#line 1 "verify/verify-unit-test/rbst-sequence.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/aplusb"
//
#line 2 "template/template.hpp"
using namespace std;
// intrinstic
#include <immintrin.h>
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cctype>
#include <cfenv>
#include <cfloat>
#include <chrono>
#include <cinttypes>
#include <climits>
#include <cmath>
#include <complex>
#include <cstdarg>
#include <cstddef>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <deque>
#include <fstream>
#include <functional>
#include <initializer_list>
#include <iomanip>
#include <ios>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <ostream>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <streambuf>
#include <string>
#include <tuple>
#include <type_traits>
#include <typeinfo>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
// utility
#line 3 "template/util.hpp"
namespace Nyaan {
using ll = long long;
using i64 = long long;
using u64 = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;
template <typename T>
using V = vector<T>;
template <typename T>
using VV = vector<vector<T>>;
using vi = vector<int>;
using vl = vector<long long>;
using vd = V<double>;
using vs = V<string>;
using vvi = vector<vector<int>>;
using vvl = vector<vector<long long>>;
template <typename T>
using minpq = priority_queue<T, vector<T>, greater<T>>;
template <typename T, typename U>
struct P : pair<T, U> {
template <typename... Args>
P(Args... args) : pair<T, U>(args...) {}
using pair<T, U>::first;
using pair<T, U>::second;
P &operator+=(const P &r) {
first += r.first;
second += r.second;
return *this;
}
P &operator-=(const P &r) {
first -= r.first;
second -= r.second;
return *this;
}
P &operator*=(const P &r) {
first *= r.first;
second *= r.second;
return *this;
}
template <typename S>
P &operator*=(const S &r) {
first *= r, second *= r;
return *this;
}
P operator+(const P &r) const { return P(*this) += r; }
P operator-(const P &r) const { return P(*this) -= r; }
P operator*(const P &r) const { return P(*this) *= r; }
template <typename S>
P operator*(const S &r) const {
return P(*this) *= r;
}
P operator-() const { return P{-first, -second}; }
};
using pl = P<ll, ll>;
using pi = P<int, int>;
using vp = V<pl>;
constexpr int inf = 1001001001;
constexpr long long infLL = 4004004004004004004LL;
template <typename T>
int sz(const T &t) {
return t.size();
}
template <typename T, typename U>
inline bool amin(T &x, U y) {
return (y < x) ? (x = y, true) : false;
}
template <typename T, typename U>
inline bool amax(T &x, U y) {
return (x < y) ? (x = y, true) : false;
}
template <typename T>
inline T Max(const vector<T> &v) {
return *max_element(begin(v), end(v));
}
template <typename T>
inline T Min(const vector<T> &v) {
return *min_element(begin(v), end(v));
}
template <typename T>
inline long long Sum(const vector<T> &v) {
return accumulate(begin(v), end(v), 0LL);
}
template <typename T>
int lb(const vector<T> &v, const T &a) {
return lower_bound(begin(v), end(v), a) - begin(v);
}
template <typename T>
int ub(const vector<T> &v, const T &a) {
return upper_bound(begin(v), end(v), a) - begin(v);
}
constexpr long long TEN(int n) {
long long ret = 1, x = 10;
for (; n; x *= x, n >>= 1) ret *= (n & 1 ? x : 1);
return ret;
}
template <typename T, typename U>
pair<T, U> mkp(const T &t, const U &u) {
return make_pair(t, u);
}
template <typename T>
vector<T> mkrui(const vector<T> &v, bool rev = false) {
vector<T> ret(v.size() + 1);
if (rev) {
for (int i = int(v.size()) - 1; i >= 0; i--) ret[i] = v[i] + ret[i + 1];
} else {
for (int i = 0; i < int(v.size()); i++) ret[i + 1] = ret[i] + v[i];
}
return ret;
};
template <typename T>
vector<T> mkuni(const vector<T> &v) {
vector<T> ret(v);
sort(ret.begin(), ret.end());
ret.erase(unique(ret.begin(), ret.end()), ret.end());
return ret;
}
template <typename F>
vector<int> mkord(int N, F f) {
vector<int> ord(N);
iota(begin(ord), end(ord), 0);
sort(begin(ord), end(ord), f);
return ord;
}
template <typename T>
vector<int> mkinv(vector<T> &v) {
int max_val = *max_element(begin(v), end(v));
vector<int> inv(max_val + 1, -1);
for (int i = 0; i < (int)v.size(); i++) inv[v[i]] = i;
return inv;
}
vector<int> mkiota(int n) {
vector<int> ret(n);
iota(begin(ret), end(ret), 0);
return ret;
}
template <typename T>
T mkrev(const T &v) {
T w{v};
reverse(begin(w), end(w));
return w;
}
template <typename T>
bool nxp(T &v) {
return next_permutation(begin(v), end(v));
}
// 返り値の型は入力の T に依存
// i 要素目 : [0, a[i])
template <typename T>
vector<vector<T>> product(const vector<T> &a) {
vector<vector<T>> ret;
vector<T> v;
auto dfs = [&](auto rc, int i) -> void {
if (i == (int)a.size()) {
ret.push_back(v);
