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 sc = new Scanner(System.in);
        int n=sc.nextInt();
        int k=sc.nextInt();
        int count=1;
        System.out.print(1);
        int temp=1;
        for(int i=k;i>0;i--){
            temp +=i*count;
            System.out.print(" "+temp);
            count*=-1;
        }
        for(int i=2+k;i<=n;i++){
            System.out.print(" "+i);
        }
        System.out.println("");
        
    
    }
}       
