)1 << left_size) - 1);
node->left = new Node(left_bits, left_size, true);
// 右の葉
const uint64_t right_size = len - left_size;
const uint64_t right_bits = node->bits >> left_size;
node->right = new Node(right_bits, right_size, true);
// nodeを内部ノードにする
node->is_leaf = false;
node->num = left_size;
node->ones = this->popCount(left_bits);
node->bits = 0;
node->bits_size = 0;
}
// nodeから辿れる葉のpos番目にbitsを格納する
void mergeNodes(Node* node, uint64_t pos, uint64_t len, uint64_t bits, uint64_t s, uint64_t ones, bool left)
{
if (node->is_leaf) {
if (left) {
node->bits = (node->bits << s) | bits;
} else {
assert(len == node->bits_size);
node->bits = node->bits | (bits << len);
}
node->bits_size += s;
return;
}
if (pos < node->num) {
node->num += s;
node->ones += ones;
mergeNodes(node->left, pos, node->num, bits, s, ones, left);
} else {
mergeNodes(node->right, pos, len - node->num, bits, s, ones, left);
}
}
// nodeの左の高さがleftHeightDiffだけ変わり，右の高さがrightHeightDiffだけ変わったときにnodeを中心に回転させる
// 高さの変化を返す
int64_t achieveBalance(Node* parent, Node* node, int64_t leftHeightDiff, int64_t rightHeightDiff)
{
assert(-1 <= node->balance and node->balance <= 1);
assert(-1 <= leftHeightDiff and leftHeightDiff <= 1);
assert(-1 <= rightHeightDiff and rightHeightDiff <= 1);
if (leftHeightDiff == 0 and rightHeightDiff == 0) {
return 0;
}
int64_t heightDiff = 0;
// 左が高いときに，左が高くなる or 右が高いときに右が高くなる
if ((node->balance <= 0 and leftHeightDiff > 0) or (node->balance >= 0 and rightHeightDiff > 0)) {
++heightDiff;
}
// 左が高いときに左が低くなる or 右が高いときに右が低くなる
if ((node->balance < 0 and leftHeightDiff < 0) or (node->balance > 0 and rightHeightDiff < 0)) {
--heightDiff;
}
node->balance += -leftHeightDiff + rightHeightDiff;
assert(-2 <= node->balance and node->balance <= 2);
// 左が2高い
if (node->balance == -2) {
assert(-1 <= node->left->balance and node->left->balance <= 1);
if (node->left->balance != 0) {
heightDiff--;
}
if (node->left->balance == 1) {
replace(node, node->left, rotateLeft(node->left));
}
replace(parent, node, rotateRight(node));
}
// 右が2高い
else if (node->balance == 2) {
assert(-1 <= node->right->balance and node->right->balance <= 1);
if (node->right->balance != 0) {
heightDiff--;
}
if (node->right->balance == -1) {
replace(node, node->right, rotateRight(node->right));
}
replace(parent, node, rotateLeft(node));
}
return heightDiff;
}
// node Bを中心に左回転する．新しい親を返す
Node* rotateLeft(Node* B)
{
Node* D = B->right;
const int64_t heightC = 0;
const int64_t heightE = heightC + D->balance;
const int64_t heightA = std::max(heightC, heightE) + 1 - B->balance;
B->right = D->left;
D->left = B;
B->balance = heightC - heightA;
D->num += B->num;
D->ones += B->ones;
D->balance = heightE - (std::max(heightA, heightC) + 1);
assert(-2 <= B->balance and B->balance <= 2);
assert(-2 <= D->balance and D->balance <= 2);
return D;
}
// node Dを中心に右回転する．新しい親を返す
Node* rotateRight(Node* D)
{
Node* B = D->left;
const int64_t heightC = 0;
const int64_t heightA = heightC - B->balance;
const int64_t heightE = std::max(heightA, heightC) + 1 + D->balance;
D->left = B->right;
B->right = D;
D->num -= B->num;
D->ones -= B->ones;
D->balance = heightE - heightC;
B->balance = std::max(heightC, heightE) + 1 - heightA;
assert(-2 <= B->balance and B->balance <= 2);
assert(-2 <= D->balance and D->balance <= 2);
return B;
}
// parentの子のoldNodeをnewNodeに置き換える
void replace(Node* parent, Node* oldNode, Node* newNode)
{
if (parent == nullptr) {
this->root = newNode;
return;
}
if (parent->left == oldNode) {
parent->left = newNode;
} else if (parent->right == oldNode) {
parent->right = newNode;
} else {
throw "old node is not child";
}
}
uint64_t popCount(uint64_t x)
{
return popcount(x);
}
};
class DynamicWaveletMatrix
{
public:
