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. 
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import java.util.*;

/**
 *
 * @author Bryan AW
 */
public class Codeforces {

    /**
     * @param args the command line arguments
     */
    public static void main(String[] args){
        
        //Diverse Permutation
                            
        Scanner sc=new Scanner(System.in);
        
        int n=sc.nextInt();
        int k=sc.nextInt();
        
        boolean[] vis=new boolean[n+1];
        
        int sum=k+2;
        
        for (int i=1;i<=k/2;i++){
            vis[i]=true;
            vis[sum-i]=true;
            System.out.print(i+" "+(sum-i)+" ");
        }
        
        for (int i=(k/2)+1;i<=n;i++){
            if (vis[i]==false){
                System.out.print(i+" ");
            }
        }
        
        System.out.println();
        
    }
    
}
