#include "transfer.h"
// author : sentheta aka vanwij
#include<iostream>
#include<iomanip>
#include<algorithm>
#include<cassert>
#include<random>
#include<chrono>
#include<cmath>
#include<string>
#include<vector>
#include<bitset>
#include<queue>
#include<stack>
#include<map>
#include<set>
using namespace std;
#define Int long long
#define V vector
#define pii pair<int,int>
#define ff first
#define ss second
mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());
#define pow2(x) (1LL<<(x))
#define msb(x) (63-__builtin_clzll(x))
#define bitcnt(x) (__builtin_popcountll(x))
#define nl '\n'
#define _ << ' ' <<
#define all(x) (x).begin(), (x).end()
#define rep(i,a,b) for(int i = (int)(a); i < (int)(b); i++)
#define dbg(x) if(1) cout << "?" << #x << " : " << (x) << endl << flush;
V<int> get_attachment(V<int> a) {
V<int> b;
int n = a.size();
a.push_back(0);
rep(i,0,n){
a[n] ^= a[i];
}
b.push_back(a[n]);
for(int k=1; k<n; k<<=1){
int x = 0;
rep(i,0,n+1) if(i&k){
x ^= a[i];
}
// cout << k _ x << nl;
b.push_back(x);
}
return b;
}
V<int> retrieve(V<int> a) {
int n;
if((int)a.size() < 200) n = 63;
else n = 255;
{
int x = 0;
rep(i,0,n) x ^= a[i];
if(x==a[n]){
return V<int>(a.begin(),a.begin()+n);
}
}
int idx = 0;
for(int k=1,j=n+1; k<n; k<<=1,j++){
int x = 0;
rep(i,0,n+1) if(i&k){
x ^= a[i];
}
// cout << k _ x << nl;
if(x!=a[j]){
idx ^= k;
}
}
a[idx] ^= 1;
return V<int>(a.begin(),a.begin()+n);
}
