noya2_Library
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test/tree/aoj_0489.test.cpp
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- Last update: 2025-01-09 04:05:33+09:00
- Problem: https://onlinejudge.u-aizu.ac.jp/problems/0489
Depends on
- data_structure/segment_tree.hpp
- misc/mo_algorithm.hpp
- template/const.hpp
- template/inout_old.hpp
- template/template.hpp
- template/utils.hpp
- Mo on Tree
(tree/Mo_on_Tree.hpp)
- Heavy Light Decomposition
(tree/heavy_light_decomposition.hpp)
Code
#define PROBLEM "https://onlinejudge.u-aizu.ac.jp/problems/0489"
#include"../../template/template.hpp"
#include"../../tree/Mo_on_Tree.hpp"
#include"../../tree/heavy_light_decomposition.hpp"
#include"../../data_structure/segment_tree.hpp"
const int geta = 1'000'000;
const int mx = geta*2+10;
int op(int a, int b){
return a + b;
}
int e(){
return 0;
}
using ar = array<int,3>;
int main(){
int n, m; in(n,m);
vector<int> a(n); in(a);
vector<ar> querys;
vector<pii> es(n-1); in(es);
{
int pre = n+1;
while (m--){
int t; in(t);
if (t == 1){
int u, w; in(u,w);
es.emplace_back(u,pre++);
a.emplace_back(w);
}
if (t == 2){
int u, v, k; in(u,v,k); u--, v--, k--;
querys.push_back({u,v,k});
}
}
n = es.size()+1;
m = querys.size();
}
MoTree_vertex<int> mo(n,a);
hld_tree g(n);
for (auto &[u, v] : es){
u--, v--;
mo.add_edge(u,v);
g.add_edge(u,v);
}
mo.build(querys.size());
for (auto [u, v, k] : querys){
mo.insert(u,v,g.lca(u,v));
}
segtree<int,op,e> seg(mx);
vector<int> ans(querys.size());
auto get = [&](int k){
auto f = [&](int cnt){
return cnt <= k;
};
return seg.max_right(0,f) - geta;
};
auto add = [&](int v){
v += geta;
seg.set(v,seg.get(v)+1);
};
auto del = [&](int v){
v += geta;
seg.set(v,seg.get(v)-1);
};
auto ask = [&](int i){
ans[i] = get(querys[i][2]);
};
mo.run(add,del,ask);
for (auto z : ans) out(z);
}#line 1 "test/tree/aoj_0489.test.cpp"
#define PROBLEM "https://onlinejudge.u-aizu.ac.jp/problems/0489"
#line 2 "template/template.hpp"
using namespace std;
#include<bits/stdc++.h>
#line 1 "template/inout_old.hpp"
namespace noya2 {
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;
}
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...);
}
template<typename T>
void out(const vector<vector<T>> &vv){
int s = (int)vv.size();
for (int i = 0; i < s; i++) out(vv[i]);
}
struct IoSetup {
IoSetup(){
cin.tie(nullptr);
ios::sync_with_stdio(false);
cout << fixed << setprecision(15);
cerr << fixed << setprecision(7);
}
} iosetup_noya2;
} // namespace noya2
#line 1 "template/const.hpp"
namespace noya2{
const int iinf = 1'000'000'007;
const long long linf = 2'000'000'000'000'000'000LL;
const long long mod998 = 998244353;
const long long mod107 = 1000000007;
const long double pi = 3.14159265358979323;
const vector<int> dx = {0,1,0,-1,1,1,-1,-1};
const vector<int> dy = {1,0,-1,0,1,-1,-1,1};
const string ALP = "ABCDEFGHIJKLMNOPQRSTUVWXYZ";
