#include <vector>
#include <iostream>
#include <cmath>
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 4;
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;
}
return;
}
void labelSub1(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;
labelLine(0,node,g,labels);
return;
}
void labelSub2(int n, vector<int> &labels) {
for(int i=0; i<n; i++)
labels[i] = i+1;
return;
}
void labelSub3(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++)
labelLine((i+1)*1'000+1,g[root][i],g,labels);
}
void dfs(int node, int base, int offset, vector<vector<int>> &g, vector<int> &labels) {
if(labels[node]!=-1) return;
labels[node] = base + offset;
for(int i=0; i<g[node].size(); i++)
dfs(g[node][i],labels[node],offset/10*(i+1),g,labels);
return;
}
void labelSub4(int n, vector<vector<int>> &g, vector<int> &labels) {
dfs(0,0,pow(10,7),g,labels);
return;
}
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);
// print(g);
int subtask = labelSubDecision(n,k,g,u,v);
vector<int> labels(n,-1);
switch(subtask) {
case 1: labelSub1(n,g,labels); return labels;
case 2: labelSub2(n,labels); return labels;
case 3: labelSub3(n,g,labels); return labels;
case 4: labelSub4(n,g,labels); return labels;
}
}
int findSubDecision(int s, int t, vector<int> &c) {
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 findSub1(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 findSub2(int s, int t, vector<int> &c) {
for(int i=c.size()-1; i>=0; i--)
if(ancestor(c[i],t)) return c[i];
return c[0];
}
int findSub3(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) {
if(s < t) {
for(int elem: c)
if(elem > s) return elem;
}
else {
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 findSub4(int s, int t, vector<int> &c) {
for(int i=c.size()-1; i>=0; i--)
if(ancestor4(c[i],t)) return c[i];
return c[0];
}
int find_next_station(int s, int t, std::vector<int> c) {
int subtask = findSubDecision(s,t,c);
switch(subtask) {
case 1: return findSub1(s,t,c);
case 2: return findSub2(s,t,c);
case 3: return findSub3(s,t,c);
case 4: return findSub4(s,t,c);
}
return c[0];
}
