#include <bits/stdc++.h>
#define ff first
#define ss second
#define mp make_pair
#define pb push_back
#define all(x) (x).begin(), (x).end()
using namespace std;
typedef long long ll;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
std::vector<int> get_attachment(std::vector<int> source) {
int n = source.size(), k;
if(n == 63)
k = 7;
else
k = 9;
vector<int> ret(k);
for(int i = 0; i < n; ++i){
for(int j = 0; j < (k-1); ++j)
if((1<<j)&(i+1))
ret[j] ^= source[i];
ret[k-1] ^= source[i];
}
return ret;
}
std::vector<int> retrieve(std::vector<int> data) {
int n, k;
if(data.size() == 70){
n = 63, k = 7;
}
else{
n = 255, k = 9;
}
vector<int> ori(data.begin(), data.begin()+n);
int tot = data.back();
vector<vector<int>> vals(2, vector<int>(k-1));
vals[1] = vector<int>(data.begin()+n, data.end()-1);
for(int i = 0; i < k-1; ++i)
vals[0][i] = vals[1][i]^tot;
vector<vector<int>> cur(2, vector<int>(k-1));
for(int i = 0; i < n; ++i)
for(int j = 0; j < (k-1); ++j)
cur[((1<<j)&(i+1)) > 0][j] ^= ori[i];
int cnt = 0;
for(int i = 0; i < (k-1); ++i){
if(cur[0][i] != vals[0][i] && cur[1][i] != vals[1][i]){
return ori;
}
if(cur[0][i] != vals[0][i] || cur[1][i] != vals[1][i])
++cnt;
}
if(cnt == 0)
return ori;
if(cnt != k-1)
return ori;
int falidx = -1;
for(int i = 0; i < (k-1); ++i)
if(cur[1][i] != vals[1][i])
falidx += (1<<i);
if(falidx >= 0)
ori[falidx] ^= 1;
return ori;
}