const string alp = "abcdefghijklmnopqrstuvwxyz";
const string NUM = "0123456789";
void yes(){ cout << "Yes\n"; }
void no(){ cout << "No\n"; }
void YES(){ cout << "YES\n"; }
void NO(){ cout << "NO\n"; }
void yn(bool t){ t ? yes() : no(); }
void YN(bool t){ t ? YES() : NO(); }
} // namespace noya2
#line 2 "template/utils.hpp"
#line 6 "template/utils.hpp"
namespace noya2{
unsigned long long inner_binary_gcd(unsigned long long a, unsigned long long b){
if (a == 0 || b == 0) return a + b;
int n = __builtin_ctzll(a); a >>= n;
int m = __builtin_ctzll(b); b >>= m;
while (a != b) {
int mm = __builtin_ctzll(a - b);
bool f = a > b;
unsigned long long c = f ? a : b;
b = f ? b : a;
a = (c - b) >> mm;
}
return a << std::min(n, m);
}
template<typename T> T gcd_fast(T a, T b){ return static_cast<T>(inner_binary_gcd(std::abs(a),std::abs(b))); }
long long sqrt_fast(long long n) {
if (n <= 0) return 0;
long long x = sqrt(n);
while ((x + 1) * (x + 1) <= n) x++;
while (x * x > n) x--;
return x;
}
template<typename T> T floor_div(const T n, const T d) {
assert(d != 0);
return n / d - static_cast<T>((n ^ d) < 0 && n % d != 0);
}
template<typename T> T ceil_div(const T n, const T d) {
assert(d != 0);
return n / d + static_cast<T>((n ^ d) >= 0 && n % d != 0);
}
template<typename T> void uniq(std::vector<T> &v){
std::sort(v.begin(),v.end());
v.erase(unique(v.begin(),v.end()),v.end());
}
template <typename T, typename U> inline bool chmin(T &x, U y) { return (y < x) ? (x = y, true) : false; }
template <typename T, typename U> inline bool chmax(T &x, U y) { return (x < y) ? (x = y, true) : false; }
template<typename T> inline bool range(T l, T x, T r){ return l <= x && x < r; }
} // namespace noya2
#line 8 "template/template.hpp"
#define rep(i,n) for (int i = 0; i < (int)(n); i++)
#define repp(i,m,n) for (int i = (m); i < (int)(n); i++)
#define reb(i,n) for (int i = (int)(n-1); i >= 0; i--)
#define all(v) (v).begin(),(v).end()
using ll = long long;
using ld = long double;
using uint = unsigned int;
using ull = unsigned long long;
using pii = pair<int,int>;
using pll = pair<ll,ll>;
using pil = pair<int,ll>;
using pli = pair<ll,int>;
namespace noya2{
/* ~ (. _________ . /) */
}
using namespace noya2;
#line 2 "tree/Mo_on_Tree.hpp"
#line 2 "misc/mo_algorithm.hpp"
/*
usage : https://nyaannyaan.github.io/library/modulo/multipoint-binomial-sum.hpp
*/
#line 10 "misc/mo_algorithm.hpp"
namespace noya2{
struct Mo {
int width;
std::vector<int> left, right, order;
Mo(int N = 1, int Q = 1): order(Q) {
width = std::max<int>(1, 1.0 * N / std::max<double>(1.0, std::sqrt(Q * 2.0 / 3.0)));
std::iota(begin(order), end(order), 0);
}
void insert(int l, int r) { /* [l, r) */
left.emplace_back(l);
right.emplace_back(r);
}
template <typename AL, typename AR, typename DL, typename DR, typename REM>
void run(const AL& add_left, const AR& add_right, const DL& delete_left,
