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[] args) {

        
        Scanner in = new Scanner(System.in);
        

        long n=in.nextLong();
        long k=in.nextLong();
        long ans[]= new long[(int)n];
        
        boolean b[]= new boolean[(int)n+1];
        
        
        long diff=k;
        ans[0]=1;
        b[1]=true;
        int index=1;
        while(diff>0){
            if((ans[index-1]-diff)>0&&b[(int)(ans[index-1]-diff)]==false){
            ans[index]=ans[index-1]-diff;
            b[(int)(ans[index-1]-diff)]=true;
            }
            else{
                ans[index]=ans[index-1]+diff;
                b[(int) (ans[index-1]+diff)]=true;
            }
            diff--;
            index++;
        }
        
        for(int i=1;i<=n;i++){
            if(b[i]==false){
                ans[index]=i;
                index++;

            }
        }
        for(int i=0;i<ans.length;i++)
            System.out.print(ans[i]+" ");
    }
}
