#include "split.h"
#include <bits/stdc++.h>
using namespace std;
int n,a,b,c,label[3]={1,2,3},d[100001],up[100001],sz[100001],vis[100001],node,t,f[100001],ch[100001],tin[100001],tout[100001];
vector <int> ke[100001],child[100001],del2[100001],res,ve;
vector <pair <int, int>> add[100001],del[100001];
void dfs(int u){
tin[u]=++t;
vis[u]=sz[u]=1;
for (int v:ke[u])
if (!vis[v]){
child[u].push_back(v);
d[v]=d[u]+1;
up[v]=u;
dfs(v);
sz[u]+=sz[v];
}
tout[u]=t;
}
void dfs2(int u, int cur, int i){
if (d[up[u]]<d[cur]){
add[cur].push_back({u,i});
del[up[u]].push_back({u,i});
cur=up[u];
}
for (int v:child[u])
dfs2(v,cur,i);
}
void dfs3(int u){
if (ch[u])
return;
ve.push_back(u);
for (int v:child[u])
dfs3(v);
}
void update(int i, int val){
i++;
for (;i<=n;i+=i&(-i))
f[i]+=val;
}
int get(int i){
i++;
int res=0;
for (;i;i-=i&(-i))
res+=f[i];
return res;
}
bool check(int l, int r){
vector <int> ve;
set <pair <int, int>> s;
set <int> s2;
for (int i=0;i<n;i++){
if (sz[i]>=l&&sz[i]<=r){
node=i;
return true;
}
add[i].clear();
del[i].clear();
del2[i].clear();
if (sz[i]>r)
ve.push_back(i);
}
memset(f,0,sizeof(f));
memset(ch,0,sizeof(ch));
sort(ve.begin(),ve.end(),[](int i, int j){return d[i]<d[j];});
for (int i=0;i<ve.size();i++){
for (int j:child[ve[i]])
if (sz[j]<l)
dfs2(j,ve[i],i);
del2[up[ve[i]]].push_back(i);
}
s.insert({0,ve.size()});
for (int i=ve.size()-1;i>=0;i--){
for (auto [j,k]:del[ve[i]]){
update(k,-sz[j]);
s2.erase(j);
}
for (auto [j,k]:add[ve[i]]){
update(k,sz[j]);
s2.insert(j);
}
for (int j:del2[ve[i]])
s.erase({-sz[ve[j]],j});
auto it=s.lower_bound({a-sz[ve[i]],-1});
auto [val,pos]=*it;
if (sz[ve[i]]+val<=b){
node=ve[i];
ch[ve[pos]]=1;
return true;
}
if (sz[ve[i]]+val-get(pos-1)<=b){
node=ve[i];
ch[ve[pos]]=1;
int cnt=sz[ve[i]]+val;
for (int j:s2){
if (pos<ve.size()&&tin[ve[pos]]<=tin[j]&&tout[ve[pos]]>=tout[j])
continue;
cnt-=sz[j];
ch[j]=1;
if (cnt<=r)
break;
}
return true;
}
s.insert({-sz[ve[i]],i});
}
return false;
}
vector <int> find_split(int N, int A, int B, int C, vector <int> p, vector <int> q){
n=N,a=A,b=B,c=C;
if (a>b){
swap(a,b);
swap(label[0],label[1]);
}
if (b>c){
swap(b,c);
swap(label[1],label[2]);
}
if (a>b){
swap(a,b);
swap(label[0],label[1]);
}
for (int i=0;i<p.size();i++){
ke[p[i]].push_back(q[i]);
ke[q[i]].push_back(p[i]);
}
dfs(0);
for (int i=0;i<n;i++)
for (int j:ke[i])
if (d[j]<d[up[i]])
up[i]=j;
res.assign(n,0);
if (check(b,n-a)){
swap(a,b);
swap(label[0],label[1]);
}
else if (!check(a,n-b))
return res;
dfs3(node);
sort(ve.begin(),ve.end(),[](int i, int j){return d[i]<d[j];});
for (int i=0;i<ve.size();i++)
res[ve[i]]=label[(i>=a)*2];
ve.clear();
for (int i=0;i<n;i++)
if (!res[i])
ve.push_back(i);
queue <int> Q;
memset(d,0,sizeof(d));
d[ve[0]]=1;
Q.push(ve[0]);
while (!Q.empty()){
int u=Q.front();
Q.pop();
for (int v:ke[u])
if (!res[v]&&!d[v]){
d[v]=d[u]+1;
Q.push(v);
}
}
sort(ve.begin(),ve.end(),[](int i, int j){return d[i]<d[j];});
for (int i=0;i<ve.size();i++)
res[ve[i]]=label[(i>=b)+1];
return res;
}
