#include "encoder.h"
#include "encoderlib.h"
#include<bits/stdc++.h>
#pragma GCC optimize("O3,unroll-loops")
using namespace std;
int base=321;
struct bignum{
array<int,256> d;
bignum(int x=0){
for(int i=0;i<256;i++){
d[i]=x%base;
x/=base;
}
}
bignum& operator+=(const bignum &rhs){
for(int i=0;i<256;i++){
d[i]+=rhs.d[i];
if(d[i]>=base)d[i]-=base,d[i+1]++;
}
return *this;
}
bignum& operator-=(const bignum &rhs){
for(int i=0;i<256;i++){
d[i]-=rhs.d[i];
if(d[i]<0)d[i]+=base,d[i+1]--;
}
return *this;
}
bignum& operator*=(const int &rhs){
int carry=0;
for(int i=0;i<256;i++){
d[i]*=rhs;
d[i]+=carry;
carry=d[i]/base;
d[i]%=base;
}
return *this;
}
friend bignum operator+(const bignum &lhs,const bignum &rhs){return bignum(lhs)+=rhs;}
friend bignum operator-(const bignum &lhs,const bignum &rhs){return bignum(lhs)-=rhs;}
friend bignum operator*(const bignum &lhs,const int &rhs){return bignum(lhs)*=rhs;}
int cmp(const bignum &rhs){
for(int i=255;i>=0;i--)if(d[i]!=rhs.d[i])return d[i]<rhs.d[i]?-1:1;
return 0;
}
bool operator==(const bignum &rhs){return this->cmp(rhs)==0;}
bool operator<(const bignum &rhs){return this->cmp(rhs)==-1;}
bool operator>(const bignum &rhs){return this->cmp(rhs)==1;}
bool operator<=(const bignum &rhs){return !(*this>rhs);}
bool operator>=(const bignum &rhs){return !(*this<rhs);}
friend ostream& operator<<(ostream &os,const bignum &o){
bool ok=false;
for(int i=255;i>=0;i--){
if(ok)os << "," << o.d[i];
else if(o.d[i])os << o.d[i],ok=true;
}
if(!ok)os << 0;
return os;
}
};
bool ok=false;
bignum dp[256][321];
void encode(int N, int M[]){
int lim=ceil(4.08*N);
base=lim+1;
if(!ok){
ok=true;
dp[0][0]=1;
for(int i=1;i<256;i++){
bignum sum=0;
for(int j=0;j<321;j++){
sum+=dp[i-1][j];
dp[i][j]+=sum;
}
}
for(int i=0;i<256;i++)for(int j=1;j<321;j++)dp[i][j]+=dp[i][j-1];
}
vector<bignum> pw(N+1);
pw[0]=1;
for(int i=1;i<=N;i++)pw[i]+=pw[i-1]*256;
bignum cur;
for(int i=0;i<N;i++)cur+=pw[i]*M[i];
int all=lim;
for(int i=255;i>=0;i--){
int num=0;
for(int j=0;j<base;j++){
if(all-j<0||cur<=dp[i][all-j])break;
cur-=dp[i][all-j];
num++;
}
all-=num;
for(int j=0;j<num;j++)send(i);
}
}
#include "decoder.h"
#include "decoderlib.h"
#include<bits/stdc++.h>
#pragma GCC optimize("O3,unroll-loops")
using namespace std;
int Base=321;
struct Bignum{
array<int,256> d;
Bignum(int x=0){
for(int i=0;i<256;i++){
d[i]=x%Base;
x/=Base;
}
}
Bignum& operator+=(const Bignum &rhs){
for(int i=0;i<256;i++){
d[i]+=rhs.d[i];
if(d[i]>=Base)d[i]-=Base,d[i+1]++;
}
return *this;
}
Bignum& operator-=(const Bignum &rhs){
for(int i=0;i<256;i++){
d[i]-=rhs.d[i];
if(d[i]<0)d[i]+=Base,d[i+1]--;
}
return *this;
}
Bignum& operator*=(const int &rhs){
int carry=0;
for(int i=0;i<256;i++){
d[i]*=rhs;
d[i]+=carry;
carry=d[i]/Base;
d[i]%=Base;
}
return *this;
}
friend Bignum operator+(const Bignum &lhs,const Bignum &rhs){return Bignum(lhs)+=rhs;}
friend Bignum operator-(const Bignum &lhs,const Bignum &rhs){return Bignum(lhs)-=rhs;}
friend Bignum operator*(const Bignum &lhs,const int &rhs){return Bignum(lhs)*=rhs;}
int cmp(const Bignum &rhs){
for(int i=255;i>=0;i--)if(d[i]!=rhs.d[i])return d[i]<rhs.d[i]?-1:1;
return 0;
}
bool operator==(const Bignum &rhs){return this->cmp(rhs)==0;}
bool operator<(const Bignum &rhs){return this->cmp(rhs)==-1;}
bool operator>(const Bignum &rhs){return this->cmp(rhs)==1;}
bool operator<=(const Bignum &rhs){return !(*this>rhs);}
bool operator>=(const Bignum &rhs){return !(*this<rhs);}
bool operator!=(const Bignum &rhs){return !(*this==rhs);}
friend ostream& operator<<(ostream &os,const Bignum &o){
bool ok=false;
for(int i=255;i>=0;i--){
if(ok)os << "," << o.d[i];
else if(o.d[i])os << o.d[i],ok=true;
}
if(!ok)os << 0;
return os;
}
};
bool Ok=false;
Bignum Dp[256][321];
void decode(int N, int L, int X[]){
int lim=ceil(4.08*N);
Base=lim+1;
Dp[0][0]=1;
if(!Ok){
Ok=true;
Dp[0][0]=1;
for(int i=1;i<256;i++){
Bignum sum=0;
for(int j=0;j<321;j++){
sum+=Dp[i-1][j];
Dp[i][j]+=sum;
}
}
for(int i=0;i<256;i++)for(int j=1;j<321;j++)Dp[i][j]+=Dp[i][j-1];
}
vector<Bignum> pw(N+1);
pw[0]=1;
for(int i=1;i<=N;i++)pw[i]+=pw[i-1]*256;
Bignum cur,res;
for(int i=0;i<L;i++)cur.d[X[i]]++;
int all=lim;
if(cur!=0)res=1;
for(int i=255;i>=0;i--){
for(int j=0;j<cur.d[i];j++){
res+=Dp[i][all-j];
}
all-=cur.d[i];
}
vector<int> ans(N);
for(int i=N-1;i>=0;i--){
int num=0;
for(int j=0;j<256;j++){
if(res<pw[i])break;
res-=pw[i];
num++;
}
ans[i]=num;
}
for(auto x:ans)output(x);
}
