// So annoying to implement
#include "doll.h"
#include <algorithm>
#include <cassert>
#include <iostream>
#include <vector>
using namespace std;
#define rep(i, a, b) for (auto i = (a); i < (b); ++i)
#define trav(x, v) for (auto &x : v)
#define all(x) begin(x), end(x)
#define lb(x...) lower_bound(x)
#define eb(x...) emplace_back(x)
#define sz(x) int((x).size())
using vi = vector<int>;
const int inf = 1e9;
vi x, y;
int p(const int& x) {
int ret = 0;
while ((1 << ret) < x) ++ret;
return ret;
}
int cntr = 1;
template<class it>
void f(it st, it en, int i, int d, const vi &a) {
int l = en - st;
if (d == 1) {
assert(l == 1 || l == 2);
x[i] = a[*st];
y[i] = l == 1 ? -1 : a[*(st + 1)];
} else if (p(l) == d) {
x[i] = -++cntr;
int r = 1 << (d - 1);
f(st, st + r, cntr, d - 1, a);
y[i] = -++cntr;
f(st + r, en, cntr, d - 1, a);
} else {
assert(p(l) < d);
x[i] = -++cntr;
f(st, en, cntr, d - 1, a);
y[i] = -1;
}
}
void create_circuit(int m, vi a) {
a.eb(0); int n = a.size();
int k = p(n), sz = 1 << k;
vi rev(sz);
rep(i, 0, sz) rev[i] = rev[i >> 1] >> 1 | (i & 1) << (k - 1);
rev.resize(n);
vi tmp(rev); sort(all(tmp));
trav(x, rev) x = lb(all(tmp), x) - begin(tmp);
x.resize(2 * sz, inf); y.resize(2 * sz, inf);
f(all(rev), 1, k, a);
while (x.back() == inf) x.pop_back();
while (y.back() == inf) y.pop_back();
x.erase(begin(x)); y.erase(begin(y));
vi c(m + 1); sort(all(a));
c[0] = -1;
rep(i, 0, m) c[i + 1] = binary_search(all(a), i + 1) ? -1 : 0;
answer(c, x, y);
}