const DR& delete_right, const REM& rem) {
assert(left.size() == order.size());
sort(begin(order), end(order), [&](int a, int b) {
int ablock = left[a] / width, bblock = left[b] / width;
if (ablock != bblock) return ablock < bblock;
if (ablock & 1) return right[a] < right[b];
return right[a] > right[b];
});
int nl = 0, nr = 0;
for (auto idx : order) {
while (nl > left[idx]) add_left(--nl);
while (nr < right[idx]) add_right(nr++);
while (nl < left[idx]) delete_left(nl++);
while (nr > right[idx]) delete_right(--nr);
rem(idx);
}
}
};
}
#line 5 "tree/Mo_on_Tree.hpp"
/*
MoTree_edge is verified with : https://atcoder.jp/contests/pakencamp-2022-day1/submissions/43052952
*/
namespace noya2{
template<class T>
struct MoTree_edge {
int n;
vector<vector<pair<int,T>>> es;
MoTree_edge (int _n) : n(_n) {
es.resize(n);
}
void add_edge(int u, int v, T w){
es[u].emplace_back(v,w);
es[v].emplace_back(u,w);
}
vector<int> in;
vector<pair<int,T>> vals;
Mo mo;
void build(int q){
int tnow = 0;
auto dfs = [&](auto dfs, int v, int f) -> void {
in[v] = tnow++;
for (auto [u, w] : es[v]){
if (u == f) continue;
vals.emplace_back(u,w);
dfs(dfs,u,v);
vals.emplace_back(u,w);
tnow++;
}
};
in.resize(n);
dfs(dfs,0,-1);
mo = Mo(2*n-2,q);
}
void insert(int u, int v){
u = in[u], v = in[v];
if (u > v) swap(u,v);
mo.insert(u,v);
}
template<typename ADD, typename DEL, typename REM>
void run(const ADD &add, const DEL &del, const REM &rem){
vector<bool> contain(n,false);
auto change = [&](int i){
int id = vals[i].first;
if (contain[id]){
del(vals[i].second);
contain[id] = false;
}
else {
add(vals[i].second);
contain[id] = true;
}
};
mo.run(change,change,change,change,rem);
}
};
template<class T>
struct MoTree_vertex {
int n;
vector<vector<int>> es;
vector<T> b;
MoTree_vertex (int _n, vector<T> _b) : n(_n), b(_b) {
es.resize(n);
}
void add_edge(int u, int v){
es[u].emplace_back(v);
es[v].emplace_back(u);
}
vector<int> in;
vector<pair<int,T>> vals;
vector<int> lcas;
Mo mo;
void build(int q){
vals.reserve(2*n-2);
lcas.reserve(q);
int tnow = 0;
auto dfs = [&](auto dfs, int v, int f) -> void {
in[v] = tnow++;
for (auto u : es[v]){
if (u == f) continue;
vals.emplace_back(u,b[u]);
dfs(dfs,u,v);
vals.emplace_back(u,b[u]);
tnow++;
}
};
in.resize(n);
dfs(dfs,0,-1);
mo = Mo(2*n-2,q);
}
void insert(int u, int v, int lca){
u = in[u], v = in[v];
if (u > v) swap(u,v);
mo.insert(u,v);
lcas.push_back(lca);
}
template<typename ADD, typename DEL, typename REM>
void run(const ADD &add, const DEL &del, const REM &rem){
vector<bool> contain(n,false);
auto change = [&](int i){
int id = vals[i].first;
if (contain[id]){
del(vals[i].second);
contain[id] = false;
}
else {
add(vals[i].second);
contain[id] = true;
}
};
auto rem_add_lca = [&](int i){
add(b[lcas[i]]);
rem(i);
del(b[lcas[i]]);
};
mo.run(change,change,change,change,rem_add_lca);
}
};
} // namespace noya2
#line 2 "tree/heavy_light_decomposition.hpp"
