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.ArrayList;
import java.util.Scanner;


public class Diverse_Permutation {

    public static void main(String[] args) {
        // TODO Auto-generated method stub
        

        Scanner in=new Scanner(System.in);
        int n=in.nextInt();
        int k=in.nextInt();
        
        int []permutation =new int[n];
        boolean []permutationVisited =new boolean[n];
    for (int i = 0; i < n; i++) {
    permutation[i]=i+1;
               }
    for (int i = 0; i < permutation.length; i++) {
        if(i+k<permutation.length&&permutationVisited[i]==false
                &&i+k>=0){
            System.out.print(permutation[i]+" ");
            permutationVisited[i]=true;
            if(permutationVisited[i+k]==false){
                System.out.print(permutation[i+k]+" ");
            permutationVisited[i+k]=true;
            }
            k-=2;
            if(k<0) k=0;
        }
        
    }   
    
    
    
    
    }

}
