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 java_for_cp{
    public static void main(String []args){
        Scanner in = new Scanner(System.in);
        int n,k; n=in.nextInt(); k=in.nextInt();
        if(k>=n) System.out.print("-1");
        int front=1,back=n;
        int count=0;
        ArrayList<Integer> all = new ArrayList<Integer>();
        while(count<k) {
            all.add(front);
            count++;
            front++;
            if (count == k) break;
            all.add(back);
            count++;
            back--;
            if (count == k) break;
        }
        int ss=all.size();
        if(all.get(ss-1)==back+1){
            for(int i=back;i>=front;i--) all.add(i);
        }
        else{
            for(int i=front;i<=back;i++) all.add(i);
        }

        for(int u: all) System.out.print(u+" ");
        System.out.println();
    }
}