#line 6 "tree/heavy_light_decomposition.hpp"
#include <ranges>
#line 9 "tree/heavy_light_decomposition.hpp"
// #include "data_structure/csr.hpp"
namespace noya2 {
struct hld_tree {
int n, root;
std::vector<int> down, nxt, sub, tour;
// noya2::internal::csr<int> childs;
// default constructor (nop)
hld_tree () {}
// tree with _n node
// after construct, call input_edges / input_parents / add_edge _n - 1 times
hld_tree (int _n, int _root = 0) : n(_n), root(_root), down(n), nxt(n), sub(n, 1), tour(n) {
if (n == 1){
nxt[0] = -1;
down[0] = -1;
build_from_parents();
}
}
// par[i] < i, par[0] == -1
hld_tree (const std::vector<int> &par) : n(par.size()), root(0), down(n, -1), nxt(par), sub(n, 1), tour(n){
build_from_parents();
}
// par[i] < i, par[0] == -1
hld_tree (std::vector<int> &&par) : n(par.size()), root(0), down(n, -1), sub(n, 1), tour(n) {
nxt.swap(par);
build_from_parents();
}
// distinct unweighted undirected n - 1 edges of tree
hld_tree (const std::vector<std::pair<int, int>> &es, int _root = 0) : n(es.size() + 1), root(_root), down(n), nxt(n), sub(n, 1), tour(n) {
for (auto &[u, v] : es){
down[u]++;
down[v]++;
nxt[u] ^= v;
nxt[v] ^= u;
}
build_from_edges();
}
// input parents from cin
template<int indexed = 1>
void input_parents(){
// using std::cin;
nxt[0] = -1;
for (int u = 1; u < n; u++){
cin >> nxt[u];
nxt[u] -= indexed;
}
build_from_parents();
}
// input n - 1 edges from cin
template<int indexed = 1>
void input_edges(){
// using std::cin;
for (int i = 1; i < n; i++){
int u, v; cin >> u >> v;
u -= indexed;
v -= indexed;
down[u]++;
down[v]++;
nxt[u] ^= v;
nxt[v] ^= u;
}
build_from_edges();
}
void add_edge(int u, int v){
down[u]++;
down[v]++;
nxt[u] ^= v;
nxt[v] ^= u;
// use tour[0] as counter
if (++tour[0] == n - 1){
build_from_edges();
}
}
size_t size() const {
return n;
}
// top vertex of heavy path which contains v
int leader(int v) const {
return nxt[v] < 0 ? v : nxt[v];
}
// level ancestor
// ret is ancestor of v, dist(ret, v) == d
// if d > depth(v), return -1
int la(int v, int d) const {
while (v != -1){
int u = leader(v);
if (down[v] - d >= down[u]){
v = tour[down[v] - d];
break;
}
d -= down[v] - down[u] + 1;
v = (u == root ? -1 : ~nxt[u]);
}
return v;
}
// lowest common ancestor of u and v
int lca(int u, int v) const {
int du = down[u], dv = down[v];
if (du > dv){
std::swap(du, dv);
std::swap(u, v);
}
if (dv < du + sub[u]){
return u;
}
while (du < dv){
v = ~nxt[leader(v)];
dv = down[v];
}
return v;
}
// distance from u to v
int dist(int u, int v) const {
int _dist = 0;
while (leader(u) != leader(v)){
if (down[u] > down[v]) std::swap(u, v);
_dist += down[v] - down[leader(v)] + 1;
v = ~nxt[leader(v)];
}
_dist += std::abs(down[u] - down[v]);
return _dist;
}
// d times move from to its neighbor (direction of to)
// if d > dist(from, to), return -1
int jump(int from, int to, int d) const {
int _from = from, _to = to;
