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.Scanner;

public class C275 
{

    public static void main(String argsp[])
    {
        Scanner s=new Scanner(System.in);
        int n=s.nextInt();int k=s.nextInt();
        
        int a[]=new int[n];
        for(int i=0;i<n;i+=2)
        {
            a[i]=n-i/2;
        }
        for(int i=1;i<n;i+=2)
        {
            a[i]=(int)Math.ceil(i/2.0);
        }
        
        
        if((k-1)%2==0)
        for(int i=k;i<n;i++)
            a[i]=a[i-1]-1;
        else
            for(int i=k;i<n;i++)
                a[i]=a[i-1]+1;
        StringBuilder ans=new StringBuilder();
        for(int i=0;i<n;i++)
        ans.append(a[i]+" ");
        
        System.out.println(ans);
            
        
    }
}