return;
}
for (int j = 0; j < a[i]; j++) v.push_back(j), rc(rc, i + 1), v.pop_back();
};
dfs(dfs, 0);
return ret;
}
// F : void(T&), mod を取る操作
// T : 整数型のときはオーバーフローに注意する
template <typename T, typename F>
T Power(T a, long long n, const T &I, F &&f) {
static_assert(std::is_invocable_r_v<void, F &, T &>,
"Power callback must be callable as void(T&)");
T res = I;
for (; n; std::invoke(f, a = a * a), n >>= 1) {
if (n & 1) std::invoke(f, res = res * a);
}
return res;
}
// T : 整数型のときはオーバーフローに注意する
template <typename T>
T Power(T a, long long n, const T &I = T{1}) {
auto no_op = [](T &) -> void {};
return Power(a, n, I, no_op);
}
template <typename T>
T Rev(const T &v) {
T res = v;
reverse(begin(res), end(res));
return res;
}
template <typename T>
vector<T> Transpose(const vector<T> &v) {
using U = typename T::value_type;
if(v.empty()) return {};
int H = v.size(), W = v[0].size();
vector res(W, T(H, U{}));
for (int i = 0; i < H; i++) {
for (int j = 0; j < W; j++) {
res[j][i] = v[i][j];
}
}
return res;
}
template <typename T>
vector<T> Rotate(const vector<T> &v, int clockwise = true) {
using U = typename T::value_type;
int H = v.size(), W = v[0].size();
vector res(W, T(H, U{}));
for (int i = 0; i < H; i++) {
for (int j = 0; j < W; j++) {
if (clockwise) {
res[W - 1 - j][i] = v[i][j];
} else {
res[j][H - 1 - i] = v[i][j];
}
}
}
return res;
}
} // namespace Nyaan
#line 58 "template/template.hpp"
// bit operation
#line 1 "template/bitop.hpp"
namespace Nyaan {
__attribute__((target("popcnt"))) inline int popcnt(const u64 &a) {
return __builtin_popcountll(a);
}
inline int lsb(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }
inline int ctz(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }
inline int msb(const u64 &a) { return a ? 63 - __builtin_clzll(a) : -1; }
template <typename T>
inline int gbit(const T &a, int i) {
return (a >> i) & 1;
}
template <typename T>
inline void sbit(T &a, int i, bool b) {
if (gbit(a, i) != b) a ^= T(1) << i;
}
constexpr long long PW(int n) { return 1LL << n; }
constexpr long long MSK(int n) { return (1LL << n) - 1; }
} // namespace Nyaan
#line 61 "template/template.hpp"
// inout
#line 1 "template/inout.hpp"
namespace Nyaan {
template <typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &p) {
os << p.first << " " << p.second;
return os;
}
template <typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &p) {
is >> p.first >> p.second;
return is;
}
template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
int s = (int)v.size();
for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];
return os;
}
template <typename T>
istream &operator>>(istream &is, vector<T> &v) {
for (auto &x : v) is >> x;
return is;
}
istream &operator>>(istream &is, __int128_t &x) {
string S;
is >> S;
x = 0;
int flag = 0;
for (auto &c : S) {
if (c == '-') {
flag = true;
continue;
}
x *= 10;
x += c - '0';
}
if (flag) x = -x;
return is;
}
istream &operator>>(istream &is, __uint128_t &x) {
string S;
is >> S;
x = 0;
for (auto &c : S) {
x *= 10;
x += c - '0';
}
return is;
}
ostream &operator<<(ostream &os, __int128_t x) {
if (x == 0) return os << 0;
if (x < 0) os << '-', x = -x;
string S;
while (x) S.push_back('0' + x % 10), x /= 10;
reverse(begin(S), end(S));
return os << S;
}
ostream &operator<<(ostream &os, __uint128_t x) {
if (x == 0) return os << 0;
string S;
while (x) S.push_back('0' + x % 10), x /= 10;
reverse(begin(S), end(S));
return os << S;
}
void in() {}
template <typename T, class... U>
void in(T &t, U &...u) {
cin >> t;
in(u...);
}
void out() { cout << "\n"; }
template <typename T, class... U, char sep = ' '>
void out(const T &t, const U &...u) {
cout << t;
if (sizeof...(u)) cout << sep;
out(u...);
}
struct IoSetupNya {
IoSetupNya() {
cin.tie(nullptr);
ios::sync_with_stdio(false);
cout << fixed << setprecision(15);
cerr << fixed << setprecision(7);
}
} iosetupnya;
} // namespace Nyaan
#line 64 "template/template.hpp"
// debug
#line 1 "template/debug.hpp"
namespace DebugImpl {
template <typename U, typename = void>
struct is_specialize : false_type {};
template <typename U>
struct is_specialize<
U, typename conditional<false, typename U::iterator, void>::type>
: true_type {};
template <typename U>
struct is_specialize<
U, typename conditional<false, decltype(U::first), void>::type>
: true_type {};
template <typename U>
struct is_specialize<U, enable_if_t<is_integral<U>::value, void>> : true_type {
};
void dump(const char& t) { cerr << t; }
void dump(const string& t) { cerr << t; }
void dump(const bool& t) { cerr << (t ? "true" : "false"); }
void dump(__int128_t t) {
if (t == 0) cerr << 0;
if (t < 0) cerr << '-', t = -t;
string S;
while (t) S.push_back('0' + t % 10), t /= 10;
