#include "doll.h"
#include<bits/stdc++.h>
using namespace std;
using ll = int;
void create_circuit(int M, std::vector<int> A) {
int N = A.size();
std::vector<int> C(M + 1,0);
C[0] = A[0];
if (N == 1){
for (int i = 1; i <= M; ++i) C[i] = 0;
vector<int> X,Y;
answer(C, X, Y);
return;
}else if (N==16){
for (int i = 1; i <= M; ++i) {
C[i] = -1;
}
ll GN = 1<<(__lg(N-1)+1);
while (A.size()<GN) A.push_back(-1);
A.push_back(0);
vector<int> X(GN-1),Y(GN-1);
ll it = 0;
function<ll(ll,ll,ll)> dfs;
dfs = [&](ll cnt, ll st, ll lv){
if (cnt==1){
return A[st+1];
}
ll i = it++;
X[i] = dfs(cnt-cnt/2,st,lv+1);
Y[i] = dfs(cnt/2,st+(1<<lv),lv+1);
return -1-i;
};
dfs(GN,0,0);
answer(C, X, Y);
return;
}
A.push_back(0);
vector<vector<ll>> nxt(M);
for(ll i = 0;i<N;i++){
nxt[A[i]-1].push_back(A[i+1]);
}
for(auto &o : nxt){
if (o.size()>2) {
ll old = o.back();
o.pop_back();
o.resize(1<<(__lg(o.size())+1),-1);
o.back() = old;
}
}
vector<int> X,Y;
ll it = 0;
vector<ll> CUR;
ll root;
function<ll(ll,ll,ll)> dfs;
dfs = [&](ll cnt, ll st, ll lv){
//cerr << "dfs " << cnt << " " << st << " " << lv << " " << CUR[st] << "\n";
if (cnt==1){
return CUR[st]==-1?root:CUR[st];
}
ll i = it++;
X.emplace_back();
Y.emplace_back();
X[i] = dfs(cnt-cnt/2,st,lv+1);
Y[i] = dfs(cnt/2,st+(1<<lv),lv+1);
return -1-i;
};
for(ll i = 0;i<M;i++){
CUR = nxt[i];
if (CUR.size()>1){
C[i+1] = root = -1-it;
dfs(CUR.size(),0,0);
}else if(CUR.size()==1){
C[i+1] = CUR[0];
}
}
for(ll i = 0;i<N;i++) {
//cerr << "nxt " << i << ":";
//for(ll j : nxt[i]) cerr << " " << j;
//cerr << "\n";
}
answer(C, X, Y);
}
