#include "beechtree.h"
#include <bits/stdc++.h>
using namespace std;
const int lim=200001,mxn=2e7+1;
int n,m,bad[lim],sz[lim],tin[lim],tout[lim],t,id,pos[lim],order[lim],root[lim][2],last[lim],cur,a[lim],b[lim];
int le[mxn],ri[mxn],st[mxn];
vector <int> p,c,res,ke[lim],ve[lim],s[lim],sc[lim],tmp;
vector <pair <int, int>> ve2;
void dfs(int u){
sz[u]=1;
tin[u]=++t;
for (int v:ke[u]){
dfs(v);
sz[u]+=sz[v];
}
tout[u]=t;
ve[sz[u]].push_back(u);
}
int update(int node, int l, int r, int i){
cur++;
if (l==r){
st[cur]++;
return cur;
}
int tmp=cur,mid=(l+r)>>1;
le[tmp]=le[node];
ri[tmp]=ri[node];
if (mid<i)
ri[tmp]=update(ri[node],mid+1,r,i);
else
le[tmp]=update(le[node],l,mid,i);
st[tmp]=st[le[tmp]]+st[ri[tmp]];
return tmp;
}
int get(int node, int l, int r, int u, int v){
if (l>v||r<u||!node)
return 0;
if (l>=u&&r<=v)
return st[node];
int mid=(l+r)>>1;
return get(le[node],l,mid,u,v)+get(ri[node],mid+1,r,u,v);
}
int get(int i, int j, int k){
int res=get(root[i][k],1,n,tin[j],tout[j])-1;
return res-(k&&c[i]==c[j]);
}
void dfs2(int u){
if (ke[u].empty()){
s[u].push_back(pos[u]);
return;
}
int mx=0,bigchild=-1;
for (int v:ke[u])
if (sz[v]>mx){
bigchild=v;
mx=sz[v];
}
for (int v:ke[u]){
dfs2(v);
bad[u]|=bad[v];
}
if (bad[u])
return;
swap(s[u],s[bigchild]);
s[u].push_back(pos[u]);
for (int v:ke[u])
if (v!=bigchild){
for (int i:s[v]){
a[order[i]]=get(order[i],u,0);
b[order[i]]=get(order[i],u,1);
}
for (int i:s[v])
if (b[order[i]]!=a[p[order[i]]]){
bad[u]=1;
return;
}
}
if (get(bigchild,u,1)){
bad[u]=1;
return;
}
for (int v:ke[u])
if (v!=bigchild){
for (int i:s[v]){
s[u].push_back(i);
tmp.push_back(a[order[i]]);
sc[c[order[i]]].push_back(b[order[i]]);
}
s[v].clear();
}
sc[c[bigchild]].push_back(get(bigchild,u,1));
tmp.push_back(0);
tmp.push_back(sz[u]);
sort(tmp.begin(),tmp.end());
int last=-1;
ve2.clear();
for (int i:tmp){
int x=i-last-1;
if (x)
ve2.push_back({x,last});
last=i;
}
tmp.clear();
int cnt=0;
for (int v:ke[u]){
int i=c[v];
int num=get(::last[i],1,n,tin[u],tout[u])-(c[u]==i);
int id=0;
pair <int, int> cur=ve2[0];
sc[i].push_back(num);
sort(sc[i].begin(),sc[i].end());
int last=-1;
for (int j:sc[i]){
int x=j-last-1;
if (x){
cnt+=x;
if (!(x<=cur.first&&last==cur.second)){
bad[u]=1;
for (int v:ke[u])
sc[c[v]].clear();
return;
}
cur.first-=x;
if (!cur.first){
id++;
cur=(id==ve2.size()?make_pair(0,0):ve2[id]);
}
}
last=j;
}
sc[i].clear();
}
if (cnt<sz[bigchild]-1)
bad[u]=1;
}
vector <int> beechtree(int N, int M, vector<int> P, vector<int> C){
n=N,m=M,p=P,c=C;
for (int i=1;i<n;i++)
ke[P[i]].push_back(i);
dfs(0);
for (int i=n;i>=0;i--){
sort(ve[i].begin(),ve[i].end(),[](int u, int v){return pos[p[u]]<pos[p[v]];});
for (int j:ve[i]){
pos[j]=++id;
order[id]=j;
}
}
for (int i=1;i<=n;i++){
int j=order[i];
root[j][0]=update(root[order[i-1]][0],1,n,tin[j]);
root[j][1]=update(last[c[j]],1,n,tin[j]);
last[c[j]]=root[j][1];
}
dfs2(0);
for (int i=0;i<n;i++)
res.push_back(bad[i]^1);
return res;
}