reverse(begin(S), end(S));
cerr << S;
}
void dump(__uint128_t t) {
if (t == 0) cerr << 0;
string S;
while (t) S.push_back('0' + t % 10), t /= 10;
reverse(begin(S), end(S));
cerr << S;
}
template <typename U,
enable_if_t<!is_specialize<U>::value, nullptr_t> = nullptr>
void dump(const U& t) {
cerr << t;
}
template <typename T>
void dump(const T& t, enable_if_t<is_integral<T>::value>* = nullptr) {
string res;
if (t == Nyaan::inf) res = "inf";
if constexpr (is_signed<T>::value) {
if (t == -Nyaan::inf) res = "-inf";
}
if constexpr (sizeof(T) == 8) {
if (t == Nyaan::infLL) res = "inf";
if constexpr (is_signed<T>::value) {
if (t == -Nyaan::infLL) res = "-inf";
}
}
if (res.empty()) res = to_string(t);
cerr << res;
}
template <typename T, typename U>
void dump(const pair<T, U>&);
template <typename T>
void dump(const pair<T*, int>&);
template <typename T>
void dump(const T& t,
enable_if_t<!is_void<typename T::iterator>::value>* = nullptr) {
cerr << "[ ";
for (auto it = t.begin(); it != t.end();) {
dump(*it);
cerr << (++it == t.end() ? "" : ", ");
}
cerr << " ]";
}
template <typename T, typename U>
void dump(const pair<T, U>& t) {
cerr << "( ";
dump(t.first);
cerr << ", ";
dump(t.second);
cerr << " )";
}
template <typename T>
void dump(const pair<T*, int>& t) {
cerr << "[ ";
for (int i = 0; i < t.second; i++) {
dump(t.first[i]);
cerr << (i == t.second - 1 ? "" : ", ");
}
cerr << " ]";
}
void trace() { cerr << endl; }
template <typename Head, typename... Tail>
void trace(Head&& head, Tail&&... tail) {
cerr << " ";
dump(head);
if (sizeof...(tail) != 0) cerr << ",";
trace(std::forward<Tail>(tail)...);
}
} // namespace DebugImpl
#ifdef NyaanDebug
#define trc(...) \
do { \
cerr << "## " << #__VA_ARGS__ << " = "; \
DebugImpl::trace(__VA_ARGS__); \
} while (0)
#else
#define trc(...) (void(0))
#endif
#ifdef NyaanLocal
#define trc2(...) \
do { \
cerr << "## " << #__VA_ARGS__ << " = "; \
DebugImpl::trace(__VA_ARGS__); \
} while (0)
#else
#define trc2(...) (void(0))
#endif
#line 67 "template/template.hpp"
// macro
#line 1 "template/macro.hpp"
#define each(x, v) for (auto&& x : v)
#define each2(x, y, v) for (auto&& [x, y] : v)
#define all(v) (v).begin(), (v).end()
#define rep(i, N) for (long long i = 0; i < (long long)(N); i++)
#define repr(i, N) for (long long i = (long long)(N)-1; i >= 0; i--)
#define rep1(i, N) for (long long i = 1; i <= (long long)(N); i++)
#define repr1(i, N) for (long long i = (N); (long long)(i) > 0; i--)
#define reg(i, a, b) for (long long i = (a); i < (b); i++)
#define regr(i, a, b) for (long long i = (b)-1; i >= (a); i--)
#define fi first
#define se second
#define ini(...) \
int __VA_ARGS__; \
in(__VA_ARGS__)
#define inl(...) \
long long __VA_ARGS__; \
in(__VA_ARGS__)
#define ins(...) \
string __VA_ARGS__; \
in(__VA_ARGS__)
#define in2(s, t) \
for (int i = 0; i < (int)s.size(); i++) { \
in(s[i], t[i]); \
}
#define in3(s, t, u) \
for (int i = 0; i < (int)s.size(); i++) { \
in(s[i], t[i], u[i]); \
}
#define in4(s, t, u, v) \
for (int i = 0; i < (int)s.size(); i++) { \
in(s[i], t[i], u[i], v[i]); \
}
#define die(...) \
do { \
Nyaan::out(__VA_ARGS__); \
return; \
} while (0)
#line 70 "template/template.hpp"
namespace Nyaan {
void solve();
}
int main() { Nyaan::solve(); }
#line 4 "verify/verify-unit-test/rbst-sequence.test.cpp"
//
#line 2 "segment-tree/rbst-sequence.hpp"
#line 4 "segment-tree/rbst-sequence.hpp"
using namespace std;
#line 2 "segment-tree/rbst-segment-tree.hpp"
#line 5 "segment-tree/rbst-segment-tree.hpp"
#line 2 "internal/internal-type-traits.hpp"
#line 4 "internal/internal-type-traits.hpp"
using namespace std;
namespace nyaan_internal {
template <typename T>
using is_broadly_integral =
typename conditional_t<is_integral_v<T> || is_same_v<T, __int128_t> ||
is_same_v<T, __uint128_t>,
true_type, false_type>::type;
template <typename T>
using is_broadly_signed =
typename conditional_t<is_signed_v<T> || is_same_v<T, __int128_t>,
true_type, false_type>::type;
template <typename T>
using is_broadly_unsigned =
typename conditional_t<is_unsigned_v<T> || is_same_v<T, __uint128_t>,
true_type, false_type>::type;
#define ENABLE_VALUE(x) \
template <typename T> \
constexpr bool x##_v = x<T>::value;
ENABLE_VALUE(is_broadly_integral);
ENABLE_VALUE(is_broadly_signed);
ENABLE_VALUE(is_broadly_unsigned);
#undef ENABLE_VALUE
#define ENABLE_HAS_TYPE(var) \
template <class, class = void> \
struct has_##var : false_type {}; \
template <class T> \
struct has_##var<T, void_t<typename T::var>> : true_type {}; \
template <class T> \
constexpr auto has_##var##_v = has_##var<T>::value;
#define ENABLE_HAS_VAR(var) \
template <class, class = void> \
struct has_##var : false_type {}; \
template <class T> \