std::vector<DynamicBitVector> bit_arrays;
std::vector<uint64_t> begin_one; // 各bitの1の開始位置
uint64_t size; // 与えられた配列のサイズ
uint64_t maximum_element; // 最大の文字
uint64_t bit_size; // 文字を表すのに必要なbit数
public:
// max_element: 入ってくる中で一番大きい数値
DynamicWaveletMatrix(uint64_t maximum_element) : size(0), maximum_element(maximum_element + 1)
{
this->bit_size = this->get_num_of_bit(maximum_element);
if (bit_size == 0) {
bit_size = 1;
}
this->begin_one.resize(bit_size);
for (uint64_t i = 0; i < bit_size; ++i) {
DynamicBitVector sv;
bit_arrays.push_back(sv);
}
}
DynamicWaveletMatrix(uint64_t num_of_alphabet, const std::vector<uint64_t>& array) : size(0), maximum_element(num_of_alphabet + 1)
{
this->bit_size = this->get_num_of_bit(num_of_alphabet);
if (bit_size == 0) {
bit_size = 1;
}
this->begin_one.resize(bit_size);
if (array.size() == 0) {
for (uint64_t i = 0; i < bit_size; ++i) {
DynamicBitVector sv;
bit_arrays.push_back(sv);
}
return;
}
size = array.size();
std::vector<uint64_t> v(array), b(array.size(), 0);
for (uint64_t i = 0; i < bit_size; ++i) {
std::vector<uint64_t> temp;
// 0をtempにいれてく
for (uint64_t j = 0; j < v.size(); ++j) {
uint64_t c = v.at(j);
uint64_t bit = (c >> (bit_size - i - 1)) & 1; // 上からi番目のbit
if (bit == 0) {
temp.push_back(c);
b[j] = 0;
}
}
this->begin_one.at(i) = temp.size();
// 1をtempにいれてく
for (uint64_t j = 0; j < v.size(); ++j) {
uint64_t c = v.at(j);
uint64_t bit = (c >> (bit_size - i - 1)) & 1; // 上からi番目のbit
if (bit == 1) {
temp.push_back(c);
b[j] = 1;
}
}
DynamicBitVector dbv(b);
bit_arrays.emplace_back(dbv);
v = temp;
}
}
// v[pos]
uint64_t access(uint64_t pos)
{
if (pos >= this->size) { return NOTFOUND; }
uint64_t c = 0;
for (uint64_t i = 0; i < bit_arrays.size(); ++i) {
uint64_t bit = bit_arrays.at(i).access(pos); // もとの数値がのi番目のbit
c = (c <<= 1) | bit;
pos = bit_arrays.at(i).rank(bit, pos);
if (bit) {
pos += this->begin_one.at(i);
}
}
return c;
}
// i番目のcの位置 + 1を返す。rankは1-origin
uint64_t select(uint64_t c, uint64_t rank)
{
assert(rank > 0);
if (c >= maximum_element) {
return NOTFOUND;
}
uint64_t left = 0;
for (uint64_t i = 0; i < bit_size; ++i) {
const uint64_t bit = (c >> (bit_size - i - 1)) & 1; // 上からi番目のbit
left = bit_arrays.at(i).rank(bit, left); // cのi番目のbitと同じ数値の数
if (bit) {
left += this->begin_one.at(i);
}
}
uint64_t index = left + rank;
for (uint64_t i = 0; i < bit_arrays.size(); ++i) {
uint64_t bit = ((c >> i) & 1); // 下からi番目のbit
if (bit == 1) {
index -= this->begin_one.at(bit_size - i - 1);
}
index = this->bit_arrays.at(bit_size - i - 1).select(bit, index);
}
return index;
}
// posにcを挿入する
void insert(uint64_t pos, uint64_t c)
{
assert(pos <= this->size);
for (uint64_t i = 0; i < bit_arrays.size(); ++i) {
const uint64_t bit = (c >> (bit_size - i - 1)) & 1; // 上からi番目のbit
bit_arrays.at(i).insert(pos, bit);
pos = bit_arrays.at(i).rank(bit, pos);
if (bit) {
pos += this->begin_one.at(i);
} else {
this->begin_one.at(i)++;
}
}
this->size++;
}
// posを削除する
void erase(uint64_t pos)
{
assert(pos < this->size);
if (pos >= this->size) {
throw "Segmentation fault";
}
for (uint64_t i = 0; i < bit_arrays.size(); ++i) {
uint64_t bit = bit_arrays.at(i).access(pos); // もとの数値のi番目のbit
auto next_pos = bit_arrays.at(i).rank(bit, pos);
bit_arrays.at(i).erase(pos);
if (bit) {
next_pos += this->begin_one.at(i);
} else {
this->begin_one.at(i)--;
}
pos = next_pos;
}
this->size--;
}
// posにcをセットする
void update(uint64_t pos, uint64_t c)
{
assert(pos < this->size);
this->erase(pos);
this->insert(pos, c);
}
// v[begin_pos, end_pos)で最小値のindexを返す
uint64_t minRange(uint64_t begin_pos, uint64_t end_pos)
{
return quantileRange(begin_pos, end_pos, 0);
}
// v[begin_pos, end_pos)でk番目に小さい数値のindexを返す(kは0-origin)
// つまり小さい順に並べてk番目の値
