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

public class CF_Div2_275_C {

    static int INFINITY = 2000000000;

    public static void main(String[] args) throws IOException {
        br = new BufferedReader(new InputStreamReader(System.in));
        out = new PrintWriter(System.out);
        sc = new StringTokenizer("");

        int n = nxtInt();
        int k = nxtInt();
        int temp=k;

        HashSet<Integer> set = new HashSet<Integer>();

        int array[] = new int[n];
        array[0] = 1;
        set.add(1);
        int i = 1;
        int sign=1;
        while (k > 0) {
            int next = array[i - 1] + (sign*k);
            set.add(next);
            array[i] = next;
            k--;
            i++;
            sign*=-1;
        }

        if(i<n){
            array[i]=temp+2;
            i++;
        }
        for (int j = i; j < array.length; j++) {
            int next=array[j-1]+1;
//          if(set.contains(next) || next<1)
//          {   
//              int c=1;
//              while(set.contains(array[i-1]+c)){
//                  c++;
//              }
//              next=array[i-1]+c;
//          }
            array[j]=next;
            set.add(next);
        }
        
        for (int j = 0; j < array.length; j++) {
            if(j!=n-1){
            System.out.print(array[j]+" ");
            }else{
                System.out.print(array[j]);
            }
        }
        
        
        HashSet<Integer> s = new HashSet<Integer>();
        
        int prev=array[0];
        int counter=0;
        for (int j = 1; j < array.length; j++) {
            if(!s.contains(Math.abs(array[j]-prev))){
                s.add(Math.abs(array[j]-prev));
                counter++;
            }
            prev=array[j];
        }
//      System.out.println(counter+"---");
    }// end Main.

    static BufferedReader br;
    static StringTokenizer sc;
    static PrintWriter out;

    static String nxtTok() throws IOException {
        while (!sc.hasMoreTokens()) {
            String s = br.readLine();
            if (s == null)
                return null;
            sc = new StringTokenizer(s.trim());
        }
        return sc.nextToken();
    }

    static int nxtInt() throws IOException {
        return Integer.parseInt(nxtTok());
    }

    static long nxtLng() throws IOException {
        return Long.parseLong(nxtTok());
    }

    static double nxtDbl() throws IOException {
        return Double.parseDouble(nxtTok());
    }

    static int[] nxtIntArr(int n) throws IOException {
        int[] a = new int[n];
        for (int i = 0; i < n; i++)
            a[i] = nxtInt();
        return a;
    }

    static long[] nxtLngArr(int n) throws IOException {
        long[] a = new long[n];
        for (int i = 0; i < n; i++)
            a[i] = nxtLng();
        return a;
    }

    static char[] nxtCharArr() throws IOException {
        return nxtTok().toCharArray();
    }

}// end class
