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.io.*;
import java.util.*;
import java.text.*;
import java.math.*;
import java.util.regex.*;

public class a {

    public static void main(String[] args) {
        Scanner s = new Scanner(System.in);
        int n = s.nextInt();
        int k=s.nextInt();
        int a[]=new int[n];
        int j=0;
        int a1=1;
        int b1=n;
        for(int i=0;i<k;i++){
          if(i%2==0){
             a[j++]=a1++;
          }
          else
            a[j++]=b1--;  
        }
        int l=a[k-1];
       if(k%2==1){ 
        l++;
        for(int i=k;i<n;i++)
          a[j++]=l++;
       }
       else{
        l--;
        for(int i=k;i<n;i++)
          a[j++]=l--;
       }   
       
        for(int i=0;i<n;i++)
          System.out.print(a[i]+" ");  
    }
}