int dist_from_lca = 0, dist_to_lca = 0;
while (leader(_from) != leader(_to)){
if (down[_from] > down[_to]){
dist_from_lca += down[_from] - down[leader(_from)] + 1;
_from = ~nxt[leader(_from)];
}
else {
dist_to_lca += down[_to] - down[leader(_to)] + 1;
_to = ~nxt[leader(_to)];
}
}
if (down[_from] > down[_to]){
dist_from_lca += down[_from] - down[_to];
}
else {
dist_to_lca += down[_to] - down[_from];
}
if (d <= dist_from_lca){
return la(from, d);
}
d -= dist_from_lca;
if (d <= dist_to_lca){
return la(to, dist_to_lca - d);
}
return -1;
}
// parent of v (if v is root, return -1)
int parent(int v) const {
if (v == root) return -1;
return (nxt[v] < 0 ? ~nxt[v] : tour[down[v] - 1]);
}
// visiting time in euler tour
// usage : seg.set(index(v), X[v])
int index(int vertex) const {
return down[vertex];
}
// usage : seg.set(index_edge(e.u, e.v), e.val)
int index(int vertex1, int vertex2) const {
return std::max(down[vertex1], down[vertex2]);
}
// subtree size of v
int subtree_size(int v) const {
return sub[v];
}
// prod in subtree v : seg.prod(subtree_l(v), subtree_r(v))
int subtree_l(int v) const {
return down[v];
}
int subtree_r(int v) const {
return down[v] + sub[v];
}
// v is in subtree r
bool is_in_subtree(int r, int v) const {
return subtree_l(r) <= subtree_l(v) && subtree_r(v) <= subtree_r(r);
}
// distance table from s
std::vector<int> dist_table(int s) const {
std::vector<int> table(n, -1);
table[s] = 0;
while (s != root){
table[parent(s)] = table[s] + 1;
s = parent(s);
}
for (int v : tour){
if (table[v] == -1){
table[v] = table[parent(v)] + 1;
}
}
return table;
}
// dist, v1, v2
std::tuple<int, int, int> diameter() const {
std::vector<int> dep = dist_table(root);
int v1 = std::ranges::max_element(dep) - dep.begin();
std::vector<int> fromv1 = dist_table(v1);
int v2 = std::ranges::max_element(fromv1) - fromv1.begin();
return {fromv1[v2], v1, v2};
}
// vertex array {from, ..., to}
std::vector<int> path(int from, int to) const {
int d = dist(from, to);
std::vector<int> _path(d + 1);
int front = 0, back = d;
while (from != to){
if (down[from] > down[to]){
_path[front++] = from;
from = parent(from);
}
else {
_path[back--] = to;
to = parent(to);
}
}
_path[front] = from;
return _path;
}
// path decomposition and query (vertex weighted)
// if l < r, decsending order tour[l, r)
// if l > r, acsending order tour(l, r]
template<bool vertex = true>
void path_query(int u, int v, auto f) const {
while (leader(u) != leader(v)){
if (down[u] < down[v]){
f(down[leader(v)], down[v] + 1);
v = ~nxt[leader(v)];
}
else {
f(down[u] + 1, down[leader(u)]);
u = ~nxt[leader(u)];
}
}
if constexpr (vertex){
if (down[u] < down[v]){
f(down[u], down[v] + 1);
}
else {
f(down[u] + 1, down[v]);
}
}
else {
if (down[u] != down[v]){
f(down[u] + 1, down[v] + 1);
}
}
}
// {parent, mapping} : cptree i is correspond to tree mapping[i]. parent[i] is parent of i in cptree.
