#include <bits/stdc++.h>
using namespace std;
typedef vector<int> vi;
#define siz(x) (int)x.size()
vi get_attachment(vi v){
int xr = 0, on = 0;
for (int i = 0; i < siz(v); i++) xr ^= (i+1)*v[i];
vi res;
for (int i = 0; i < __lg(siz(v)+1); i++){
res.push_back(xr&(1<<i)?1:0);
if (xr&(1<<i)) on ^= 1;
}
res.push_back(on);
return res;
}
vi retrieve(vi v){
int n = (siz(v) < 100? 63 : 255), xr = 0, check = 0;
vi res;
for (int i = 0; i < n; i++){
xr ^= (i+1)*v[i];
res.push_back(v[i]);
}
for (int i = 0; i < __lg(n+1); i++) if (v[n+i]) check ^= (1<<i);
if (xr != check && __builtin_popcount(check)%2 == v.back()) res[(xr^check)-1] ^= 1;
return res;
}
