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.Scanner;


public class C275 {

    public static void main(String[] args) {
        Scanner sc=new Scanner(System.in);
        
        int n=sc.nextInt();
        int k=sc.nextInt();
        
        int l=1;
        int a=1;
        
        boolean[] b=new boolean[n+1];

        StringBuilder ans=new StringBuilder();
        ans.append(1);
        
        b[1]=true;
        while(k>0){
            l+=k*a;
            ans.append(" ").append(l);
            b[l]=true;
            k--;
            a*=-1;
        }
        
        for(int i=1;i<n+1;i++){
            if(!b[i])
                ans.append(" ").append(i);
        }
        
        System.out.println(ans);
    }
}
