#line 1 "verify/verify-unit-test/rbst-segment-tree.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-segment-tree.test.cpp"
//
#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 6 "verify/verify-unit-test/rbst-segment-tree.test.cpp"
//
#line 2 "misc/all.hpp"
#line 2 "misc/fastio.hpp"
#line 9 "misc/fastio.hpp"
using namespace std;
#line 13 "misc/fastio.hpp"
namespace fastio {
static constexpr int SZ = 1 << 17;
static constexpr int offset = 64;
char inbuf[SZ], outbuf[SZ];
int in_left = 0, in_right = 0, out_right = 0;
struct Pre {
char num[40000];
constexpr Pre() : num() {
for (int i = 0; i < 10000; i++) {
int n = i;
for (int j = 3; j >= 0; j--) {
num[i * 4 + j] = n % 10 + '0';
n /= 10;
}
}
}
} constexpr pre;
void load() {
int len = in_right - in_left;
memmove(inbuf, inbuf + in_left, len);
in_right = len + fread(inbuf + len, 1, SZ - len, stdin);
in_left = 0;
}
void flush() {
fwrite(outbuf, 1, out_right, stdout);
out_right = 0;
}
void skip_space() {
if (in_left + offset > in_right) load();
while (inbuf[in_left] <= ' ') in_left++;
}
void single_read(char& c) {
if (in_left + offset > in_right) load();
skip_space();
c = inbuf[in_left++];
}
void single_read(string& S) {
skip_space();
while (true) {
if (in_left == in_right) load();
int i = in_left;
for (; i != in_right; i++) {
if (inbuf[i] <= ' ') break;
}
copy(inbuf + in_left, inbuf + i, back_inserter(S));
in_left = i;
if (i != in_right) break;
}
}
template <typename T,
enable_if_t<nyaan_internal::is_broadly_integral_v<T>>* = nullptr>
void single_read(T& x) {
if (in_left + offset > in_right) load();
skip_space();
char c = inbuf[in_left++];
[[maybe_unused]] bool minus = false;
if constexpr (nyaan_internal::is_broadly_signed_v<T>) {
if (c == '-') minus = true, c = inbuf[in_left++];
}
x = 0;
while (c >= '0') {
x = x * 10 + (c & 15);
c = inbuf[in_left++];
}
if constexpr (nyaan_internal::is_broadly_signed_v<T>) {
if (minus) x = -x;
}
}
void rd() {}
template <typename Head, typename... Tail>
void rd(Head& head, Tail&... tail) {
single_read(head);
rd(tail...);
}
void single_write(const char& c) {
if (out_right > SZ - offset) flush();
outbuf[out_right++] = c;
}
void single_write(const bool& b) {
if (out_right > SZ - offset) flush();
outbuf[out_right++] = b ? '1' : '0';
}
void single_write(const string& S) {
flush(), fwrite(S.data(), 1, S.size(), stdout);
}
void single_write(const char* p) { flush(), fwrite(p, 1, strlen(p), stdout); }
template <typename T,
enable_if_t<nyaan_internal::is_broadly_integral_v<T>>* = nullptr>
void single_write(const T& _x) {
if (out_right > SZ - offset) flush();
if (_x == 0) {
outbuf[out_right++] = '0';
return;
}
T x = _x;
if constexpr (nyaan_internal::is_broadly_signed_v<T>) {
if (x < 0) outbuf[out_right++] = '-', x = -x;
}
constexpr int buffer_size = sizeof(T) * 10 / 4;
char buf[buffer_size];
int i = buffer_size;
while (x >= 10000) {
i -= 4;
memcpy(buf + i, pre.num + (x % 10000) * 4, 4);
x /= 10000;
}
if (x < 100) {
if (x < 10) {
outbuf[out_right] = '0' + x;
++out_right;
} else {
uint32_t q = (uint32_t(x) * 205) >> 11;
uint32_t r = uint32_t(x) - q * 10;
outbuf[out_right] = '0' + q;