struct has_##var<T, void_t<decltype(T::var)>> : true_type {}; \
template <class T> \
constexpr auto has_##var##_v = has_##var<T>::value;
} // namespace nyaan_internal
#line 7 "segment-tree/rbst-segment-tree.hpp"
ENABLE_HAS_VAR(lazy);
ENABLE_HAS_VAR(shift);
template <typename Node, typename I, typename T, typename E, T (*f)(T, T),
T (*g)(T, E), E (*h)(E, E), T (*ti)(), E (*ei)()>
struct RBSTSegmentTreeBase {
protected:
using Ptr = Node *;
template <typename... Args>
static Ptr _my_new(Args... args) {
return new Node(args...);
}
static void _my_del(Ptr t) { delete t; }
static int _count(const Ptr t) { return t ? t->cnt : 0; }
static T _sum(const Ptr &t) { return t ? t->sum : ti(); }
static uint64_t _rng() {
static uint64_t x_ = 88172645463325252ULL;
return x_ ^= x_ << 7, x_ ^= x_ >> 9, x_ & 0xFFFFFFFFull;
}
static Ptr _merge(Ptr l, Ptr r) {
if (!l || !r) return l ? l : r;
if (int((_rng() * (l->cnt + r->cnt)) >> 32) < l->cnt) {
_push(l);
l->r = _merge(l->r, r);
return _update(l);
} else {
_push(r);
r->l = _merge(l, r->l);
return _update(r);
}
}
static Ptr _build(int l, int r, const vector<pair<I, T>> &dat) {
if (l == r) return nullptr;
if (l + 1 == r) return _my_new(dat[l].first, dat[l].second);
int m = (l + r) / 2;
return _merge(_build(l, m, dat), _build(m, r, dat));
};
static void _push([[maybe_unused]] Ptr t) {
if constexpr (has_lazy_v<Node>) {
if (!t) return;
if (t->lazy != ei()) {
if (t->l) _propagate(t->l, t->lazy);
if (t->r) _propagate(t->r, t->lazy);
t->lazy = ei();
}
}
if constexpr (has_shift_v<Node>) {
if (!t) return;
if (t->shift != I{}) {
if (t->l) _shift(t->l, t->shift);
if (t->r) _shift(t->r, t->shift);
t->shift = I{};
}
}
}
static void _propagate([[maybe_unused]] Ptr t, [[maybe_unused]] const E &x) {
if constexpr (has_lazy_v<Node>) {
if (!t) return;
t->lazy = h(t->lazy, x);
t->val = g(t->val, x);
t->sum = g(t->sum, x);
}
}
static void _shift([[maybe_unused]] Ptr t, [[maybe_unused]] const I &sh) {
if constexpr (has_shift_v<Node>) {
if (!t) return;
t->key += sh, t->shift += sh;
}
}
static Ptr _update(Ptr t) {
if (!t) return t;
t->cnt = 1;
t->sum = t->val;
if (t->l) t->cnt += t->l->cnt, t->sum = f(t->l->sum, t->sum);
if (t->r) t->cnt += t->r->cnt, t->sum = f(t->sum, t->r->sum);
return t;
}
// key が k であるノードを探す, なければ nullptr
static Ptr _find(Ptr t, I k) {
while (t) {
_push(t);
if (k == t->key) return t;
t = k < t->key ? t->l : t->r;
}
return nullptr;
}
static void _erase(Ptr &t, I k) {
if (!t) return;
_push(t);
if (k == t->key) {
Ptr tl = t->l, tr = t->r;
_my_del(t);
t = _merge(tl, tr);
} else if (k < t->key) {
_erase(t->l, k);
_update(t);
} else {
_erase(t->r, k);
_update(t);
}
}
// [k 未満, k 以上]
static pair<Ptr, Ptr> _split_by_key(Ptr t, I k) {
if (!t) return {nullptr, nullptr};
_push(t);
if (k == t->key) {
Ptr tl = t->l;
t->l = nullptr;
return {tl, _update(t)};
} else if (k < t->key) {
auto s = _split_by_key(t->l, k);
t->l = s.second;
return {s.first, _update(t)};
} else {
auto s = _split_by_key(t->r, k);
t->r = s.first;
return {_update(t), s.second};
}
}
// [k 未満, k, k 超過]
static array<Ptr, 3> _split_by_key3(Ptr t, I k) {
if (!t) return {{nullptr, nullptr, nullptr}};
_push(t);
if (k == t->key) {
Ptr tl = t->l, tr = t->r;
t->l = t->r = nullptr;
return {{tl, _update(t), tr}};
} else if (k < t->key) {
auto s = _split_by_key3(t->l, k);
t->l = s[2];
return {{s[0], s[1], _update(t)}};
} else {
auto s = _split_by_key3(t->r, k);
t->r = s[0];
return {{_update(t), s[1], s[2]}};
}
}
// (-inf, i] の prod について check(prod) の (true / false) で切る
template <typename C>
static pair<Ptr, Ptr> _split_max_right(Ptr t, const C &check, T prod = ti()) {
assert(check(prod));
if (!t) return {nullptr, nullptr};
_push(t);
T p1 = f(prod, _sum(t->l));
if (check(p1)) {
prod = p1;
} else {
auto s = _split_max_right(t->l, check, prod);
t->l = s.second;
return {s.first, _update(t)};
}
prod = f(prod, t->val);
if (!check(prod)) {
Ptr tl = t->l;
t->l = nullptr;
return {tl, _update(t)};
}
p1 = f(prod, _sum(t->r));
if (check(p1)) {
return {t, nullptr};
} else {
auto s = _split_max_right(t->r, check, prod);
t->r = s.first;
return {_update(t), s.second};
}
}
// [i, inf) の prod について check(prod) の (false / true) で切る
template <typename C>
static pair<Ptr, Ptr> _split_min_left(Ptr t, const C &check, T prod = ti()) {
assert(check(prod));
if (!t) return {nullptr, nullptr};
_push(t);
T p1 = f(_sum(t->r), prod);
if (check(p1)) {
prod = p1;
} else {
auto s = _split_min_left(t->r, check, prod);
t->r = s.first;
return {_update(t), s.second};
}
prod = f(t->val, prod);
if (!check(prod)) {
Ptr tr = t->r;
t->r = nullptr;
return {_update(t), tr};
}
p1 = f(_sum(t->l), prod);
if (check(p1)) {
return {nullptr, t};
} else {
auto s = _split_min_left(t->l, check, prod);