// parent[i] < i, parent[0] == -1
std::pair<std::vector<int>, std::vector<int>> compressed_tree(std::vector<int> vs) const {
if (vs.empty()){
return {{},{}};
}
auto comp = [&](int l, int r){
return down[l] < down[r];
};
std::ranges::sort(vs, comp);
int sz = vs.size(); vs.reserve(2*sz);
for (int i = 0; i < sz-1; i++){
vs.emplace_back(lca(vs[i], vs[i+1]));
}
std::sort(vs.begin() + sz, vs.end(), comp);
std::ranges::inplace_merge(vs, vs.begin() + sz, comp);
auto del = std::ranges::unique(vs);
vs.erase(del.begin(), del.end());
sz = vs.size();
std::stack<int> st;
std::vector<int> par(sz);
par[0] = -1;
st.push(0);
for (int i = 1; i < sz; i++){
while (!is_in_subtree(vs[st.top()], vs[i])) st.pop();
par[i] = st.top();
st.push(i);
}
return {par, vs};
}
/* CSR
// build csr for using operator()
void build_csr(){
childs = noya2::internal::csr<int>(n, n - 1);
for (int v = 0; v < n; v++){
if (v == root) continue;
childs.add(parent(v), v);
}
childs.build();
}
const auto operator()(int v) const {
return childs[v];
}
auto operator()(int v){
return childs[v];
}
*/
// hld_tree g;
// euler tour order : `for (int v : g)`
// with range_adaptor : `for (int v : g | std::views::reverse)`
// bottom-up DP : `for (int v : g | std::views::drop(1) | std::views::reverse){ update dp[g.parent(v)] by dp[v] }`
auto begin() const {
return tour.begin();
}
auto end() const {
return tour.end();
}
private:
// nxt[v] : parent of v, nxt[0] == -1
void build_from_parents(){
for (int u = n - 1; u >= 1; u--){
int v = nxt[u];
sub[v] += sub[u];
down[v] = std::max(down[v], sub[u]);
}
for (int u = n - 1; u >= 1; u--){
int v = nxt[u];
if (down[v] == sub[u]){
sub[u] = ~sub[u];
down[v] = ~down[v];
}
}
sub[0] = ~down[0] + 1;
down[0] = 0;
for (int u = 1; u < n; u++){
int v = nxt[u];
int nsub = ~down[u] + 1;
if (sub[u] < 0){
down[u] = down[v] + 1;
nxt[u] = (nxt[v] < 0 ? v : nxt[v]);
}
else {
down[u] = down[v] + sub[v];
sub[v] += sub[u];
nxt[u] = ~v;
}
sub[u] = nsub;
}
for (int u = 0; u < n; u++){
tour[down[u]] = u;
}
}
// down[v] : degree of v
// nxt[v] : xor prod of neighbor of v
void build_from_edges(){
// use tour as queue
int back = 0;
for (int u = 0; u < n; u++){
if (u != root && down[u] == 1){
tour[back++] = u;
}
}
for (int front = 0; front < n - 1; front++){
int u = tour[front];
down[u] = -1;
int v = nxt[u]; // parent of v
nxt[v] ^= u;
if (--down[v] == 1 && v != root){
tour[back++] = v;
}
}
// check : now, tour is reverse of topological order
tour.pop_back();
// check : now, down[*] <= 1
for (int u : tour){
int v = nxt[u];
// subtree size (initialized (1,1,...,1))
sub[v] += sub[u];
// heaviest subtree of its child
down[v] = std::max(down[v], sub[u]);
}
for (int u : tour){
int v = nxt[u];
// whether u is not the top of heavy path
if (down[v] == sub[u]){
sub[u] = ~sub[u];
down[v] = ~down[v];
}
}
// after appearing v as u (or v == root),
// down[v] is the visiting time of euler tour
// nxt[v] is the lowest vertex of heavy path which contains v
// (if v itself, nxt[v] is ~(parent of v))
// sub[v] + down[v] is the light child's starting time of euler tour
// note : heavy child's visiting time of euler tour is (the time of its parent) + 1
sub[root] = ~down[root] + 1;
down[root] = 0;
nxt[root] = -1;
for (int u : tour | std::views::reverse){
int v = nxt[u];
int nsub = ~down[u] + 1;
// heavy child
if (sub[u] < 0){
down[u] = down[v] + 1;
