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. 
//package com.company;

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.*;

public class Main {
    static long fac(int n) {
        long count=1;
        while (n > 0) {
            count*=n;
            n--;
        }
        return count;
    }
    public static void main(String args[])throws IOException {
        FastReader sc = new FastReader();
        PrintWriter out = new PrintWriter(System.out);
        int n = sc.nextInt();
        int k = sc.nextInt();
        int[] arr = new int[n+1];
        boolean[] visited = new boolean[n+1];
        arr[1]=1;visited[1]=true;
        for(int i=2;i<=n;i++) {
            if (k > 0) {
                if (arr[i - 1] - k >=1&&!visited[arr[i - 1] - k]) {
                    arr[i]=arr[i-1]-k;
                }
                else
                    arr[i]=arr[i-1]+k;
                visited[arr[i]]=true;
                k--;
            }
            else
                break;
        }
        ArrayList<Integer> l = new ArrayList<>(n);
        for(int i=1;i<=n;i++)
            if(arr[i]!=0)
                l.add(arr[i]);
        for(int i=1;i<=n;i++)
            if(!visited[i])
                l.add(i);
        for(int i=0;i<l.size();i++) {
            out.print(l.get(i)+" ");
        }
        out.println();
        out.close();
    }

    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader()
        {
            br = new BufferedReader(new
                    InputStreamReader(System.in));
        }

        String next()
        {
            while (st == null || !st.hasMoreElements())
            {
                try
                {
                    st = new StringTokenizer(br.readLine());
                }
                catch (IOException  e)
                {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt()
        {
            return Integer.parseInt(next());
        }

        long nextLong()
        {
            return Long.parseLong(next());
        }

        double nextDouble()
        {
            return Double.parseDouble(next());
        }

        String nextLine()
        {
            String str = "";
            try
            {
                str = br.readLine();
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
            return str;
        }
    }
}