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# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.IO;
using System.Linq;
using System.Collections;
using System.Collections.Generic;
using System.Numerics;
using System.Diagnostics;
using System.Text;
using System.Text.RegularExpressions;
using System.Threading.Tasks;
using System.Runtime.InteropServices;
using System.Runtime.CompilerServices;
using static System.Math;


class P
{
    static void Main()
    {
        //1234
        //1…
        //2…
        //3…
        //4…
        int[] kn = Console.ReadLine().Split().Select(int.Parse).ToArray();
        int k = kn[0];
        int n = kn[1];
        if (k % 2 == 0) Console.WriteLine($"{k / 2} {string.Join(" ", Enumerable.Repeat(k.ToString(), n))}");
        else
        {
            //残りの真ん中
            //無
            //1…
            //2…
        }
    }
}