t->l = s.second;
return {s.first, _update(t)};
}
}
// [l, inf) である地点に apply
static void _apply_left(Ptr t, I l, const E &e) {
if (!t) return;
_push(t);
if (t->key < l) {
_apply_left(t->r, l, e);
} else if (t->key == l) {
t->val = g(t->val, e);
_propagate(t->r, e);
} else {
_apply_left(t->l, l, e);
t->val = g(t->val, e);
_propagate(t->r, e);
}
_update(t);
}
// [-inf, r) である地点に apply
static void _apply_right(Ptr t, I r, const E &e) {
if (!t) return;
_push(t);
if (t->key < r) {
_propagate(t->l, e);
t->val = g(t->val, e);
_apply_right(t->r, r, e);
} else if (t->key == r) {
_propagate(t->l, e);
} else {
_apply_right(t->l, r, e);
}
_update(t);
}
// [l, r) に apply
static void _apply(Ptr t, I l, I r, const E &e) {
if (!t) return;
_push(t);
if (t->key < l) {
_apply(t->r, l, r, e);
} else if (t->key == l) {
t->val = g(t->val, e);
_apply_right(t->r, r, e);
} else if (t->key < r) {
_apply_left(t->l, l, e);
t->val = g(t->val, e);
_apply_right(t->r, r, e);
} else if (t->key == r) {
_apply_left(t->l, l, e);
} else {
_apply(t->l, l, r, e);
}
_update(t);
}
// l 以上
static T _fold_left(Ptr t, I l) {
if (!t) return ti();
_push(t);
if (t->key < l) {
return _fold_left(t->r, l);
} else if (t->key == l) {
return f(t->val, _fold_left(t->r, l));
} else {
T tl = _fold_left(t->l, l);
return f(f(tl, t->val), _sum(t->r));
}
}
// r 未満
static T _fold_right(Ptr t, I r) {
if (!t) return ti();
_push(t);
if (t->key < r) {
T tr = _fold_right(t->r, r);
return f(f(_sum(t->l), t->val), tr);
} else if (t->key == r) {
return _sum(t->l);
} else {
return _fold_right(t->l, r);
}
}
static T _fold(Ptr t, I l, I r) {
if (!t) return ti();
_push(t);
if (t->key < l) {
return _fold(t->r, l, r);
} else if (t->key == l) {
return f(t->val, _fold_right(t->r, r));
} else if (t->key < r) {
T tl = _fold_left(t->l, l);
T tr = _fold_right(t->r, r);
return f(f(tl, t->val), tr);
} else if (t->key == r) {
return _fold_left(t->l, l);
} else {
return _fold(t->l, l, r);
}
}
// t を根とする木の上で最小の key は？ (t が空の場合は failed)
static pair<I, T> _get_min_keyval(Ptr t, const I &failed) {
if (!t) return {failed, ti()};
while (t->l) _push(t), t = t->l;
return {t->key, t->val};
}
// t を根とする木の上で最小の key は？ (t が空の場合は failed)
static pair<I, T> _get_max_keyval(Ptr t, const I &failed) {
if (!t) return {failed, ti()};
while (t->r) _push(t), t = t->r;
return {t->key, t->val};
}
// t を根とする木のうち、[0, i の区間 fold が true になる最大の i は何か？
// exclusive かつ (空 または[0,右]が真の場合) の場合は failed(inf)
// inclusive かつ (空 または[0,0] が偽の場合) の場合は failed
template <typename C, bool exclusive>
static I _max_right(Ptr t, C check, const I &failed) {
if (!t) return failed;
_push(t);
Ptr now = t;
T prod_now = ti();
[[maybe_unused]] I prev = failed;
while (true) {
if (now->l != nullptr) {
_push(now->l);
auto pl = f(prod_now, now->l->sum);
if (check(pl)) {
prod_now = pl;
} else {
now = now->l;
continue;
}
}
auto pl = f(prod_now, now->val);
if (!check(pl)) {
if constexpr (exclusive) {
return now->key;
} else {
return now->l ? _get_max_keyval(now->l, failed).first : prev;
}
}
prod_now = pl;
if (now->r == nullptr) {
if constexpr (exclusive) {
return failed;
} else {
return now->key;
}
}
_push(now->r);
if constexpr (!exclusive) prev = now->key;
now = now->r;
}
}
// t を根とする木のうち、i, inf) の区間 fold が true になる最小の i は何か？
// inclusive かつ (空 または 存在しない) 場合は failed
// exlucisve かつ (空 または [左, inf) が真) の場合は failed
template <typename C, bool inclusive>
static I _min_left(Ptr t, C check, const I &failed) {
if (!t) return failed;
_push(t);
Ptr now = t;
T prod_now = ti();
[[maybe_unused]] I prev = failed;
while (true) {
if (now->r != nullptr) {
_push(now->r);
auto pr = f(now->r->sum, prod_now);
if (check(pr)) {
prod_now = pr;
} else {
now = now->r;
continue;
}
}
auto pr = f(now->val, prod_now);
if (!check(pr)) {
if constexpr (inclusive) {
return now->r ? _get_min_keyval(now->r, failed).first : prev;
} else {
return now->key;
}
}
prod_now = pr;
if (now->l == nullptr) {
if constexpr (inclusive) {
return now->key;
} else {
return failed;
}
}
_push(now->l);
if constexpr (inclusive) prev = now->key;
now = now->l;
}
}
static void _clear(Ptr t) {
if (!t) return;
if (t->l) _clear(t->l);
if (t->r) _clear(t->r);
_my_del(t);
}
static Ptr _deepcopy(Ptr t) {
if (!t) return nullptr;
Ptr u = _my_new(*t);
if (u->l) u->l = _deepcopy(u->l);
if (u->r) u->r = _deepcopy(u->r);
return u;
}
static void _dump(Ptr t) {
if (!t) return;
_push(t);
_dump(t->l);
cerr << "## key = " << t->key << ",";
cerr << "\tval = " << t->val << ", ";
cerr << "\tsum = " << t->sum << ", ";
cerr << "\tchild = ";
cerr << "( ";
if (t->l) cerr << t->l->key;
if (!t->l) cerr << "nil";
cerr << ", ";
if (t->r) cerr << t->r->key;
if (!t->r) cerr << "nil";
cerr << " )" << endl;
