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.util.*;

public class Solution {

    private BufferedReader in;
    private PrintWriter out;
    private StringTokenizer st;

    private String next() throws Exception {
        if(st == null || !st.hasMoreElements())
            st = new StringTokenizer(in.readLine());
        return st.nextToken();
    }

    private int nextInt() throws Exception {
        return Integer.parseInt(next());
    }
    private long nextLong() throws Exception {
        return Long.parseLong(next());
    }
    private double nextDouble() throws Exception {
        return Double.parseDouble(next());
    }

    private void run() throws Exception {
        in = new BufferedReader(new InputStreamReader(System.in));
        out = new PrintWriter(System.out);
        // The solution of the problem goes here
        int n = nextInt();
        int k = nextInt();
        int[] a = new int[n];
        if (k == 1) {
            for (int i = 0; i < n; i++)
                out.print((i + 1) + " ");
            out.println();
            out.close();
            return;
        }
        for (int i = k + 1; i < n; ++i)
            a[i] = i + 1;
        int j = 1, l = k + 1;
        for (int i = 0; i <= k; i += 2) {
            a[i] = j++;
            if (i < k)
                a[i + 1] = l--;
        }
        Set<Integer> set1 = new HashSet<Integer>();
        Set<Integer> set2 = new HashSet<Integer>();
        for (int i = 0; i < n; i++) {
            out.print(a[i] + " ");
        }
        out.println();
        // for (int i = 0; i < n - 1; i++)
        //     set2.add(Math.abs(a[i] - a[i + 1]));
        // if (set1.size() == n && set2.size() == k) {
        //     out.println("ok");
        // } else {
        //     out.println("fail");
        // }

        out.close();
    }

    public static void main(String[] args) throws Exception {
        new Solution().run();
    }
}