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.*;
import java.math.*;
import java.util.regex.*;
public class DiversePerm
{
	public static void main(String args[])throws Exception
	{
		Scanner sc = new Scanner(System.in);
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

		//the code goes here
        int n = sc.nextInt();
        int k = sc.nextInt();

        int perm[] = new int[n];

        int i;
        int j = 1;
        for(i=0;i<=k;i+=2)
        {
            perm[i] = j;
            j++;
        }
        j = k+1;
        for(i=1;i<=k;i+=2)
        {
            perm[i] = j;
            j--;
        }

        for(i=k+1;i<n;i++)
        {
            perm[i] = i+1;
        }

        for(i=0;i<n;i++) System.out.print(perm[i]+" ");

	}
}