// Iterative segtree implementation makes it easy to implement yay
#include "doll.h"
#include <iostream>
#include <vector>
using namespace std;
#define rep(i, a, b) for (auto i = (a); i < (b); ++i)
#define eb(x...) emplace_back(x)
const int inf = 1e9, N = 1 << 18;
int tree[N << 1], rev[N];
void create_circuit(int m, vector<int> a) {
a.eb(0); int n = a.size(), sz = 1;
while (sz < n) sz <<= 1;
rep(i, 0, sz) tree[i + sz] = inf;
for (int i = 0, j = 0; i < sz; ++i) {
rev[i] = rev[i >> 1];
if (i & 1) rev[i] |= sz;
rev[i] >>= 1;
if (rev[i] < sz - n) continue;
tree[rev[i] + sz] = a[j++];
}
int cnt = 0;
vector<int> x, y;
for (int i = sz; --i; )
if (tree[i << 1 | 0] != tree[i << 1 | 1]) {
tree[i] = -++cnt;
x.eb(tree[i << 1|0]);
y.eb(tree[i << 1|1]);
} else tree[i] = tree[i << 1];
rep(i, 0, cnt) {
if (x[i] == inf) x[i] = tree[1];
if (y[i] == inf) y[i] = tree[1];
}
answer(vector<int>(m + 1, tree[1]), x, y);
}
