#include "doll.h"
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<int, int> PII;
#define fi first
#define se second
#define pb push_back
#define mp make_pair
#define pct __builtin_popcount
#define INF 1000000007
vector<PII> ff(vector<int> a) {
int n = (int) a.size();
int p = 1;
while (p < n) p *= 2;
vector<PII> s(p-1);
vector<bool> t(p-1, 0);
for (int i = 0; i < p/2-1; i ++)
s[i] = mp(-(i*2+1 +1), -(i*2+2 +1));
for (int i = 0; i < p; i ++) {
int x = 0;
while (x < p-1) {
if (t[x] == 1) {
t[x] = 0;
x = x*2+2;
} else {
t[x] = 1;
x = x*2+1;
}
}
int ne = -1;
if (i >= p-n) ne = a[i-(p-n)];
if (x%2) s[(x-1)/2].fi = ne;
else s[(x-1)/2].se = ne;
}
return s;
}
bool gg(int m, vector<int> a) {
int n = a.size();
vector<int> sc(m + 1, -1);
sc[0] = a[0];
vector<vector<int> > p(m+1);
for (int i = 0; i < n; i ++) {
int ne = 0;
if (i != n-1) ne = a[i+1];
p[a[i]].pb(ne);
if (p[a[i]].size() >= 5) return false;
}
vector<int> sx, sy;
int nc = 0;
for (int i = 1; i <= m; i ++) {
if (p[i].empty()) {
sc[i] = 0;
continue;
}
if (p[i].size() == 1) {
sc[i] = p[i][0];
continue;
}
vector<PII> v = ff(p[i]);
sc[i] = -(nc+1);
for (int j = 0; j < (int) v.size(); j ++) {
int w = v[j].fi;
if (w < 0) w -= nc;
sx.pb(w);
w = v[j].se;
if (w < 0) w -= nc;
sy.pb(w);
}
nc += (int) v.size();
}
answer(sc, sx, sy);
return true;
}
void create_circuit(int m, vector<int> a) {
if (gg(m, a)) return;
int n = a.size();
a.pb(0);
vector<int> sc(m + 1, 0);
sc[0] = a[0];
if (n == 1) {
answer(sc, {}, {});
return;
}
for (int i = 1; i <= m; i ++) sc[i] = -1;
int p = 1;
while (p < n) p *= 2;
vector<int> wx(p-1, INF);
vector<int> wy(p-1, INF);
vector<bool> t(p-1, 0);
for (int i = 0; i < p/2-1; i ++) {
wx[i] = -(i*2+1 +1);
wy[i] = -(i*2+2 +1);
}
for (int i = 0; i < p; i ++) {
int x = 0;
while (x < p-1) {
if (t[x] == 1) {
t[x] = 0;
x = x*2+2;
} else {
t[x] = 1;
x = x*2+1;
}
}
int ne = -1;
if (i >= p-n) ne = a[i-(p-n)+1];
if (x%2) wx[(x-1)/2] = ne;
else wy[(x-1)/2] = ne;
}
answer(sc, wx, wy);
}
