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. 
/* package whatever; // don't place package name! */

import java.util.*;
import java.lang.*;
import java.io.*;

/* Name of the class has to be "Main" only if the class is public. */
public class Ideone
{
    public static void main (String[] args) throws java.lang.Exception
    {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int k = sc.nextInt();
        int a[] = new int[n];
        for(int i = 0;i<n;i++){
            a[i]=i+1;
        }
        int stack =0;
        for(int i = n-1;i>=0;i--){
            stack = Math.min(k-1,n-1-i);
            if(stack%2==0){
                a[i]=a[i]+stack/2;
            }
            else{
                a[i]=n-(a[i]+(stack-1)/2);
            }
        }
        for(int i = 0;i<n;i++){
            System.out.println(a[i]);
        }
    }
}