/*
________ ___ ________ ________ ________ ___ ________ ________ ________
|\ ____\|\ \|\ ____\|\ __ \ |\ ___ \|\ \|\ ____\|\ ____\|\ __ \
\ \ \___|\ \ \ \ \___|\ \ \|\ \ \ \ \\ \ \ \ \ \ \___|\ \ \___|\ \ \|\ \
\ \ \ __\ \ \ \ \ __\ \ __ \ \ \ \\ \ \ \ \ \ \ __\ \ \ __\ \ __ \
\ \ \|\ \ \ \ \ \|\ \ \ \ \ \ \ \ \\ \ \ \ \ \ \|\ \ \ \|\ \ \ \ \ \
\ \_______\ \__\ \_______\ \__\ \__\ \ \__\\ \__\ \__\ \_______\ \_______\ \__\ \__\
\|_______|\|__|\|_______|\|__|\|__| \|__| \|__|\|__|\|_______|\|_______|\|__|\|__|
________ ________ ________ ________ ___ ___ ________ _________ ___ ________ ________
|\ __ \|\ __ \|\ __ \|\ ___ \|\ \|\ \|\ ____\\___ ___\\ \|\ __ \|\ ___ \
\ \ \|\ \ \ \|\ \ \ \|\ \ \ \_|\ \ \ \\\ \ \ \___\|___ \ \_\ \ \ \ \|\ \ \ \\ \ \
\ \ ____\ \ _ _\ \ \\\ \ \ \ \\ \ \ \\\ \ \ \ \ \ \ \ \ \ \ \\\ \ \ \\ \ \
\ \ \___|\ \ \\ \\ \ \\\ \ \ \_\\ \ \ \\\ \ \ \____ \ \ \ \ \ \ \ \\\ \ \ \\ \ \
\ \__\ \ \__\\ _\\ \_______\ \_______\ \_______\ \_______\ \ \__\ \ \__\ \_______\ \__\\ \__\
\|__| \|__|\|__|\|_______|\|_______|\|_______|\|_______| \|__| \|__|\|_______|\|__| \|__|
Written by: giga nigga
*/
// #include "largest.h"
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
#define MASK(i) (1ULL << (i))
#define GETBIT(mask, i) (((mask) >> (i)) & 1)
#define ALL(v) (v).begin(), (v).end()
ll max(ll a, ll b){return (a > b) ? a : b;}
ll min(ll a, ll b){return (a < b) ? a : b;}
ll gcd(ll a, ll b){return __gcd(a, b);}
ll lcm(ll a, ll b){return a / gcd(a, b) * b;}
ll LASTBIT(ll mask){return (mask) & (-mask);}
int pop_cnt(ull mask){return __builtin_popcountll(mask);}
int ctz(ull mask){return __builtin_ctzll(mask);}
int logOf(ull mask){return 63 - __builtin_clzll(mask);}
// mt19937_64 rng(chrono::high_resolution_clock::now().time_since_epoch().count());
mt19937_64 rng(1);
ll rngesus(ll l, ll r){return l + (ull) rng() % (r - l + 1);}
double rngesus_d(double l, double r){
double wow = (double) ((ull) rng()) / ((ull)(0-1));
return wow * (r - l) + l;
}
template <class T1, class T2>
bool maximize(T1 &a, T2 b){
if (a < b) {a = b; return true;}
return false;
}
template <class T1, class T2>
bool minimize(T1 &a, T2 b){
if (a > b) {a = b; return true;}
return false;
}
template <class T>
void printArr(T container, string separator = " ", string finish = "\n", ostream &out = cout){
for(auto item: container) out << item << separator;
out << finish;
}
template <class T>
void remove_dup(vector<T> &a){
sort(ALL(a));
a.resize(unique(ALL(a)) - a.begin());
}
#include "transfer.h"
vector<int> get_attachment(vector<int> source) {
vector<int> ans;
int sum = 0;
for(int i: source) sum ^= i;
ans.push_back(sum);
for(int j = 0; MASK(j) < source.size(); ++j){
int sum = 0;
for(int i = 0; i < (int) source.size(); ++i) if (!GETBIT(i, j))
sum ^= source[i];
ans.push_back(sum);
}
return ans;
}
vector<int> retrieve(vector<int> data) {
int n = data.size();
if (n < 255) n = 63;
else n = 255;
int sum = 0;
for(int i = 0; i < n; ++i) sum ^= data[i];
if (sum == data[n]) return vector<int>(data.begin(), data.begin() + n);
else{
vector<int> ans(data.begin(), data.begin() + n);
vector<int> sum_bit;
for(int i = n+1; i < (int) data.size(); ++i) sum_bit.push_back(data[i]);
int diff = 0;
for(int j = 0; j < (int) sum_bit.size(); ++j){
int sum = 0;
for(int i = 0; i < n; ++i) if (!GETBIT(i, j))
sum ^= data[i];
if (sum == sum_bit[j]) diff += MASK(j);
}
if (diff < 63)
ans[diff] ^= 1;
return ans;
}
}
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