#include "doll.h"
#include "bits/stdc++.h"
#define MAXN 200009
#define INF 1000000007
#define mp(x,y) make_pair(x,y)
#define all(v) v.begin(),v.end()
#define pb(x) push_back(x)
#define wr cout<<"----------------"<<endl;
#define ppb() pop_back()
#define tr(ii,c) for(__typeof((c).begin()) ii=(c).begin();ii!=(c).end();ii++)
#define ff first
#define ss second
#define my_little_dodge 46
#define debug(x) cerr<< #x <<" = "<< x<<endl;
using namespace std;
typedef long long ll;
typedef pair<int,int> PII;
template<class T>bool umin(T& a,T b){if(a>b){a=b;return 1;}return 0;}
template<class T>bool umax(T& a,T b){if(a<b){a=b;return 1;}return 0;}
vector<int>X,Y;
int S,M,ans[MAXN<<2],shift[MAXN<<2],ind[MAXN<<2];
void rec(int nd,int pos,int rem,int id){
if(rem<0){
ans[pos]=id;
return;
}
shift[nd]^=1;
if(shift[nd])rec(nd*2,pos,rem-1,id);
else rec(nd*2+1,pos+(1<<rem),rem-1,id);
}
vector<int>v;int root,rem;
int XX[MAXN<<2],YY[MAXN<<2];
int dfs(int l,int r){
if(r<rem)
return root;
if(l==r)
return v[ans[l]];
int ata=--S;
int mid=(l+r)>>1;
XX[-ata-1]=dfs(l,mid);
YY[-ata-1]=dfs(mid+1,r);
return ata;
}
bool cmp(int x,int y){
return (ans[x]<ans[y]);
}
int solve(){
int sz=int(v.size()),K=0;
if(sz==0)return 0;
if(sz==1)return v[0];
while((1<<K)<sz)K++;
for(int i=0;i<(1<<K);i++)
rec(1,0,K-1,i),ind[i]=i;
root=S-1,rem=(1<<K)-sz;
for(int i=0;i<rem;i++)
ans[i]=(1<<K);
sort(ind,ind+(1<<K),cmp);
for(int i=0;i<(1<<K);i++)
ans[ind[i]]=i;
dfs(0,(1<<K)-1);
return root;
}
vector<int>adj[MAXN];
void create_circuit(int m, std::vector<int> A) {
M=m;A.pb(0);vector<int>C(M+1);
int N=int(A.size());
for(int i=0;i<N;i++)
adj[A[i]].pb(A[(i+1)%N]);
for(int i=0;i<=M;i++)
v=adj[i],C[i]=solve();
for(int i=0;i<-S;i++)
X.pb(XX[i]),Y.pb(YY[i]);
answer(C,X,Y);
}
