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.io.*;
import java.math.*;
import java.text.*;
import java.util.*;

public class Solution{
    BufferedReader br;
    PrintWriter out;
    static String input[];
    static int id = 0;
    public String next() throws Exception{
        if(input == null || input.length == id){
            input = br.readLine().split(" ");
            id=0;
        }
        return input[id++];
    }
    public String ns() throws Exception{
        return next();
    }
    public int ni() throws Exception{
        return Integer.parseInt(next());
    }
    public long nl() throws Exception{
        return Long.parseLong(next());
    }
    public double nd() throws Exception{
        return Double.parseDouble(next());
    }
    public int[] na(int n) throws Exception{
        int[] arr = new int[n];
        for(int i=0;i<n;i++){
            arr[i] = ni();
        }
        return arr;
    }

    public void run() throws Exception{
        br = new BufferedReader(new InputStreamReader(System.in));
        out = new PrintWriter(System.out);
        int T=1;
        for(int t=1;t<=T;t++){
            solve();
        }
        out.flush();
    }

    public static void main(String[] args) throws Exception{new Solution().run();}
    
    static int lsize,rsize;
    public void solve() throws Exception{
        int n = ni();
        int k = ni();
        LinkedList<Integer> al = new LinkedList<Integer>();
        int x = n/2 + 1;
        al.add(x);
        int i=x-1;
        int j=x+1;
        for(int it = 1; it <= k; it++){
            if(it%2 ==1){
                al.add(i--);
            }
            else{
                al.add(j++);
            }
        }
        if(k%2 == 1){
            while(j<=n){
                al.addFirst(j++);
            }
            while(i>=1){
                al.add(i--);
            }
        }
        else{
            while(j<=n){
                al.add(j++);
            }
            while(i>=1){
                al.addFirst(i--);
            }
        }
        Iterator<Integer> itr = al.iterator();
        StringBuilder sb = new StringBuilder("");
        while(itr.hasNext()){
            sb.append(itr.next()+" ");
        }
        out.println(new String(sb));
    }
}