#include "doll.h"
#include <iostream>
#include <cstdio>
#include <algorithm>
#include <vector>
using namespace std;
#define endl '\n'
#define ll long long
#define pi pair<int, int>
#define f first
#define s second
#define vi vector<int>
const int mxn = 1 << 19;
int n, k, t;
bool b[mxn];
vi f, u(mxn), v(mxn);
int bld(int l, int r){
if(l == r) return 0;
if(r < k - n - (n & 1)) return -1;
int it = t++, mid = (l + r) / 2;
u[it] = bld(l, mid), v[it] = bld(mid + 1, r);
return -it - 1;
}
void add(int x, int y){
x = -x - 1;
int &z = b[x] ? u[x] : v[x];
b[x] ^= 1;
if(!z) z = y;
else add(z, y);
}
/*
void answer(vi f, vi u, vi v){
for(int i = 0; i < f.size(); i++){
cout << i << ": " << f[i] << endl;
}
for(int i = 0; i < u.size(); i++){
cout << (-i - 1) << ": " << u[i] << " " << v[i] << endl;
}
}
*/
void create_circuit(int m, vi a){
n = a.size(), k = 1 << (__lg(n - 1) + 1);
bld(0, k - 1);
for(int i = 1; i < n; i++) add(-1, a[i]);
add(-1, 0);
f.assign(m + 1, -1), u.resize(t), v.resize(t);
f[0] = a[0];
answer(f, u, v);
}
/*
int main(){
ios::sync_with_stdio(0);
cin.tie(0);
int n, m;
cin >> n >> m;
vi a(n);
for(int i = 0; i < n; i++) cin >> a[i];
create_circuit(m, a);
return 0;
}
*/
