/* AUTHOR: TUAN ANH - BUI */
// ~~ icebear ~~
#include "incursion.h"
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<int, int> ii;
typedef pair<int, ii> iii;
template<class X, class Y>
bool minimize(X &x, const Y &y) {
if (x > y) return x = y, true;
return false;
}
template<class X, class Y>
bool maximize(X &x, const Y &y) {
if (x < y) return x = y, true;
return false;
}
#define FOR(i,a,b) for(int i=(a); i<=(b); ++i)
#define FORR(i,a,b) for(int i=(a); i>=(b); --i)
#define REP(i, n) for(int i=0; i<(n); ++i)
#define RED(i, n) for(int i=(n)-1; i>=0; --i)
#define MASK(i) (1LL << (i))
#define BIT(S, i) (((S) >> (i)) & 1)
#define mp make_pair
#define pb push_back
#define fi first
#define se second
#define all(x) x.begin(), x.end()
#define task "icebear"
/*END OF TEMPLATE. ICEBEAR AND THE CAT WILL WIN TST26 */
const int MOD = 1e9 + 7;
const int inf = (int)1e9 + 27092008;
const ll INF = (ll)1e18 + 27092008;
const int N = 2e5 + 5;
vector<int> G[N];
int n, sz[N], par[N], h[N], A, forbid = 0;
void loadGraph(vector<pair<int, int>> F) {
n = (int)F.size() + 1;
FOR(i, 1, n) {
G[i].clear();
}
for(auto e : F) {
G[e.fi].pb(e.se);
G[e.se].pb(e.fi);
}
}
void dfs(int u, int p = 0, int depth = 0) {
par[u] = p;
h[u] = depth;
sz[u] = 1;
for(int v : G[u]) if (v != par[u]) {
dfs(v, u, depth + 1);
sz[u] += sz[v];
}
}
vector<int> find_center() {
dfs(1);
int mx = max_element(h + 1, h + n + 1) - h;
dfs(mx);
int r = max_element(h + 1, h + n + 1) - h;
int best = h[r];
vector<int> center;
while(r > 0) {
if (h[r] == best / 2 || h[r] == (best + 1) / 2) center.pb(r);
r = par[r];
}
return center;
}
void find_treasure(int u) {
vector<ii> childs;
for(int v : G[u]) if (v != par[u]) {
childs.emplace_back(sz[v], v);
}
sort(all(childs), greater<ii>());
for(auto &x : childs) {
int T = visit(A = x.se);
if (T == 1) {
find_treasure(x.se);
break;
}
visit(A = u);
}
}
vector<int> mark(vector<pair<int, int>> E, int safe) {
loadGraph(E);
vector<int> center = find_center();
int nearest = 0, best = inf;
for(int x : center) {
dfs(x);
if (minimize(best, h[safe])) nearest = x;
}
dfs(nearest);
vector<int> T(n,0);
while(safe > 0) {
T[safe-1] = 1;
safe = par[safe];
}
return T;
}
void locate(vector<pair<int, int>> E, int S, int T) {
loadGraph(E);
vector<int> center = find_center();
int best = inf, nearest = 0;
for(int x : center) {
dfs(x);
if (minimize(best, h[S])) nearest = x;
}
dfs(nearest);
while(S != nearest && !T) T = visit(S = par[S]);
if (T == 0) {
nearest = S = nearest ^ center[0] ^ center[1];
T = visit(S);
}
dfs(nearest);
find_treasure(S);
}
