#include "encoder.h"
#include "encoderlib.h"
#include <bits/stdc++.h>
using namespace std;
namespace encoding {
#define all(x) begin(x),end(x)
template<typename A, typename B> ostream& operator<<(ostream &os, const pair<A, B> &p) { return os << '(' << p.first << ", " << p.second << ')'; }
template<typename T_container, typename T = typename enable_if<!is_same<T_container, string>::value, typename T_container::value_type>::type> ostream& operator<<(ostream &os, const T_container &v) { string sep; for (const T &x : v) os << sep << x, sep = " "; return os; }
#define debug(a) cerr << "(" << #a << ": " << a << ")\n";
typedef vector<int> vi;
typedef pair<int,int> pi;
const int B = 256;
const int Base=B*B;
struct bigint {
vi v = {0};
int size() const {return v.size();}
void trim() {
int carry=0;
for(int i=0;i<size();++i) {
v[i]+=carry;
carry = v[i]/Base;
v[i]%=Base;
}
while(carry) {
v.push_back(carry%Base);
carry/=Base;
}
while(!v.empty() and v.back()==0) v.pop_back();
}
bigint() {}
bigint(int a) {
v = {a};
trim();
}
bigint(int n, int A[]) { // in base B
v= {};
for(int i=0;i<n;i+=2) {
v.push_back(A[i]);
if(i+1<n) v.back()+=A[i+1]*B;
}
trim();
}
bigint& operator+=(const bigint& o) {
if(o.size()>size()) {
v.resize(o.size());
}
for(int i=0;i<o.size();++i) {
v[i]+=o.v[i];
}
trim();
return *this;
}
bool operator>(const bigint& o) const {
if(size()>o.size()) return true;
if(size()<o.size()) return false;
for(int i=size()-1;i>=0;--i) {
if(v[i]>o.v[i]) return true;
if(v[i]<o.v[i]) return false;
}
return false;
}
bool operator>=(const bigint& o) const {
if(v==o.v) return true;
return *this>o;
}
bigint operator+(bigint o) {
o+=*this;
return o;
}
vi digs() {
vi res;
for(auto i : v) {
for(int j=0;j<2;++j) {
res.push_back(i%B);
i/=B;
}
}
return res;
}
};
struct NCR {
map<pi,bigint> mp;
bigint ncr(int n, int k) {
if(k<0 or k>n) return {0};
if(k==0 or k==n) return {1};
if(mp.count({n,k})) return mp[{n,k}];
auto& tmp = mp[{n,k}] = ncr(n-1,k-1)+ncr(n-1,k);
return tmp;
}
bigint paths(int n, int m) {
return ncr(n+m,m);
}
};
}
void encode(int N, int M[]) {
using namespace encoding;
NCR c;
bigint used = 0;
bigint total(N,M);
int L=0;
while(true) {
bigint tmp = c.paths(L,B-1);
if(total>=used+tmp) {
used+=tmp;
} else break;
++L;
}
vi res;
int at=0;
while(res.size()!=L) {
int left = L-res.size();
bigint tmp = c.paths(left-1,B-1-at);
auto nxt = tmp+used;
if(nxt>total) {
res.push_back(at);
} else {
used=nxt;
++at;
}
}
for(auto& i : res) send(i);
}
#include "decoder.h"
#include "decoderlib.h"
#include "bits/stdc++.h"
using namespace std;
namespace decoding {
#define all(x) begin(x),end(x)
template<typename A, typename B> ostream& operator<<(ostream &os, const pair<A, B> &p) { return os << '(' << p.first << ", " << p.second << ')'; }
template<typename T_container, typename T = typename enable_if<!is_same<T_container, string>::value, typename T_container::value_type>::type> ostream& operator<<(ostream &os, const T_container &v) { string sep; for (const T &x : v) os << sep << x, sep = " "; return os; }
#define debug(a) cerr << "(" << #a << ": " << a << ")\n";
typedef vector<int> vi;
typedef pair<int,int> pi;
const int B = 256;
const int Base=B*B;
struct bigint {
vi v = {0};
int size() const {return v.size();}
void trim() {
int carry=0;
for(int i=0;i<size();++i) {
v[i]+=carry;
carry = v[i]/Base;
v[i]%=Base;
}
while(carry) {
v.push_back(carry%Base);
carry/=Base;
}
while(!v.empty() and v.back()==0) v.pop_back();
}
bigint() {}
bigint(int a) {
v = {a};
trim();
}
bigint(int n, int A[]) { // in base B
for(int i=0;i<n;i+=2) {
v.push_back(A[i]);
if(i+1<n) v.back()+=A[i+1]*B;
}
trim();
}
bigint& operator+=(const bigint& o) {
if(o.size()>size()) {
v.resize(o.size());
}
for(int i=0;i<o.size();++i) {
v[i]+=o.v[i];
}
trim();
return *this;
}
bool operator>(const bigint& o) const {
if(size()>o.size()) return true;
if(size()<o.size()) return false;
for(int i=size()-1;i>=0;--i) {
if(v[i]>o.v[i]) return true;
if(v[i]<o.v[i]) return false;
}
return false;
}
bool operator>=(const bigint& o) const {
if(v==o.v) return true;
return *this>o;
}
bigint operator+(bigint o) {
o+=*this;
return o;
}
vi digs() {
vi res;
for(auto i : v) {
for(int j=0;j<2;++j) {
res.push_back(i%B);
i/=B;
}
}
return res;
}
};
struct NCR {
map<pi,bigint> mp;
bigint ncr(int n, int k) {
if(k<0 or k>n) return {0};
if(k==0 or k==n) return {1};
if(mp.count({n,k})) return mp[{n,k}];
auto& tmp = mp[{n,k}] = ncr(n-1,k-1)+ncr(n-1,k);
return tmp;
}
bigint paths(int n, int m) {
return ncr(n+m,m);
}
};
}
void decode(int N, int L, int X[]) {
using namespace decoding;
NCR c;
sort(X,X+L);
bigint res = 0;
for(int i=0;i<L;++i) {
res+=c.paths(i,B-1);
}
int last=0;
for(int i=0;i<L;++i) {
int cur = X[i];
while(last<cur) {
int goright = L-i-1;
res+=c.paths(goright,B-1-last);
++last;
}
}
auto digs = res.digs();
digs.resize(N);
for(auto i : digs) output(i);
}