outbuf[out_right + 1] = '0' + r;
out_right += 2;
}
} else {
if (x < 1000) {
memcpy(outbuf + out_right, pre.num + (x << 2) + 1, 3);
out_right += 3;
} else {
memcpy(outbuf + out_right, pre.num + (x << 2), 4);
out_right += 4;
}
}
memcpy(outbuf + out_right, buf + i, buffer_size - i);
out_right += buffer_size - i;
}
void wt() {}
template <typename Head, typename... Tail>
void wt(const Head& head, const Tail&... tail) {
single_write(head);
wt(std::forward<const Tail>(tail)...);
}
template <typename... Args>
void wtn(const Args&... x) {
wt(std::forward<const Args>(x)...);
wt('\n');
}
struct Dummy {
Dummy() { atexit(flush); }
} dummy;
} // namespace fastio
using fastio::rd;
using fastio::skip_space;
using fastio::wt;
using fastio::wtn;
#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 2 "misc/timer.hpp"
#line 4 "misc/timer.hpp"
using namespace std;
struct Timer {
chrono::high_resolution_clock::time_point st;
Timer() { reset(); }
void reset() { st = chrono::high_resolution_clock::now(); }
long long elapsed() {
auto ed = chrono::high_resolution_clock::now();
return chrono::duration_cast<chrono::milliseconds>(ed - st).count();
}
long long operator()() { return elapsed(); }
};
#line 8 "verify/verify-unit-test/rbst-segment-tree.test.cpp"
//
#line 2 "segment-tree/lazy-segment-tree.hpp"
// LazySegmentTree
template <typename T, typename E, typename F, typename G, typename H>
struct LazySegmentTree {
int n, height;
F f;
G g;
H h;
T ti;
E ei;
vector<T> dat;
vector<E> laz;
LazySegmentTree(int _n, F _f, G _g, H _h, T _ti, E _ei)
: f(_f), g(_g), h(_h), ti(_ti), ei(_ei) {
init(_n);
}
LazySegmentTree(const vector<T> &v, F _f, G _g, H _h, T _ti, E _ei)
: f(_f), g(_g), h(_h), ti(_ti), ei(_ei) {
init((int)v.size());
build(v);
}
void init(int _n) {
n = 1;
height = 0;
while (n < _n) n <<= 1, height++;
dat.assign(2 * n, ti);
laz.assign(2 * n, ei);
}
void build(const vector<T> &v) {
int _n = v.size();
init(_n);
for (int i = 0; i < _n; i++) dat[n + i] = v[i];
for (int i = n - 1; i; i--)
dat[i] = f(dat[(i << 1) | 0], dat[(i << 1) | 1]);
}
inline T reflect(int k) { return laz[k] == ei ? dat[k] : g(dat[k], laz[k]); }
inline void eval(int k) {
if (laz[k] == ei) return;
laz[(k << 1) | 0] = h(laz[(k << 1) | 0], laz[k]);
laz[(k << 1) | 1] = h(laz[(k << 1) | 1], laz[k]);
dat[k] = reflect(k);
laz[k] = ei;
}
inline void thrust(int k) {
for (int i = height; i; i--) eval(k >> i);
}
inline void recalc(int k) {
while (k >>= 1) dat[k] = f(reflect((k << 1) | 0), reflect((k << 1) | 1));
}
void update(int a, int b, E x) {
if (a >= b) return;
thrust(a += n);
thrust(b += n - 1);
for (int l = a, r = b + 1; l < r; l >>= 1, r >>= 1) {
if (l & 1) laz[l] = h(laz[l], x), l++;
if (r & 1) --r, laz[r] = h(laz[r], x);
}
recalc(a);
recalc(b);
}
void set_val(int a, T x) {
thrust(a += n);
dat[a] = x;
laz[a] = ei;
recalc(a);
}
T get_val(int a) {
thrust(a += n);
return reflect(a);
}
T query(int a, int b) {
if (a >= b) return ti;
thrust(a += n);
thrust(b += n - 1);
T vl = ti, vr = ti;
for (int l = a, r = b + 1; l < r; l >>= 1, r >>= 1) {
if (l & 1) vl = f(vl, reflect(l++));
if (r & 1) vr = f(reflect(--r), vr);
}
return f(vl, vr);
}
};