_dump(t->r);
}
static void _make_array(Ptr t, vector<pair<I, T>> &v) {
if (!t) return;
_push(t);
if (t->l) _make_array(t->l, v);
v.emplace_back(t->key, t->val);
if (t->r) _make_array(t->r, v);
}
public:
Ptr root;
RBSTSegmentTreeBase() : root(nullptr) {}
RBSTSegmentTreeBase(Ptr t) : root(t) {}
RBSTSegmentTreeBase(const vector<T> xs, const vector<I> &vals = {}) {
if (!vals.empty()) assert(xs.size() == vals.size());
int n = xs.size();
vector<pair<I, T>> dat(n);
for (int i = 0; i < n; i++) dat[i] = {vals.empty() ? i : vals[i], xs[i]};
root = _build(0, n, dat);
}
RBSTSegmentTreeBase(RBSTSegmentTreeBase &&rhs) noexcept { root = rhs.root; }
RBSTSegmentTreeBase(const RBSTSegmentTreeBase &rhs) { root = rhs.root; }
~RBSTSegmentTreeBase() = default;
using RBST = RBSTSegmentTreeBase;
RBST &operator=(RBST &&rhs) noexcept {
root = rhs.root;
return *this;
}
RBST &operator=(const RBST &rhs) {
root = rhs.root;
return *this;
}
RBST deepcopy() { return _deepcopy(root); }
friend void swap(RBST &lhs, RBST &rhs) { swap(lhs.root, rhs.root); }
void swap(RBST &rhs) { swap(root, rhs.root); }
// destructive ordered _merge (max(lhs) < min(rhs))
friend RBST ordered_merge(RBST &lhs, RBST &rhs) {
assert(lhs.get_max_key() < rhs.get_min_key());
return RBST{_merge(lhs.root, rhs.root)};
}
// 1 点 値の書き換え
void set_val(I i, T x) {
auto s = _split_by_key3(root, i);
if (s[1] == nullptr) {
s[1] = _my_new(i, x);
} else {
s[1]->val = x;
}
root = _merge(_merge(s[0], _update(s[1])), s[2]);
}
// すでに要素が存在するときに値を set する。おそらく少し早い
void set_val_fast(I i, T x) {
static vector<Ptr> ps;
ps.clear();
Ptr t = root;
while (t) {
_push(t);
ps.push_back(t);
if (i == t->key) break;
t = i < t->key ? t->l : t->r;
}
if (!t) {
set_val(i, x);
return;
}
t->val = x;
for (int j = ps.size() - 1; j >= 0; j--) _update(ps[j]);
}
// 1 点取得
T get_val(I i) {
Ptr p = _find(root, i);
return p ? p->val : ti();
}
bool exist(I i) {
Ptr p = _find(root, i);
return p != nullptr;
}
// 1 点 値の書き換え
// func の返り値は void !!!!!!(参照された値を直接更新する)
template <typename F>
auto apply_val(I i, F&& func)
-> enable_if_t<is_invocable_r_v<void, F&, T&>> {
auto s = _split_by_key3(root, i);
if (s[1] == nullptr) s[1] = _my_new(i);
std::invoke(func, s[1]->val);
root = _merge(_merge(s[0], _update(s[1])), s[2]);
}
// 1 点 値の書き換え 値が既に存在するときに早い
// func の返り値は void !!!!!!(参照された値を直接更新する)
template <typename F>
auto apply_val_fast(I i, F&& func)
-> enable_if_t<is_invocable_r_v<void, F&, T&>> {
static vector<Ptr> ps;
ps.clear();
Ptr t = root;
while (t) {
_push(t);
ps.push_back(t);
if (i == t->key) break;
t = i < t->key ? t->l : t->r;
}
if (!t) {
apply_val(i, func);
return;
}
std::invoke(func, t->val);
for (int j = ps.size() - 1; j >= 0; j--) _update(ps[j]);
}
// 頂点の削除
virtual void erase(I i) { _erase(root, i); }
// 範囲作用
void apply(I l, I r, const E &e) {
if (l >= r) return;
_apply(root, l, r, e);
}
void apply_all(const E &e) { _propagate(root, e); }
// 範囲取得
T fold(I l, I r) {
if (l >= r) return ti();
return _fold(root, l, r);
}
T fold_all() { return _sum(root); }
void shift(const I &sh) { _shift(root, sh); }
// key 最小を取得
I get_min_key(I failed = {}) { return _get_min_keyval(root, failed).first; }
// key 最大を取得
I get_max_key(I failed = {}) { return _get_max_keyval(root, failed).first; }
// (key, val) 最小を取得
pair<I, T> get_min_keyval(I failed = {}) {
return _get_min_keyval(root, failed);
}
// (key, val) 最大を取得
pair<I, T> get_max_keyval(I failed = {}) {
return _get_max_keyval(root, failed);
}
// (key, val) 最小を pop
pair<I, T> pop_min_keyval(I failed = {}) {
assert(root != nullptr);
auto kv = _get_min_keyval(root, failed);
erase(kv.first);
return kv;
}
// (key, val) 最大を取得
pair<I, T> pop_max_keyval(I failed = {}) {
assert(root != nullptr);
auto kv = _get_max_keyval(root, failed);
erase(kv.first);
return kv;
}
// n 未満の i のうち、[i, n) の区間 fold が true になる最小の i は何か？
// (存在しない場合は failed を返す)
template <typename C>
I min_left(I n, C check, I failed) {
assert(check(ti()) == true);
auto [x, y] = _split_by_key(root, n);
I res = _min_left<C, true>(x, check, failed);
root = _merge(x, y);
return res;
}
// n 未満の i のうち、(i, n) の区間 fold が true になる最小の i は何か？
// (空だったり (左端, n) が 真の場合は minus_infty を返す)
template <typename C>
I min_left_exclusive(I n, C check, I minus_infty) {
assert(check(ti()) == true);
auto [x, y] = _split_by_key(root, n);
I res = _min_left<C, false>(x, check, minus_infty);
root = _merge(x, y);
return res;
}
// n 以上の i のうち、[n, i) の区間 fold が true になる最大の i は何か？
// (空だったり [n, 右端] が true の場合は infty を返す)
template <typename C>
I max_right(I n, C check, I infty) {
assert(check(ti()) == true);
auto [x, y] = _split_by_key(root, n);
I res = _max_right<C, true>(y, check, infty);
root = _merge(x, y);
return res;
}
// n 以上の i のうち、[n, i] の区間 fold が true になる最大の i は何か？
