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 Java8 (OpenJDK 1.8.0) (judge verdict: Time Limit Exceeded)

import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.List;
import java.util.Scanner;

class Main{

    static int K;

    static boolean dec(ArrayList<Integer> list, int digit){
        int pos = list.size()-1-digit;
        if(list.get(pos)==0){
            if(dec(list, digit+1))list.set(pos, K);
        }else{
            list.set(pos, list.get(pos)-1);
        }
        if(list.get(pos)>0)return true;
        return false;
    }

    public static void main(String[] args){
        Scanner scan = new Scanner(System.in);
        K = scan.nextInt();
        int N =scan.nextInt();
        ArrayList<Integer> ans = new ArrayList<>();
        if(K%2==0){
            ans.add(K/2);
            while(N-->1)ans.add(K);
        }else{
            for(int i=0;i<N;++i)ans.add((K+1)/2);
            for(int i=0;i<(N/2);++i){
                dec(ans, 0);
            }
        }
        PrintWriter pw = new PrintWriter(System.out);
        for(int i : ans)if(i!=0)pw.print(i+" ");
        pw.println();
        pw.flush();
    }
}