#line 10 "verify/verify-unit-test/rbst-segment-tree.test.cpp"
//
#line 2 "math/affine-transformation.hpp"
template <typename mint>
struct Affine {
mint a, b;
constexpr Affine() : a(1), b(0) {}
constexpr Affine(mint _a, mint _b) : a(_a), b(_b) {}
// R(L(x))
friend Affine operator*(const Affine& l, const Affine& r) {
return Affine(l.a * r.a, l.b * r.a + r.b);
}
mint operator()(mint x) const { return a * x + b; }
Affine operator()(const Affine& r) const { return r * (*this); }
bool operator==(const Affine& r) const { return a == r.a && b == r.b; }
bool operator!=(const Affine& r) const { return a != r.a || b != r.b; }
friend ostream& operator<<(ostream& os, const Affine& r) {
os << "( " << r.a << ", " << r.b << " )";
return os;
}
};
/**
* @brief アフィン変換
*/
#line 2 "modint/montgomery-modint.hpp"
#line 5 "modint/montgomery-modint.hpp"
template <uint32_t mod>
struct LazyMontgomeryModInt {
using mint = LazyMontgomeryModInt;
using i32 = int32_t;
using u32 = uint32_t;
using u64 = uint64_t;
static constexpr u32 get_r() {
u32 ret = mod;
for (i32 i = 0; i < 4; ++i) ret *= 2 - mod * ret;
return ret;
}
static constexpr u32 r = get_r();
static constexpr u32 n2 = -u64(mod) % mod;
static_assert(mod < (1 << 30), "invalid, mod >= 2 ^ 30");
static_assert((mod & 1) == 1, "invalid, mod % 2 == 0");
static_assert(r * mod == 1, "this code has bugs.");
u32 a;
constexpr LazyMontgomeryModInt() : a(0) {}
constexpr LazyMontgomeryModInt(const int64_t &b)
: a(reduce(u64(b % mod + mod) * n2)){};
static constexpr u32 reduce(const u64 &b) {
return (b + u64(u32(b) * u32(-r)) * mod) >> 32;
}
constexpr mint &operator+=(const mint &b) {
if (i32(a += b.a - 2 * mod) < 0) a += 2 * mod;
return *this;
}
constexpr mint &operator-=(const mint &b) {
if (i32(a -= b.a) < 0) a += 2 * mod;
return *this;
}
constexpr mint &operator*=(const mint &b) {
a = reduce(u64(a) * b.a);
return *this;
}
constexpr mint &operator/=(const mint &b) {
*this *= b.inverse();
return *this;
}
constexpr mint operator+(const mint &b) const { return mint(*this) += b; }
constexpr mint operator-(const mint &b) const { return mint(*this) -= b; }
constexpr mint operator*(const mint &b) const { return mint(*this) *= b; }
constexpr mint operator/(const mint &b) const { return mint(*this) /= b; }
constexpr bool operator==(const mint &b) const {
return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a);
}
constexpr bool operator!=(const mint &b) const {
return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a);
}
constexpr mint operator-() const { return mint() - mint(*this); }
constexpr mint operator+() const { return mint(*this); }
constexpr mint pow(u64 n) const {
mint ret(1), mul(*this);
while (n > 0) {
if (n & 1) ret *= mul;
mul *= mul;
n >>= 1;
}
return ret;
}
constexpr mint inverse() const {
int x = get(), y = mod, u = 1, v = 0, t = 0, tmp = 0;
while (y > 0) {
t = x / y;
x -= t * y, u -= t * v;
tmp = x, x = y, y = tmp;
tmp = u, u = v, v = tmp;
}
return mint{u};
}
friend std::ostream &operator<<(std::ostream &os, const mint &b) {
return os << b.get();
}
friend std::istream &operator>>(std::istream &is, mint &b) {
int64_t t;
is >> t;
