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. 
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import java.io.*;
import java.util.*;
import java.text.*;
import java.math.*;
import java.util.regex.*;
/**
 *
 * @author fz
 */
public class CF_rnd275C {
    Scanner in = new Scanner(System.in);

    private CF_rnd275C() throws IOException {
        //in.nextLine();
        int n = in.nextInt();
        int k = in.nextInt();
        ArrayList<Integer> res = new ArrayList<>();
        res.add(1);
        int tp = k;
        while(k != 0){
            int last = res.get(res.size() - 1);
            int num = last + k;
            res.add(num);
            if(k > 0)
                k--;
            else
                k++;
            k = -k;
        }
        for(int i = tp + 2; i <= n; i++)
            res.add(i);
        for(int i : res)
            System.out.print(i + " ");
    }
    
    
    
    private int[] ns(int n) {
        int[] a = new int[n];
        for(int i = 0; i < n; i++) {
            a[i] = in.nextInt();
        }
        return a;
    }
    private int[][] nmat(int m, int n) {//m rows and n cols
        int[][] res = new int[m][n];
        for(int i = 0; i < m; i++)
            for(int j = 0; j < n; j++)
                res[i][j] = in.nextInt();
        return res;
    }


    private static void out(Object x) {
        System.out.println(x);
    }
    public static void main(String[] args) throws IOException {
        new CF_rnd275C();
    }
}