nxt[u] = (nxt[v] < 0 ? v : nxt[v]);
}
// light child
else {
down[u] = down[v] + sub[v];
sub[v] += sub[u];
nxt[u] = ~v;
}
sub[u] = nsub;
}
// tour is inverse permutation of down
tour.push_back(0);
for (int u = 0; u < n; u++){
tour[down[u]] = u;
}
}
};
} // namespace noya2
#line 2 "data_structure/segment_tree.hpp"
namespace noya2{
template <class S, S (*op)(S, S), S (*e)()> struct segtree {
public:
segtree() : segtree(0) {}
segtree(int n) : segtree(std::vector<S>(n, e())) {}
segtree(const std::vector<S>& v) : _n(int(v.size())) {
log = 0;
size = 1;
while (size < _n) size <<= 1, log++;
d = std::vector<S>(2 * size, e());
for (int i = 0; i < _n; i++) d[size + i] = v[i];
for (int i = size - 1; i >= 1; i--) {
update(i);
}
}
void set(int p, S x) {
assert(0 <= p && p < _n);
p += size;
d[p] = x;
for (int i = 1; i <= log; i++) update(p >> i);
}
S get(int p) {
assert(0 <= p && p < _n);
return d[p + size];
}
S prod(int l, int r) {
assert(0 <= l && l <= r && r <= _n);
S sml = e(), smr = e();
l += size;
r += size;
while (l < r) {
if (l & 1) sml = op(sml, d[l++]);
if (r & 1) smr = op(d[--r], smr);
l >>= 1;
r >>= 1;
}
return op(sml, smr);
}
S all_prod() { return d[1]; }
template <bool (*f)(S)> int max_right(int l) {
return max_right(l, [](S x) { return f(x); });
}
template <class F> int max_right(int l, F f) {
assert(0 <= l && l <= _n);
assert(f(e()));
if (l == _n) return _n;
l += size;
S sm = e();
do {
while (l % 2 == 0) l >>= 1;
if (!f(op(sm, d[l]))) {
while (l < size) {
l = (2 * l);
if (f(op(sm, d[l]))) {
sm = op(sm, d[l]);
l++;
}
}
return l - size;
}
sm = op(sm, d[l]);
l++;
} while ((l & -l) != l);
return _n;
}
template <bool (*f)(S)> int min_left(int r) {
return min_left(r, [](S x) { return f(x); });
}
template <class F> int min_left(int r, F f) {
assert(0 <= r && r <= _n);
assert(f(e()));
if (r == 0) return 0;
r += size;
S sm = e();
do {
r--;
while (r > 1 && (r % 2)) r >>= 1;
if (!f(op(d[r], sm))) {
while (r < size) {
r = (2 * r + 1);
if (f(op(d[r], sm))) {
sm = op(d[r], sm);
r--;
}
}
return r + 1 - size;
}
sm = op(d[r], sm);
} while ((r & -r) != r);
return 0;
}
private:
int _n, size, log;
std::vector<S> d;
void update(int k) { d[k] = op(d[2 * k], d[2 * k + 1]); }
};
} // namespace noya2
#line 7 "test/tree/aoj_0489.test.cpp"
const int geta = 1'000'000;
const int mx = geta*2+10;
int op(int a, int b){
return a + b;
}
int e(){
return 0;
}
using ar = array<int,3>;
int main(){
int n, m; in(n,m);
vector<int> a(n); in(a);
vector<ar> querys;
vector<pii> es(n-1); in(es);
{
int pre = n+1;
while (m--){
int t; in(t);
if (t == 1){
int u, w; in(u,w);
es.emplace_back(u,pre++);
a.emplace_back(w);
}
if (t == 2){
int u, v, k; in(u,v,k); u--, v--, k--;
querys.push_back({u,v,k});
}
}
n = es.size()+1;
m = querys.size();
}
MoTree_vertex<int> mo(n,a);
hld_tree g(n);
for (auto &[u, v] : es){
u--, v--;
mo.add_edge(u,v);
g.add_edge(u,v);
}
mo.build(querys.size());
for (auto [u, v, k] : querys){
mo.insert(u,v,g.lca(u,v));
}
segtree<int,op,e> seg(mx);
vector<int> ans(querys.size());
auto get = [&](int k){
auto f = [&](int cnt){
return cnt <= k;
};
return seg.max_right(0,f) - geta;
};
auto add = [&](int v){
v += geta;
seg.set(v,seg.get(v)+1);
};
auto del = [&](int v){
v += geta;
seg.set(v,seg.get(v)-1);
};
auto ask = [&](int i){
ans[i] = get(querys[i][2]);
};
mo.run(add,del,ask);
for (auto z : ans) out(z);
}