#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace std;
using namespace __gnu_pbds;
template<typename T> using Tree = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
typedef long long int ll;
typedef long double ld;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;
#define fastio ios_base::sync_with_stdio(false); cin.tie(NULL)
#define pb push_back
#define endl '\n'
#define sz(a) (int)a.size()
#define setbits(x) __builtin_popcountll(x)
#define ff first
#define ss second
#define conts continue
#define ceil2(x,y) ((x+y-1)/(y))
#define all(a) a.begin(), a.end()
#define rall(a) a.rbegin(), a.rend()
#define yes cout << "Yes" << endl
#define no cout << "No" << endl
#define rep(i,n) for(int i = 0; i < n; ++i)
#define rep1(i,n) for(int i = 1; i <= n; ++i)
#define rev(i,s,e) for(int i = s; i >= e; --i)
#define trav(i,a) for(auto &i : a)
template<typename T>
void amin(T &a, T b) {
a = min(a,b);
}
template<typename T>
void amax(T &a, T b) {
a = max(a,b);
}
#ifdef LOCAL
#include "debug.h"
#else
#define debug(...) 42
#endif
/*
read the edi a long time ago, dont really remember much from there
*/
const int MOD = 1e9 + 7;
const int N = 1e5 + 5;
const int inf1 = int(1e9) + 5;
const ll inf2 = ll(1e18) + 5;
#include "incursion.h"
std::vector<int> mark(std::vector<std::pair<int, int>> F, int safe) {
// return {2, 2, 0};
int n = sz(F)+1;
vector<vector<int>> adj(n+5);
for(auto [u,v] : F){
adj[u].pb(v), adj[v].pb(u);
}
vector<int> par(n+5), subsiz(n+5);
auto dfs = [&](int u, int p, auto &&dfs) -> void{
par[u] = p;
subsiz[u] = 1;
trav(v,adj[u]){
if(v == p) conts;
dfs(v,u,dfs);
subsiz[u] += subsiz[v];
}
};
dfs(1,-1,dfs);
vector<int> centroids;
rep1(u,n){
bool ok = true;
trav(v,adj[u]){
int s = subsiz[v];
if(v == par[u]){
s = n-subsiz[u];
}
if(s > n/2){
ok = false;
}
}
if(ok){
centroids.pb(u);
}
}
int siz = sz(centroids);
assert(siz >= 1 and siz <= 2);
auto can_reach = [&](int u, int p, auto &&can_reach) -> bool{
bool ok = false;
if(u == safe) ok = true;
trav(v,adj[u]){
if(v == p) conts;
if(count(all(centroids),v)) conts;
ok |= can_reach(v,u,can_reach);
}
return ok;
};
int r = -1;
if(siz == 1){
r = centroids[0];
}
else{
rep(j,2){
if(can_reach(centroids[j],-1,can_reach)){
assert(r == -1);
r = centroids[j];
}
}
}
assert(r != -1);
dfs(r,-1,dfs);
vector<int> ans(n);
while(safe != -1){
ans[safe-1] = 1;
safe = par[safe];
}
return ans;
}
void locate(std::vector<std::pair<int, int>> F, int curr, int cnt) {
int n = sz(F)+1;
vector<vector<int>> adj(n+5);
for(auto [u,v] : F){
adj[u].pb(v), adj[v].pb(u);
}
vector<int> par(n+5), subsiz(n+5);
auto dfs = [&](int u, int p, auto &&dfs) -> void{
par[u] = p;
subsiz[u] = 1;
trav(v,adj[u]){
if(v == p) conts;
dfs(v,u,dfs);
subsiz[u] += subsiz[v];
}
};
dfs(1,-1,dfs);
vector<int> centroids;
rep1(u,n){
bool ok = true;
trav(v,adj[u]){
int s = subsiz[v];
if(v == par[u]){
s = n-subsiz[u];
}
if(s > n/2){
ok = false;
}
}
if(ok){
centroids.pb(u);
}
}
int siz = sz(centroids);
assert(siz >= 1 and siz <= 2);
int r = centroids[0];
dfs(r,-1,dfs);
if(siz == 1){
while(!cnt){
cnt = visit(par[curr]);
curr = par[curr];
}
while(true){
vector<pii> ord;
trav(v,adj[curr]){
if(v == par[curr]) conts;
ord.pb({subsiz[v],v});
}
sort(rall(ord));
int nxt = -1;
for(auto [s,v] : ord){
int x = visit(v);
if(x){
nxt = v;
break;
}
visit(curr);
}
if(nxt == -1) break;
curr = nxt;
}
return;
}
while(!cnt){
if(curr == r){
curr = centroids[0]^centroids[1]^curr;
visit(curr);
break;
}
cnt = visit(par[curr]);
curr = par[curr];
}
while(true){
vector<pii> ord;
trav(v,adj[curr]){
if(v == par[curr]) conts;
ord.pb({subsiz[v],v});
}
sort(rall(ord));
int nxt = -1;
for(auto [s,v] : ord){
int x = visit(v);
if(x){
nxt = v;
break;
}
visit(curr);
}
if(nxt == -1) break;
curr = nxt;
}
// int x;
// x = visit(3);
// if (x != 2) {
// return;
// }
// x = visit(1);
// if (x != 0) {
// return;
// }
// x = visit(3);
// if (x != 2) {
// return;
// }
// x = visit(2);
// if (x != 2) {
// return;
// }
// return;
}
