#include "encoder.h"
#include "encoderlib.h"
// author : sentheta aka vanwij
#ifdef VANWIJ
#include"/home/user/code/bits/stdc++.h"
#else
#include"bits/stdc++.h"
#endif
using namespace std;
#define V vector
#define pii pair<int,int>
#define ff first
#define ss second
static 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(0) cout << "?" << #x << " : " << (x) << endl << flush;
static const int A = 10;
static const int B = 60;
// 600 bit integer
// least significant bits are Int[A-1]
// most significant bits are Int[0]
#define Int array<long long,A>
static Int operator+(Int a,Int b){
Int ret;
rep(i,0,A){
ret[i] = a[i]+b[i];
}
for(int i=A-1; i>=0; i--) if(ret[i] > (1LL<<B)){
ret[i] -= 1LL<<B;
ret[i-1]++;
}
return ret;
}
static Int operator-(Int a,Int b){
for(int i=A-1; i>=0; i--){
if(a[i] < b[i]){
a[i-1]--;
a[i] += 1LL<<B;
}
a[i] -= b[i];
}
return a;
}
static void print(Int a){
return;
rep(i,0,A) cout << a[i] << " ";
cout << nl;
}
static const int N = 256;
static const int LEN = 325;
static Int dp[LEN][N];
static void buildDP(){
rep(i,0,LEN) rep(j,0,N){
rep(k,0,A) dp[i][j] [k]=0;
}
for(int x=0; x<N; x++){
dp[1][x] [A-1]=1;
}
for(int i=2; i<LEN; i++){
dp[i][0] = dp[i-1][0];
for(int x=1; x<N; x++){
dp[i][x] = dp[i-1][x] + dp[i][x-1];
}
}
}
// #########################
void encode(int n,int m[]){
buildDP();
Int v;
rep(i,0,A) v[i] = 0;
for(int i=0; i<n; i++){
for(int b=0; b<8; b++) if(m[i]&1LL<<b){
int p = 8*i+b;
v[A-1 - p/B] |= 1LL<<(p%B);
}
}
print(v);
dbg(n);
int len = 1;
while(dp[len][255] < v) len++;
for(int i=len; i>=1; i--){
int x = 0;
while(dp[i][x] < v) x++;
assert(v<dp[i][x] || v==dp[i][x]);
if(x > 0){
v = v - dp[i][x-1];
}
dbg(i);
dbg(x);
print(dp[i][x-1]);
print(v);
// cout << nl;
send(x);
}
print(v);
// rep(i,0,A) assert(v[i]==0);
// cout << "END" << nl << nl << nl;
}
#include "decoder.h"
#include "decoderlib.h"
// author : sentheta aka vanwij
#ifdef VANWIJ
#include"/home/user/code/bits/stdc++.h"
#else
#include"bits/stdc++.h"
#endif
using namespace std;
#define V vector
#define pii pair<int,int>
#define ff first
#define ss second
static 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(0) cout << "?" << #x << " : " << (x) << endl << flush;
static const int A = 10;
static const int B = 60;
// 600 bit integer
// least significant bits are Int[A-1]
// most significant bits are Int[0]
#define Int array<long long,A>
static Int operator+(Int a,Int b){
Int ret;
rep(i,0,A){
ret[i] = a[i]+b[i];
}
for(int i=A-1; i>=0; i--) if(ret[i] > (1LL<<B)){
ret[i] -= 1LL<<B;
ret[i-1]++;
}
return ret;
}
static Int operator-(Int a,Int b){
for(int i=A-1; i>=0; i--){
if(a[i] < b[i]){
a[i-1]--;
a[i] += 1LL<<B;
}
a[i] -= b[i];
}
return a;
}
static void print(Int a){
return;
rep(i,0,A) cout << a[i] << " ";
cout << nl;
}
static const int N = 256;
static const int LEN = 325;
static Int dp[LEN][N];
static void buildDP(){
rep(i,0,LEN) rep(j,0,N){
rep(k,0,A) dp[i][j] [k]=0;
}
for(int x=0; x<N; x++){
dp[1][x] [A-1]=1;
}
for(int i=2; i<LEN; i++){
dp[i][0] = dp[i-1][0];
for(int x=1; x<N; x++){
dp[i][x] = dp[i-1][x] + dp[i][x-1];
}
}
}
// #########################
void decode(int n,int len,int a[]){
buildDP();
sort(a, a+len);
Int one;
rep(i,0,A) one[i] = 0;
one[A-1] = 1;
Int v;
rep(i,0,A) v[i] = 0;
v[A-1] = 0;
bool nonZro = 0;
dbg(len);
for(int i=len; i>=1; i--){
int x = a[i-1];
nonZro |= x!=0;
if(x > 0){
v = v + dp[i][x-1];
}
else{
// v = v + one;
}
dbg(x);
}
if(nonZro) v = v+one;
print(v);
for(int i=0; i<n; i++){
int x = 0;
for(int b=0; b<8; b++){
int p = 8*i+b;
if(v[A-1 - p/B]&1LL<<(p%B)){
x |= 1LL<<b;
}
}
dbg(i);
dbg(x);
output(x);
}
}