// (存在しない場合は failed を返す)
template <typename C>
I max_right_inclusive(I n, C check, I failed) {
assert(check(ti()) == true);
auto [x, y] = _split_by_key(root, n);
I res = _max_right<C, false>(y, check, failed);
root = _merge(x, y);
return res;
}
// (key 未満, key 以上) で分割
// 呼び出し後のオブジェクトは空のセグ木になる
pair<RBST, RBST> split_by_key(const I &key) {
auto [x, y] = _split_by_key(root, key);
root = nullptr;
return make_pair(RBST{x}, RBST{y});
}
// [i, inf) の区間積が (false, true) になる境界で分割
// 呼び出し後のオブジェクトは空のセグ木になる
template <typename C>
pair<RBST, RBST> split_min_left(const C &check) {
assert(check(ti()) == true);
auto [x, y] = _split_min_left(root, check);
root = nullptr;
return make_pair(RBST{x}, RBST{y});
}
// (-inf, i] の区間積が (true, false) になる境界で分割
// 呼び出し後のオブジェクトは空のセグ木になる
template <typename C>
pair<RBST, RBST> split_max_right(const C &check) {
assert(check(ti()) == true);
auto [x, y] = _split_max_right(root, check);
root = nullptr;
return make_pair(RBST{x}, RBST{y});
}
void clear() { _clear(root), root = nullptr; }
int size() { return _count(root); }
bool empty() { return !root; }
void dump() {
cerr << "***** dump start *****" << endl;
_dump(root);
cerr << "****** dump end ******" << endl;
}
// 列を配列に変換して返す
vector<pair<I, T>> make_array() {
vector<pair<I, T>> res;
_make_array(root, res);
return res;
}
};
namespace RBSTSegmentTreeImpl {
bool _ei() { return false; }
template <typename I, typename T, typename E, T (*f)(T, T), T (*g)(T, E),
E (*h)(E, E), T (*ti)(), E (*ei)()>
struct ShiftableLazySegNode {
ShiftableLazySegNode *l, *r;
I key, shift;
T val, sum;
E lazy;
int cnt;
ShiftableLazySegNode(const I &i, const T &t = ti())
: l(), r(), key(i), shift(I{}), val(t), sum(t), lazy(ei()), cnt(1) {}
};
template <typename I, typename T, typename E, T (*f)(T, T), T (*g)(T, E),
E (*h)(E, E), T (*ti)(), E (*ei)()>
using RBSTShiftableLazySegmentTree =
RBSTSegmentTreeBase<ShiftableLazySegNode<I, T, E, f, g, h, ti, ei>, I, T, E,
f, g, h, ti, ei>;
template <typename I, typename T, typename E, T (*f)(T, T), T (*g)(T, E),
E (*h)(E, E), T (*ti)(), E (*ei)()>
struct LazySegNode {
LazySegNode *l, *r;
I key;
T val, sum;
E lazy;
int cnt;
LazySegNode(const I &i, const T &t = ti())
: l(), r(), key(i), val(t), sum(t), lazy(ei()), cnt(1) {}
};
template <typename I, typename T, typename E, T (*f)(T, T), T (*g)(T, E),
E (*h)(E, E), T (*ti)(), E (*ei)()>
using RBSTLazySegmentTree =
RBSTSegmentTreeBase<LazySegNode<I, T, E, f, g, h, ti, ei>, I, T, E, f, g, h,
ti, ei>;
template <typename I, typename T, T (*f)(T, T), T (*ti)()>
struct SegNode {
SegNode *l, *r;
I key;
T val, sum;
int cnt;
SegNode(const I &i, const T &t = ti())
: l(), r(), key(i), val(t), sum(t), cnt(1) {}
};
template <typename I, typename T, T (*f)(T, T), T (*ti)()>
using RBSTSegmentTree = RBSTSegmentTreeBase<SegNode<I, T, f, ti>, I, T, bool, f,
nullptr, nullptr, ti, _ei>;
} // namespace RBSTSegmentTreeImpl
using RBSTSegmentTreeImpl::RBSTLazySegmentTree;
using RBSTSegmentTreeImpl::RBSTSegmentTree;
using RBSTSegmentTreeImpl::RBSTShiftableLazySegmentTree;
/**
* @brief RBST-based Dynamic Lazy Segment Tree
*/
#line 7 "segment-tree/rbst-sequence.hpp"
template <typename T, typename E, T (*f)(T, T), T (*g)(T, E), E (*h)(E, E),
T (*ti)(), E (*ei)()>
struct Sequence : RBSTShiftableLazySegmentTree<int, T, E, f, g, h, ti, ei> {
using Base = RBSTShiftableLazySegmentTree<int, T, E, f, g, h, ti, ei>;
using Base::_clear;
using Base::_count;
using Base::_make_array;
using Base::_merge;
using Base::_my_del;
using Base::_my_new;
using Base::_shift;
using Base::_split_by_key;
using Base::_split_by_key3;
Sequence() : Base() {}
Sequence(const vector<T>& v) : Base(v) {}
Sequence(int n) : Base(vector<T>(n, ti())) {}
void insert(int i, const T& x) {
auto [l, r] = _split_by_key(this->root, i);
_shift(r, 1);
this->root = _merge(_merge(l, _my_new(i, x)), r);
}
void push_back(const T& x) { insert(_count(this->root), x); }
// 列のマージ 破壊的
void append(Sequence& r) {
_shift(r.root, _count(this->root));
this->root = _merge(this->root, r.root);
r.root = nullptr;
}
void append(const vector<T>& r) {
Sequence s{r};
append(s);
}
void erase(int i) override {
auto s = _split_by_key3(this->root, i);
_my_del(s[1]), _shift(s[2], -1);
this->root = _merge(s[0], s[2]);
}
void pop_back() { erase(_count(this->root) - 1); }
void erase(int l, int r) {
if (l >= r) return;
auto s = _split_by_key3(this->root, l);
auto [t, u] = _split_by_key(s[2], r);
_my_del(s[1]), _clear(t), _shift(u, l - r);
this->root = _merge(s[0], u);
}
vector<T> get_vector() {
vector<pair<int, T>> buf;
_make_array(this->root, buf);
vector<T> res;
for (auto& p : buf) res.push_back(p.second);
return res;
}
friend ostream& operator<<(ostream& os, const Sequence& s) {
