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.*;
public class A
{
      public static void main(String ar[])
      {
        Scanner s=new Scanner(System.in);
        int n=s.nextInt();  int k=s.nextInt();    int aa=1,b=k+1;
        int a[]=new int[n];
        for(int i=0;i<k+1;i++)
        {
              if(i%2==0)
             {  a[i]=aa;  aa++;  }
              else
             { a[i]=b;  b--;   }
        }
        for(int i=k+1;i<n;i++)
         a[i]=i+1;
        for(int i=0;i<n;i++)
         System.out.print(a[i]+" ");
      }
}