Permutation p is an ordered set of integers p1, p2, ..., pn, consisting of n distinct positive integers not larger than n. We'll denote as n the length of permutation p1, p2, ..., pn.

Your task is to find such permutation p of length n, that the group of numbers |p1 - p2|, |p2 - p3|, ..., |pn - 1 - pn| has exactly k distinct elements.

Input

The single line of the input contains two space-separated positive integers n, k (1 ≤ k < n ≤ 105).

Output

Print n integers forming the permutation. If there are multiple answers, print any of them.

Examples

Input

3 2


Output

1 3 2


Input

3 1


Output

1 2 3


Input

5 2


Output

1 3 2 4 5

Note

By |x| we denote the absolute value of number x. 
import java.util.*;
import java.io.*;
public class Diverse_Permutation
{
	public static void main(String args[]) throws Exception
	{
		BufferedReader f=new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st=new StringTokenizer(f.readLine());
		int one=Integer.parseInt(st.nextToken());
		int two=Integer.parseInt(st.nextToken())+1;
		int[] arr=new int[one];
		int[] vals=new int[two];
		for(int x=0;x<two;x++)
			vals[x]=x+1;
		int left=0;
		int right=two-1;
		for(int x=0;x<two;x++)
		{
			if(x%2==0)
			{
				arr[x]=vals[left];
				left++;
			}
			else
			{
				arr[x]=vals[right];
				right--;
			}
		}
		for(int x=two;x<one;x++)
			arr[x]=x+1;
		for(int x=0;x<one;x++)
			if(x==0)
				System.out.print(arr[x]);
			else
				System.out.print(" "+arr[x]);
		System.out.println();
	}
}