b = LazyMontgomeryModInt<mod>(t);
return (is);
}
constexpr u32 get() const {
u32 ret = reduce(a);
return ret >= mod ? ret - mod : ret;
}
static constexpr u32 get_mod() { return mod; }
};
#line 13 "verify/verify-unit-test/rbst-segment-tree.test.cpp"
using mint = LazyMontgomeryModInt<998244353>;
using T = pair<mint, mint>;
using E = Affine<mint>;
T f(T a, T b) { return T(a.first + b.first, a.second + b.second); }
T g(T a, E b) { return T(a.first * b.a + a.second * b.b, a.second); }
E h(E a, E b) { return a * b; };
T ti() { return T{}; }
E ei() { return E{}; }
using namespace Nyaan;
// すべての関数のテスト。ただしセグ木にぶたん系は別途 verify する
void test(const int N = 100, const int Q = 100) {
RBSTLazySegmentTree<int, T, E, f, g, h, ti, ei> seg1;
LazySegmentTree seg2(N, f, g, h, ti(), ei());
ll MOD = 998244353;
vector<function<void(void)>> funcs{
[&]() {
// set_val
int i = rng(0, N - 1);
T x{rng(0, MOD - 1), 1};
seg1.set_val(i, x);
seg2.set_val(i, x);
},
[&]() {
// set_val_fast
int i = rng(0, N - 1);
T x{rng(0, MOD - 1), 1};
seg1.set_val_fast(i, x);
seg2.set_val(i, x);
},
[&]() {
// get_val
int i = rng(0, N - 1);
T v1 = seg1.get_val(i);
T v2 = seg2.get_val(i);
assert(v1 == v2 and "get_val");
},
[&]() {
// apply_val
int i = rng(0, N - 1);
E x{rng(0, MOD - 1), rng(0, MOD - 1)};
seg1.apply_val(i, [&](T& t) { t = g(t, x); });
seg2.update(i, i + 1, x);
},
[&]() {
// apply_val_fast
int i = rng(0, N - 1);
E x{rng(0, MOD - 1), rng(0, MOD - 1)};
seg1.apply_val_fast(i, [&](T& t) { t = g(t, x); });
seg2.update(i, i + 1, x);
},
[&]() {
// erase
int i = rng(0, N - 1);
seg1.erase(i);
seg2.set_val(i, T{});
},
[&]() {
// apply
int l = rng(0, N - 1);
int r = rng(0, N - 1);
if (l > r) swap(l, r);
r++;
E x{rng(0, MOD - 1), rng(0, MOD - 1)};
seg1.apply(l, r, x);
seg2.update(l, r, x);
},
[&]() {
// fold
int l = rng(0, N - 1);
int r = rng(0, N - 1);
if (l > r) swap(l, r);
r++;
auto v1 = seg1.fold(l, r);
auto v2 = seg2.query(l, r);
assert(v1 == v2 and "fold");
},
[&]() {
// get_min_key, get_min_keyval
int v1 = -1;
while (true) {
v1 = seg1.get_min_key(-1);
if (v1 == -1) break;
T val = seg2.get_val(v1);
if (val.second == 1) break;
if (val.second == 0) {
seg1.erase(v1);
seg2.set_val(v1, T{});
} else {
assert(false and "get_min_key");
}
}
int v2 = -1;
if (seg2.query(0, N).second != 0) {
// [0, n) は非ゼロですか？
int ng = 0, ok = N;
while (ng + 1 < ok) {
int m = (ng + ok) / 2;
mint x = seg2.query(0, m).second;
(x == 0 ? ng : ok) = m;
}
v2 = ok - 1;
}
assert(v1 == v2 && "get_min_key");
if (v1 == -1) {
auto kv1 = seg1.get_min_keyval(-1);
assert(kv1.second == T{} && "get_min_keyval");
} else {
auto kv1 = seg1.get_min_keyval(-1);
auto kv2 = make_pair(v2, seg2.get_val(v2));
assert(kv1 == kv2 && "get_min_keyval");
}
},
[&]() {
// get_max_key, get_max_keyval
int v1 = -1;
while (true) {
v1 = seg1.get_max_key(-1);
if (v1 == -1) break;
T val = seg2.get_val(v1);
if (val.second == 1) break;
if (val.second == 0) {
seg1.erase(v1);
seg2.set_val(v1, T{});
} else {
assert(false and "get_max_key");
}
}
int v2 = -1;
if (seg2.query(0, N).second != 0) {
// [i, N) は非ゼロですか？
int ok = 0, ng = N;
while (ok + 1 < ng) {
int m = (ng + ok) / 2;
