#include "incursion.h"
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
#define fi first
#define se second
#define vi vector<int>
#define vll vector<long long>
#define pii pair<int, int>
#define pll pair<long long, long long>
#define pb push_back
#define mp make_pair
#define eb emplace_back
#define all(x) (x).begin(), (x).end()
#define sz(x) (int)(x).size()
mt19937 rng(chrono::high_resolution_clock::now().time_since_epoch().count());
mt19937_64 rng64(chrono::high_resolution_clock::now().time_since_epoch().count());
inline int rand(int l,int r){return uniform_int_distribution<int>(l, r)(rng);}
inline ll rand(ll l,ll r){return uniform_int_distribution<ll>(l, r)(rng64);}
#ifdef DEBUG
auto&operator<<(auto&o,pair<auto,auto>p){return o<<"("<<p.first<<", "<<p.second<<")";}
auto operator<<(auto&o,auto x)->decltype(x.end(),o){o<<"{";int i=0;for(auto e:x)o<<","+!i++<<e;return o<<"}";}
#define debug(X...)cerr<<"["#X"]: ",[](auto...$){((cerr<<$<<"; "),...)<<endl;}(X)
#else
#define debug(...){}
#endif
vi mark(vector<pii> F, int safe){
int n = sz(F) + 1;
vector<vi> g(n + 1, vi());
vi parent(n + 1, 0);
vi siz(n + 1, 0);
for(int i = 0; i < n - 1; i++){
g[F[i].fi].pb(F[i].se);
g[F[i].se].pb(F[i].fi);
}
auto dfs = [&](int v, int p, auto&&dfs) -> void{
parent[v] = p;
siz[v] = 1;
for(auto u : g[v]){
if(u != p){
dfs(u, v, dfs);
siz[v] += siz[u];
}
}
};
dfs(1, 1, dfs);
int c = 1;
while(true){
bool f = false;
for(auto u : g[c]){
if(u != parent[c] && siz[u] * 2 > n){
c = u;
f = 1;
break;
}
}
if(!f){
break;
}
}
int c2 = 0;
for(auto u : g[c]){
if(u != parent[c] && siz[u] * 2 == n){
c2 = u;
}
}
parent.assign(n + 1, -1);
parent[c] = c2;
parent[c2] = c;
auto dfs2 = [&](int v, auto&&dfs2) -> void{
for(auto u : g[v]){
if(u != parent[v]){
parent[u] = v;
dfs2(u, dfs2);
}
}
};
dfs2(c, dfs2);
if(c2){
dfs2(c2, dfs2);
}
vi res(n, 1);
int curr = safe;
while(curr != c && curr != c2){
res[curr - 1] = 0;
curr = parent[curr];
}
res[curr - 1] = 0;
return res;
}
void locate(vector<pii> F, int curr, int t){
int n = sz(F) + 1;
vector<vi> g(n + 1, vi());
vi parent(n + 1, 0);
vi siz(n + 1, 0);
for(int i = 0; i < n - 1; i++){
g[F[i].fi].pb(F[i].se);
g[F[i].se].pb(F[i].fi);
}
auto dfs = [&](int v, int p, auto&&dfs) -> void{
parent[v] = p;
siz[v] = 1;
for(auto u : g[v]){
if(u != p){
dfs(u, v, dfs);
siz[v] += siz[u];
}
}
};
dfs(1, 1, dfs);
int c = 1;
while(true){
bool f = false;
for(auto u : g[c]){
if(u != parent[c] && siz[u] * 2 > n){
c = u;
f = 1;
break;
}
}
if(!f){
break;
}
}
int c2 = 0;
for(auto u : g[c]){
if(u != parent[c] && siz[u] * 2 == n){
c2 = u;
}
}
parent.assign(n + 1, -1);
parent[c] = c2;
parent[c2] = c;
auto dfs2 = [&](int v, auto&&dfs2) -> void{
siz[v] = 1;
for(auto u : g[v]){
if(u != parent[v]){
parent[u] = v;
dfs2(u, dfs2);
siz[v] += siz[u];
}
}
};
dfs2(c, dfs2);
if(c2){
dfs2(c2, dfs2);
}
vi x(n + 1, -1);
while(t){
x[curr] = t;
t = visit(parent[curr]);
curr = parent[curr];
}
x[curr] = t;
while(true){
if(t){
t = visit(parent[curr]);
curr = parent[curr];
continue;
}
int v = -1;
for(auto u : g[curr]){
if(u == parent[curr] || x[u] != -1){
continue;
}
if(v == -1 || siz[u] > siz[v]){
v = u;
}
}
if(v == -1){
return;
}
x[v] = visit(v);
t = x[v];
curr = v;
}
return;
}
