#include "doll.h"
#include <algorithm>
#include <cstdio>
constexpr int inf = 0x3f3f3f3f;
int x[400010], y[400010], state[400010], cnt = 1, fim, pos[400010];
void solve(int id, int pot, int N) {
if(N == 1 && pot == 0) return (void)(x[id] = -1, y[id] = inf);
if(N == 2 && pot == 0) return (void)(x[id] = inf, y[id] = inf);
if(N > (1 << pot)) {
x[id] = -(++cnt);
int aq = N - (1 << pot);
solve(-x[id], pot-1, aq);
} else x[id] = -1;
y[id] = -(++cnt);
solve(-y[id], pot-1, std::min(N, 1<<pot));
}
std::vector<int> a;
void go(int u) {
if(fim == (int)(a.size())) return;
int& vai = state[u] ? y[u] : x[u];
state[u] ^= 1;
if(vai == -1) return go(1);
if(vai == inf) return (void)(vai = a[fim++], go(1));
go(-vai);
}
void create_circuit(int M, std::vector<int> A) {
int N = (int)(A.size());
if(N == 1) return answer({1, 0}, {}, {});
std::vector<int> C(M + 1);
C[0] = A[0];
A.push_back(0);
A.erase(A.begin());
a = A;
for(int i = 1; i <= M; ++i)
C[i] = -1;
solve(1, 31-__builtin_clz(N)-(__builtin_popcount(N) == 1), N);
std::vector<int> X(cnt), Y(cnt);
for(int i = 1; i <= cnt; i++)
X[i-1] = x[i], Y[i-1] = y[i];
go(1);
for(int i = 1; i <= cnt; i++)
X[i-1] = x[i], Y[i-1] = y[i];
answer(C, X, Y);
}