mint x = seg2.query(m, N).second;
(x == 0 ? ng : ok) = m;
}
v2 = ok;
}
assert(v1 == v2 && "get_max_key");
if (v1 == -1) {
auto kv1 = seg1.get_max_keyval(-1);
assert(kv1.second == T{} && "get_max_keyval");
} else {
auto kv1 = seg1.get_max_keyval(-1);
auto kv2 = make_pair(v2, seg2.get_val(v2));
assert(kv1 == kv2 && "get_mix_keyval");
}
},
[&]() {
// pop_min_key
int v2 = -1;
if (seg2.query(0, N).second != 0) {
// [0, n) は非ゼロですか？
int ng = 0, ok = N;
while (ng + 1 < ok) {
int m = (ng + ok) / 2;
mint x = seg2.query(0, m).second;
(x == 0 ? ng : ok) = m;
}
v2 = ok - 1;
}
if (v2 != -1) {
pair<int, T> kv1;
do {
kv1 = seg1.pop_min_keyval(-1);
} while (kv1.second.second == 0);
auto kv2 = make_pair(v2, seg2.get_val(v2));
assert(kv1 == kv2 && "pop_min_keyval");
seg2.set_val(v2, T{});
}
},
[&]() {
// pop_max_key
int v2 = -1;
if (seg2.query(0, N).second != 0) {
// [i, N) は非ゼロですか？
int ok = 0, ng = N;
while (ok + 1 < ng) {
int m = (ng + ok) / 2;
mint x = seg2.query(m, N).second;
(x == 0 ? ng : ok) = m;
}
v2 = ok;
}
if (v2 != -1) {
pair<int, T> kv1;
do {
kv1 = seg1.pop_max_keyval(-1);
} while (kv1.second.second == 0);
auto kv2 = make_pair(v2, seg2.get_val(v2));
assert(kv1 == kv2 && "pop_max_keyval");
seg2.set_val(v2, T{});
}
},
};
rep(_, 10) {
int qq = vector<ll>{0LL, rng(1, 10), rng(1, Q)}[rng(0, 2)];
rep(qnum, qq) {
int c = rng(0, sz(funcs) - 1);
// trc(c, "cmd");
funcs[c]();
}
{
// make_array
auto vec1 = seg1.make_array();
rep(i, sz(vec1) - 1) assert(vec1[i].fi < vec1[i + 1].fi);
vector<pair<int, T>> vec2;
rep(i, N) {
T val = seg2.get_val(i);
if (val != T{}) vec2.push_back({i, val});
}
// trc(vec1);
// trc(vec2);
int i1 = 0, i2 = 0;
while (i1 != sz(vec1) and i2 != sz(vec2)) {
while (i1 != sz(vec1) and vec1[i1].second == T{}) i1++;
if (i1 == sz(vec1)) break;
assert(vec1[i1] == vec2[i2] and "make_array");
i1++, i2++;
}
while (i1 != sz(vec1) and vec1[i1].second == T{}) i1++;
assert(i1 == sz(vec1) and i2 == sz(vec2) and "make_array");
// trc("make_array ok");
}
seg1.clear();
rep(i, N) seg2.set_val(i, T{});
}
}
void test_tl(const int N = 5 * TEN(5), const int Q = 5 * TEN(5)) {
ll MOD = 998244353;
V<T> init;
rep(i, N) init.emplace_back(rng(0, MOD - 1), rng(0, MOD - 1));
RBSTLazySegmentTree<int, T, E, f, g, h, ti, ei> seg1(init);
LazySegmentTree seg2(init, f, g, h, ti(), ei());
vector<function<void(void)>> funcs{
[&]() {
// apply
int l = +rng(0, 10);
int r = -rng(0, 10) + N;
E x{rng(0, MOD - 1), rng(0, MOD - 1)};
seg1.apply(l, r, x);
seg2.update(l, r, x);
},
[&]() {
// fold
int l = +rng(0, 10);
int r = -rng(0, 10) + N;
auto v1 = seg1.fold(l, r);
auto v2 = seg2.query(l, r);
assert(v1 == v2 and "fold");
},
};
rep(qnum, Q) {
int c = rng(0, sz(funcs) - 1);
// trc(c, "cmd");
funcs[c]();
}
}
void q() {
rep(t, 10) test(10, TEN(4));
//
rep(t, 10) test(100, TEN(4));
//
rep(t, 2) test(TEN(4), TEN(2));
//
test(10, TEN(4));
test(2, TEN(4));
test(1, TEN(4));
cerr << "test OK" << endl;
Timer timer;
test_tl();
cerr << "test_tl OK" << endl;
cerr << "time : " << timer.elapsed() << endl;
}
void Nyaan::solve() {
q();
int a, b;
cin >> a >> b;
cout << a + b << endl;
}
verify/verify-unit-test/rbst-segment-tree.test.cpp