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.*;
import java.io.*;

public class Main {

    public static void main(String[] args)throws IOException {

        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter out = new PrintWriter(System.out);

        StringTokenizer st1 = new StringTokenizer(br.readLine());

        int n = Integer.parseInt(st1.nextToken());
        int k = Integer.parseInt(st1.nextToken());

        TreeSet<Integer> hs = new TreeSet<>();

        for(int i = 1 ; i <= n ; i++)
        {
            hs.add(i);
        }

        StringBuilder sb = new StringBuilder();

        sb.append(hs.pollLast() + " ");
        int curr = n;

        boolean flag = true;

        while(k > 0)
        {
            if(flag)
            {
                sb.append((curr = curr-k) +" ");
                hs.remove(new Integer(curr));

                flag = false;
            }
            else
            {
                sb.append((curr = curr+k) +" ");
                hs.remove(new Integer(curr));

                flag = true;
            }


            k--;
        }

        while(!hs.isEmpty())
            sb.append(hs.pollLast() + " ");

        out.println(sb);

        out.flush();
        out.close();

    }
}
