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 Main
{

    public static void main (String [] args) {
        Scanner s = new Scanner(System.in);
        int n=s.nextInt(),k=s.nextInt();

        int l=1,r=n;
        while(r-l>=k){
            System.out.print(l++ + " ");
        }
        for (int i=0;l<=r;i++){
            if(i%2 == 0)
                System.out.print(r-- + " ");
            else
                System.out.print(l++ + " ");
        }
    }
}