uint64_t quantileRange(uint64_t begin_pos, uint64_t end_pos, uint64_t k)
{
if ((end_pos > size || begin_pos >= end_pos) || (k >= end_pos - begin_pos)) {
return NOTFOUND;
}
uint64_t val = 0;
for (uint64_t i = 0; i < bit_size; ++i) {
uint64_t num_of_zero_begin = bit_arrays.at(i).rank(0, begin_pos);
uint64_t num_of_zero_end = bit_arrays.at(i).rank(0, end_pos);
uint64_t num_of_zero = num_of_zero_end - num_of_zero_begin; // beginからendまでにある0の数
uint64_t bit = (k < num_of_zero) ? 0 : 1; // k番目の値の上からi番目のbitが0か1か
if (bit) {
k -= num_of_zero;
begin_pos = this->begin_one.at(i) + begin_pos - num_of_zero_begin;
end_pos = this->begin_one.at(i) + end_pos - num_of_zero_end;
} else {
begin_pos = num_of_zero_begin;
end_pos = num_of_zero_begin + num_of_zero;
}
val = ((val << 1) | bit);
}
uint64_t left = 0;
for (uint64_t i = 0; i < bit_size; ++i) {
const uint64_t bit = (val >> (bit_size - i - 1)) & 1; // 上からi番目のbit
left = bit_arrays.at(i).rank(bit, left); // cのi番目のbitと同じ数値の数
if (bit) {
left += this->begin_one.at(i);
}
}
uint64_t rank = begin_pos + k - left + 1;
return select(val, rank) - 1;
}
private:
uint64_t get_num_of_bit(uint64_t x)
{
if (x == 0) return 0;
x--;
uint64_t bit_num = 0;
while (x >> bit_num) {
++bit_num;
}
return bit_num;
}
};
int main()
{
constexpr ll MAX = 1LL << 40;
std::cin.tie(nullptr), std::ios::sync_with_stdio(false);
using node = bbst_node::key_node<ull, bbst_node::lazy_node<sum_plus<ull, ull>>, std::less<ull>>;
using tree = base_rbstree<node>;
const auto [n, q] = reads<usize, usize>();
const auto m = ceil2(n);
auto a = read<uint64_t>(n);
std::vector<tree> sorted(2 * m);
DynamicWaveletMatrix wm((1UL << 40) - 1, a);
auto median = [&](const usize l, const usize r) { return wm.access(wm.quantileRange(l, r, (r - l) / 2)); };
// stopwatch sw;
segments segs{n};
for (usize i = 1; i < 2 * m; i++) {
const auto [l, r] = segs[i];
for (usize j = l; j < std::min(r, n); j++) { sorted[i].insert({a[j], a[j]}); }
}
// std::cerr << sw.rap() << "ms\n";
ull s = 0;
constexpr ull pmask = (1ULL << 16) - 1;
constexpr ull vmask = (1ULL << 40) - 1;
for (usize i = 0; i < q; i++) {
const usize t = read<usize>();
if (t == 1) {
const usize sp = s & pmask;
const ull sv = s & vmask;
const auto x = (read<usize>() ^ (sp)) - 1;
const auto y = (read<ull>() ^ sv);
const auto inds = segs.over(x);
for (const usize i : inds) {
auto& lst = sorted[i];
auto rst = lst.split_lower(a[x]);
auto rst2 = rst.split_at(1);
lst.merge(std::move(rst2));
lst.insert({y, y});
}
wm.update(x, y);
a[x] = y;
// std::cerr << "Q1: " << sw.rap<std::chrono::microseconds>() << "us\n";
} else {
const usize sp = s & pmask;
auto l = (read<usize>() ^ (sp)), r = (read<usize>() ^ (sp));
if (l > r) { std::swap(l, r); }
l--;
const usize sz = r - l;
const auto inds = segs.under(l, r);
// auto less = [&](const ll x) -> usize {
// usize ans = 0;
// for (const usize i : inds) { ans += sorted[i].fold_lower(x).data().sz; }
// return ans;
// };
// ll inf = -1LL, sup = MAX;
// while (sup - inf > 1) {
// const ll mid = (inf + sup) / 2LL;
// (less(mid) < (sz + 1) / 2 ? inf : sup) = mid;
// }
// const ll m = inf;
//std::cerr << "Q2 binsearch: " << sw.rap<std::chrono::microseconds>() << "us\n";
const ull m = median(l, r);
ull ans = 0;
for (const usize i : inds) {
auto& lst = sorted[i];
auto rst = sorted[i].split_lower(m);
const usize l = lst.top().data().sz;
const usize r = rst.top().data().sz;
const ull lsum = (ull)l * m - lst.top().data().merged;
const ull rsum = rst.top().data().merged - (ull)r * m;
ans += (lsum + rsum);
lst.merge(std::move(rst));
}
s ^= ans;
// std::cerr << "Q2 query: " << sw.rap<std::chrono::microseconds>() << "us\n";
std::cout << ans << "\n";
}
}
// std::cerr << sw.total() << "ms" << std::endl;
return 0;
}