vector<pair<int, T>> p = s.make_array();
for (int i = 0; i < (int)p.size(); i++) {
os << (i ? " " : "") << p[i].second;
}
os << "\n";
return os;
}
};
#line 6 "verify/verify-unit-test/rbst-sequence.test.cpp"
//
#line 2 "misc/rng.hpp"
#line 7 "misc/rng.hpp"
using namespace std;
#line 2 "internal/internal-seed.hpp"
#line 4 "internal/internal-seed.hpp"
using namespace std;
namespace nyaan_internal {
unsigned long long non_deterministic_seed() {
unsigned long long m =
chrono::duration_cast<chrono::nanoseconds>(
chrono::high_resolution_clock::now().time_since_epoch())
.count();
m ^= 9845834732710364265uLL;
m ^= m << 24, m ^= m >> 31, m ^= m << 35;
return m;
}
unsigned long long deterministic_seed() { return 88172645463325252UL; }
// 64 bit の seed 値を生成 (手元では seed 固定)
// 連続で呼び出すと同じ値が何度も返ってくるので注意
// #define RANDOMIZED_SEED するとシードがランダムになる
unsigned long long seed() {
#if defined(NyaanLocal) && !defined(RANDOMIZED_SEED)
return deterministic_seed();
#else
return non_deterministic_seed();
#endif
}
} // namespace nyaan_internal
#line 10 "misc/rng.hpp"
namespace my_rand {
using i64 = long long;
using u64 = unsigned long long;
// [0, 2^64 - 1)
u64 rng() {
static u64 _x = nyaan_internal::seed();
return _x ^= _x << 7, _x ^= _x >> 9;
}
// [l, r]
i64 rng(i64 l, i64 r) {
assert(l <= r);
return l + rng() % u64(r - l + 1);
}
// [l, r)
i64 randint(i64 l, i64 r) {
assert(l < r);
return l + rng() % u64(r - l);
}
// choose n numbers from [l, r) without overlapping
vector<i64> randset(i64 l, i64 r, i64 n) {
assert(l <= r && n <= r - l);
unordered_set<i64> s;
for (i64 i = n; i; --i) {
i64 m = randint(l, r + 1 - i);
if (s.find(m) != s.end()) m = r - i;
s.insert(m);
}
vector<i64> ret;
for (auto& x : s) ret.push_back(x);
sort(begin(ret), end(ret));
return ret;
}
// [0.0, 1.0)
double rnd() { return rng() * 5.42101086242752217004e-20; }
// [l, r)
double rnd(double l, double r) {
assert(l < r);
return l + rnd() * (r - l);
}
template <typename T>
void randshf(vector<T>& v) {
int n = v.size();
for (int i = 1; i < n; i++) swap(v[i], v[randint(0, i + 1)]);
}
} // namespace my_rand
using my_rand::randint;
using my_rand::randset;
using my_rand::randshf;
using my_rand::rnd;
using my_rand::rng;
#line 8 "verify/verify-unit-test/rbst-sequence.test.cpp"
using namespace Nyaan;
// min add
namespace SequenceTestImpl {
using T = ll;
using E = ll;
T f(T a, T b) { return min(a, b); }
E g(T a, E b) { return a + b; }
E h(T a, E b) { return a + b; }
T ti() { return infLL; }
E ei() { return 0; }
using Seq = Sequence<T, E, f, g, h, ti, ei>;
void test() {
Seq s;
vl v;
// constructor
if (rng(0, 2)) {
int n = rng(0, 10);
if (rng(0, 1)) {
s = Seq{n};
v = vl(n, ti());
} else {
rep(_, n) v.push_back(rng(0, TEN(9)));
s = Seq{v};
}
auto v2 = s.get_vector();
auto v3 = s.make_array();
if (v != v2) {
trc2(v);
trc2(v2);
}
assert(v == v2);
rep(i, sz(v)) assert(v3[i].fi == i);
if (s.fold_all() == ti()) v.clear(), s.clear();
}
rep(t, 1000) {
// if (t % 100 == 0) cerr << sz(v) << " ";
// if (t == 999) cerr << "\n";
int cmd = rng(0, 10);
if (cmd == 0) {
// insert
int i = rng(0, sz(v));
ll x = rng(0, TEN(9));
s.insert(i, x);
v.insert(begin(v) + i, x);
} else if (cmd == 1) {
// push_back
ll x = rng(0, TEN(9));
s.push_back(x);
v.push_back(x);
} else if (cmd == 2) {
// erase
if (sz(v) != 0) {
int i = rng(0, sz(v) - 1);
s.erase(i);
v.erase(begin(v) + i);
}
} else if (cmd == 3) {
// pop_back
if (sz(v) != 0) {
s.pop_back();
v.pop_back();
}
} else if (cmd == 4) {
// apply
int l = rng(0, sz(v));
int r = rng(0, sz(v));
if (l > r) swap(l, r);
ll x = rng(0, TEN(9));
s.apply(l, r, x);
reg(i, l, r) v[i] += x;
} else if (cmd == 5) {
// fold
int l = rng(0, sz(v));
int r = rng(0, sz(v));
if (l > r) swap(l, r);
ll f1 = s.fold(l, r);
ll f2 = ti();
reg(i, l, r) f2 = f(f2, v[i]);
/*
if (f1 != f2) {
auto w = s.get_vector();
trc2(v);
trc2(w);
trc2(l, r, f1, f2);
}
*/
assert(f1 == f2);
} else if (cmd == 6) {
// append
int n = rng(0, 15);
vector<ll> w(n);
each(x, w) x = rng(1, TEN(9));
copy(all(w), back_inserter(v));
s.append(w);
} else if (cmd == 7) {
// erase(range)
if (sz(v)) {
int l = rng(0, sz(v));
int r = rng(0, sz(v));
if (l > r) swap(l, r);
if (r - l > 8) r = l + 8;
s.erase(l, r);
v.erase(begin(v) + l, begin(v) + r);
}
}
auto v2 = s.get_vector();
auto v3 = s.make_array();
/*
if (v != v2) {
trc2(cmd);
trc2(sz(v), v);
trc2(sz(v2), v2);
}
*/
assert(v == v2);
rep(i, sz(v3)) assert(v3[i].fi == i);
}
}
} // namespace SequenceTestImpl
void q() {
rep(_, 1000) SequenceTestImpl::test();
cerr << "OK" << endl;
int a, b;
cin >> a >> b;
cout << a + b << endl;
}
void Nyaan::solve() {
int t = 1;
// in(t);
while (t--) q();
}
verify/verify-unit-test/rbst-sequence.test.cpp