#include <bits/stdc++.h>
#include "doll.h"
using namespace std;
typedef long long ll;
vector<int> C, X, Y, state;
int connect(int a, int bSize, int b, int orig = 0, int mask = 0, int bit = 0) {
if (!bit && orig) return b;
X.push_back(0);
Y.push_back(0);
int id = X.size() - 1;
bool first = false;
if (!orig) {
first = true;
orig = -X.size();
mask = bSize - 1;
if (mask == 0) {
X.pop_back();
Y.pop_back();
return b;
}
bit = 1 << (int)log2(mask);
}
if (mask & bit) {
X[id] = connect(a, bSize - (1 << ((int)log2(bSize) - 1)), b, orig, mask, bit >> 1);
Y[id] = connect(a, 1 << ((int)log2(bSize) - 1), b, orig, ~0, bit >> 1);
}
else {
X[id] = orig;
Y[id] = connect(a, 1 << ((int)log2(bSize) - 1), b, orig, mask, bit >> 1);
}
if (first) {
Y[X.size() - 1] = 0;
}
return -id - 1;
}
void create_circuit(int M, vector<int> A) {
A.push_back(0);
C = vector<int>(M + 1);
X = vector<int>(); Y = vector<int>();
vector<vector<int>> adj(M + 1);
int prev = 0;
for(auto &e : A) {
adj[prev].push_back(e);
prev = e;
}
for (int i = 0; i < adj.size(); i++) {
if (adj[i].empty()) continue;
C[i] = connect(i, adj[i].size(), adj[i][0]);
}
state = vector<int>(X.size());
int pos = 0;
for (int i = 0; i < A.size(); i++) {
int prev = pos;
do {
prev = pos;
if (pos >= 0) {
pos = C[pos];
}
else {
pos = state[-pos - 1] ? Y[-pos - 1] : X[-pos - 1];
state[-prev - 1] = !state[-prev - 1];
}
} while (pos < 0);
if (pos != A[i]) {
(!state[-prev - 1] ? Y[-prev - 1] : X[-prev - 1]) = A[i];
pos = A[i];
}
}
answer(C, X, Y);
return;
}
