#include <vector>
#include <iostream>
#include <cmath>
#include <algorithm>
using namespace std;
template <typename T> void print(T elem) {cout << elem << " ";}
template <typename T> void print(vector<T> &v) {for(auto elem: v) print(elem); cout << endl;}
template <typename T> void print(vector<vector<T>> &v) {for(auto elem: v) print(elem); cout << endl;}
void makeG(vector<vector<int>> &g, vector<int> &u, vector<int> &v) {
for(int i=0; i<u.size(); i++) {
g[u[i]].push_back(v[i]);
g[v[i]].push_back(u[i]);
}
}
int labelSubDecision(int n, int k, vector<vector<int>> &g, vector<int> &u, vector<int> &v) {
if (k==pow(10,9)) return 5;
int cnt = 0;
for(int i=0; i<n; i++) if (g[i].size()>2) cnt++;
if (cnt==0) return 1;
bool subtask2 = true;
for(int i=0; i<u.size(); i++)
if (!(u[i]==i+1 && v[i]==i/2 || u[i]==i/2 && v[i]==i+1)) subtask2= false;
if (subtask2) return 2;
if (cnt==1) return 3;
}
void labelLine(int cnt, int node, vector<vector<int>> &g, vector<int> &labels) {
while(labels[node]==-1) {
labels[node] = cnt++;
for(int elem: g[node]) if (labels[elem]==-1) node = elem;
}
}
void label1(int n, vector<vector<int>> &g, vector<int> &labels) {
int node = 0;
for(int i=0; i<n; i++) if(g[i].size()==1) {node=i; break;}
labelLine(0,node,g,labels);
}
void label2(int n, vector<int> &labels) {
for(int i=0; i<n; i++) labels[i] = i+1;
}
void label3(int n, vector<vector<int>> &g, vector<int> &labels) {
int root = 0;
for(int i=0; i<n; i++) if(g[i].size() > 2) {root = i; break;}
labels[root] = 1'000;
for(int i=0; i<g[root].size(); i++) {
int child = g[root][i];
labelLine((i+1)*1'000+1,child,g,labels);
}
}
void dfs(int node, int offset, vector<vector<int>> &g, vector<int> &labels) {
for(int i=0; i<g[node].size(); i++) {
int child = g[node][i];
if(labels[child]!=-1) continue;
labels[child] = labels[node] + offset*(i+1);
dfs(child,offset/10,g,labels);
}
}
void label4(vector<vector<int>> &g, vector<int> &labels) {
labels[0] = pow(10,7);
dfs(0,pow(10,6),g,labels);
}
int dfs2(int node, int cnt, int d, vector<vector<int>> &g, vector<int> &pre, vector<int> &post, vector<int> &dist) {
if (pre[node]!=-1) return cnt;
pre[node] = cnt++;
dist[node] = d++;
for(int child: g[node])
cnt = dfs2(child,cnt,d,g,pre,post,dist);
post[node] = cnt++;
return cnt;
}
void relabel(int n, vector<int> &labels) {
vector<pair<int,int>> temp;
for(int i=0; i<n; i++)
temp.push_back({labels[i],i});
sort(temp.begin(),temp.end());
for(int i=0; i<n; i++)
labels[temp[i].second] = i;
}
void label5(int n, vector<vector<int>> &g, vector<int> &labels) {
vector<int> pre(n,-1), post(n,-1), dist(n,-1);
dfs2(0,0,0,g,pre,post,dist);
for(int i=0; i<n; i++)
labels[i] = dist[i]%2? post[i]:pre[i];
relabel(n, labels);
// print(labels);
}
std::vector<int> label(int n, int k, std::vector<int> u, std::vector<int> v) {
vector<vector<int>> g(n);
makeG(g,u,v);
int subtask = labelSubDecision(n,k,g,u,v);
vector<int> labels(n,-1);
switch(subtask) {
case 1: label1(n,g,labels); return labels;
case 2: label2(n,labels); return labels;
case 3: label3(n,g,labels); return labels;
case 4: label4(g,labels); return labels;
case 5: label5(n,g,labels); return labels;
}
}
int findSubDecision(int s, int t, vector<int> &c) {
return 5;
// if (s >= pow(10,7)) return 4;
// if (s >= 1'000 && t >= 1'000) return 3;
for(int i=0; i<c.size(); i++)
if (c[i] < s-1 || c[i] > s+1) return 2;
return 1;
}
int find1(int s, int t, vector<int> &c) {
if (c.size()==1) return c[0];
else return t<s? c[0]:c[1];
}
bool ancestor(int a, int b) {
if (a==0) return true;
while(b!=0) { if(a==b) return true; else b >>= 1; }
return false;
}
int find2(int s, int t, vector<int> &c) {
reverse(c.begin(),c.end());
for(int elem: c) if(ancestor(elem,t)) return elem;
return c[c.size()-1];
}
int find3(int s, int t, vector<int> &c) {
if (s==1'000) { for(int elem: c) if(t/1000==elem/1000) return elem; }
else if (s/1000 == t/1000 && s < t) { for(int elem: c) if(elem > s) return elem; }
else { for(int elem: c) if(elem < s) return elem; }
}
bool ancestor4(int a, int b) {
int divisor = 1;
for(int i=0; i<=7; i++) {
if (b - b % divisor == a) return true;
divisor *= 10;
}
return false;
}
int find4(int s, int t, vector<int> &c) {
reverse(c.begin(),c.end());
for(int elem: c) if(ancestor4(elem,t)) return elem;
return c[c.size()-1];
}
int find5(int s, int t, vector<int> &c) {
int m = c.size();
// cout << "s:" << s << " t:" << t<< endl;
if (m==1) return c[0];
else if (s==0) { for(int elem: c) if(t<=elem) return elem; }
else if (s<c[0]) { // s is pre and c[i] is post.
if (t<s) return c[m-1];
for(int i=0; i<m-1; i++) if (t<=c[i]) return c[i];
return c[m-1];
}
else { // s is post and c[i] is pre.
if (t>s) return c[0];
for(int i=1; i<m; i++)
if(t < c[i]) return c[i-1];
return c[m-1];
}
}
int find_next_station(int s, int t, std::vector<int> c) {
int subtask = findSubDecision(s,t,c);
switch(subtask) {
case 1: return find1(s,t,c);
case 2: return find2(s,t,c);
case 3: return find3(s,t,c);
case 4: return find4(s,t,c);
case 5: return find5(s,t,c);
}
return c[0];
}
