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.Collections.Generic;
using System.Linq;

namespace arc084_c
{
	class Program
	{
		static List<int> Back(List<int> list, int max, int limitlen)
		{
			if (list.Last() == 1)
			{
				list.RemoveAt(list.Count - 1);
			}
			else
			{
				list[list.Count - 1]--;
				if (list.Count != limitlen) list.Add(max);
			}
			return list;
		}
		static void Main(string[] args)
		{
			int[] x = Console.ReadLine().Split().Select(int.Parse).ToArray();
			if (x[0] % 2 == 0)
			{
				Console.Write(x[0] / 2);
				for (int i = 1; i < x[1]; i++) Console.Write(" " + x[0]);
				Console.WriteLine();
			}
			else
			{
				List<int> list = new List<int>();
				for (int i = 0; i < x[1]; i++) list.Add(x[0] / 2 + 1);
				for (int i = 0; i < x[1] / 2; i++)
				{
					list = Back(list, x[0], x[1]);
				}
				Console.WriteLine(string.Join(" ", list));
			}
		}
	}
}