#pragma GCC target("avx2")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#include <bits/stdc++.h>
using namespace std;
#ifdef tabr
#include "library/debug.cpp"
#else
#define debug(...)
#endif
#define encoder
#ifdef tabr
int dat[100];
int id = 0;
void send(int x) {
dat[id++] = x;
}
void output(int x) {
cout << x << '\n';
}
#else
#include "decoder.h"
#include "decoderlib.h"
#include "encoder.h"
#include "encoderlib.h"
#endif
long long f(long long n, int c) { // count x <= n, popcount(x) == c
vector<long long> dp(c + 1);
int d = 0;
for (int i = 40; i >= 0; i--) {
for (int j = c - 1; j >= 0; j--) {
dp[j + 1] += dp[j];
}
if (n & (1LL << i)) {
if (d <= c) {
dp[d]++;
}
d++;
}
}
if (__builtin_popcountll(n) == c) {
dp[c]++;
}
return dp[c];
}
#ifdef encoder
void encode(int n, int a[]) {
for (int beg = 0; beg < n; beg += 4) {
int c = min(4, n - beg);
long long z = 0;
for (int i = beg; i < min(n, beg + 4); i++) {
z *= 256;
z += a[i];
}
long long low = -1;
long long high = 1LL << 40;
while (high - low > 1) {
long long mid = (high + low) >> 1;
if (f(mid, c * 5) >= z + 1) {
high = mid;
} else {
low = mid;
}
}
long long k = high;
vector<int> b;
int lst = 0;
for (int i = 0; i < c * 5 + 16; i++) {
if (k & (1LL << i)) {
b.emplace_back(lst);
} else {
lst++;
}
}
for (int i : b) {
send(i + beg * 4);
}
}
}
#endif
#ifdef decoder
void decode(int n, int l, int a[]) {
sort(a, a + l);
for (int beg = 0; beg < n; beg += 4) {
int c = min(4, n - beg);
vector<int> b;
for (int i = beg * 5; i < min(n, beg + 4) * 5; i++) {
b.emplace_back(a[i] - beg * 4);
}
long long k = 0;
for (int i = 0; i < (int) b.size(); i++) {
k |= 1 << (i + b[i]);
}
long long z = f(k, c * 5) - 1;
b.clear();
for (int i = 0; i < c; i++) {
b.emplace_back((int) (z % 256));
z /= 256;
}
reverse(b.begin(), b.end());
for (int i : b) {
output(i);
}
}
}
#endif
#ifdef tabr
int main() {
ios::sync_with_stdio(false);
cin.tie(0);
int n = 6;
int a[] = {1, 1, 4, 5, 1, 4};
encode(n, a);
decode(n, id, dat);
return 0;
}
#endif
#pragma GCC target("avx2")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#include <bits/stdc++.h>
using namespace std;
#ifdef tabr
#include "library/debug.cpp"
#else
#define debug(...)
#endif
#define decoder
#ifdef tabr
int dat[100];
int id = 0;
void send(int x) {
dat[id++] = x;
}
void output(int x) {
cout << x << '\n';
}
#else
#include "decoder.h"
#include "decoderlib.h"
#include "encoder.h"
#include "encoderlib.h"
#endif
long long f(long long n, int c) { // count x <= n, popcount(x) == c
vector<long long> dp(c + 1);
int d = 0;
for (int i = 40; i >= 0; i--) {
for (int j = c - 1; j >= 0; j--) {
dp[j + 1] += dp[j];
}
if (n & (1LL << i)) {
if (d <= c) {
dp[d]++;
}
d++;
}
}
if (__builtin_popcountll(n) == c) {
dp[c]++;
}
return dp[c];
}
#ifdef encoder
void encode(int n, int a[]) {
for (int beg = 0; beg < n; beg += 4) {
int c = min(4, n - beg);
long long z = 0;
for (int i = beg; i < min(n, beg + 4); i++) {
z *= 256;
z += a[i];
}
long long low = -1;
long long high = 1LL << 40;
while (high - low > 1) {
long long mid = (high + low) >> 1;
if (f(mid, c * 5) >= z + 1) {
high = mid;
} else {
low = mid;
}
}
long long k = high;
vector<int> b;
int lst = 0;
for (int i = 0; i < c * 5 + 16; i++) {
if (k & (1LL << i)) {
b.emplace_back(lst);
} else {
lst++;
}
}
for (int i : b) {
send(i + beg * 4);
}
}
}
#endif
#ifdef decoder
void decode(int n, int l, int a[]) {
sort(a, a + l);
for (int beg = 0; beg < n; beg += 4) {
int c = min(4, n - beg);
vector<int> b;
for (int i = beg * 5; i < min(n, beg + 4) * 5; i++) {
b.emplace_back(a[i] - beg * 4);
}
long long k = 0;
for (int i = 0; i < (int) b.size(); i++) {
k |= 1 << (i + b[i]);
}
long long z = f(k, c * 5) - 1;
b.clear();
for (int i = 0; i < c; i++) {
b.emplace_back((int) (z % 256));
z /= 256;
}
reverse(b.begin(), b.end());
for (int i : b) {
output(i);
}
}
}
#endif
#ifdef tabr
int main() {
ios::sync_with_stdio(false);
cin.tie(0);
int n = 6;
int a[] = {1, 1, 4, 5, 1, 4};
encode(n, a);
decode(n, id, dat);
return 0;
}
#endif
