Problem:
Score : 800 points

Problem Statement

In Finite Encyclopedia of Integer Sequences (FEIS), all integer sequences of lengths between 1 and N (inclusive) consisting of integers between 1 and K (inclusive) are listed.

Let the total number of sequences listed in FEIS be X. Among those sequences, find the (X/2)-th (rounded up to the nearest integer) lexicographically smallest one.

Constraints

1 \leq N,K \leq 3 × 10^5

N and K are integers.

Input

Input is given from Standard Input in the following format:

K N

Output

Print the (X/2)-th (rounded up to the nearest integer) lexicographically smallest sequence listed in FEIS, with spaces in between, where X is the total number of sequences listed in FEIS.

Sample Input 1

3 2

Sample Output 1

2 1

There are 12 sequences listed in FEIS: (1),(1,1),(1,2),(1,3),(2),(2,1),(2,2),(2,3),(3),(3,1),(3,2),(3,3).
The (12/2 = 6)-th lexicographically smallest one among them is (2,1).

Sample Input 2

2 4

Sample Output 2

1 2 2 2

Sample Input 3

5 14

Sample Output 3

3 3 3 3 3 3 3 3 3 3 3 3 2 2

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
using namespace std;
using LL = long long;

template<typename T>bool chmax(T&a,T b){if(a<b){a=b;return true;}return false;}
template<typename T>bool chmin(T&a,T b){if(a>b){a=b;return true;}return false;}


// std::vector Declaration
template<typename T>
vector<T> make_v(size_t a) { return vector<T>(a); }
template<typename T,typename... Ts>
auto make_v(size_t a,Ts... ts) {
   return vector<decltype(make_v<T>(ts...))>(a,make_v<T>(ts...));
}

// std::vector Initialization
template<typename T>
void fill_all(T& arr, const T& v) { arr = v; }
template<typename T, typename U>
void fill_all(T& arr, const U& v) { for (auto& i : arr) fill_all(i, v); }

// std::vector Debug
template<typename T>
ostream& operator<<(ostream& os, const vector<T>& v) {
   os << "[";
   bool a = 1;
   for (auto e : v ) {
      os << (a ? "" : " "); 
      os << e;
      a = 0;
   }
   os << "]";
   return os;
}

// std::pair Debug
template<typename T, typename U>
ostream& operator<<(ostream& os, const pair<T, U>& p) {
   os << "(" << p.first << " " << p.second << ")";
   return os;
}

// std::set Debug
template<typename T>
ostream& operator<<(ostream& os, const set<T>& st) {
   os << "{";
   bool a = 1;
   for (auto e : st) {
      os << (a ? "" : " ");
      os << e;
      a = 0;
   }
   os << "}";
   return os;
}

// std::map Debug
template<typename T, typename U>
ostream& operator<<(ostream& os, const map<T, U>& mp) {
   os << "{";
   bool a = 1;
   for (auto e : mp) {
      os << (a ? "" : " ");
      os << e.first << ":" << e.second;
      a = 0;
   }
   os << "}";
   return os;
}

// std::tuple Debug
template<int N,class Tuple>
void out(ostream &os,const Tuple &t){}
template<int N,class Tuple,class H,class ...Ts>
void out(ostream &os,const Tuple &t){
   if(N)os<<" ";
   os<<get<N>(t);
   out<N+1,Tuple,Ts...>(os,t);
}
template<class ...Ts>
ostream& operator<<(ostream &os, const tuple<Ts...> &t){
   os<<"(";
   out<0,tuple<Ts...>,Ts...>(os,t);
   os<<")";
   return os;
}

// Debug
#define DUMP(x) cout<<#x<<" = "<<(x)<<endl

struct edge { int to, cost; };

const LL LINF = 1LL<<60;
const int IINF = 1<<30;
const LL MOD = 1e9+7;

int K, N;


void back(auto& v) {
   --v[v.size()-1];
   if (v[v.size()-1] == 0) {
      v.pop_back();
   } else {
      while (v.size() < N) {
         v.push_back(K);
      }
   }
}

int main()
{
   cin >> K >> N;

   if (K % 2 == 0) {
      cout << K / 2;
      for (int i = 0; i < N-1; ++i) {
         cout << " " << K;
      }
      cout << endl;
      return 0;
   }

   vector<int> ans(N, K / 2 + 1);

   for (int i = 0; i < N/2; ++i) {
      back(ans);
   }

   for (int i = 0; i < ans.size(); ++i) {
      cout << ans[i] << (i == ans.size()-1 ? "\n" : " ");
   }

   return 0;
}