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 javax.print.attribute.IntegerSyntax;
import java.io.*;
import java.math.BigInteger;
import java.util.*;

public class SolveProblem {
    private BufferedReader in;
    private PrintWriter out;

    SolveProblem() {
        try {
            in = new BufferedReader(new FileReader("input.txt"));
            out = new PrintWriter(new FileWriter("output.txt"),true);
            solve();
        } catch (Exception e) {
            e.printStackTrace();
            in = new BufferedReader(new InputStreamReader(System.in));
            out = new PrintWriter(System.out);
            solve();
        } finally {
            try {
                in.close();
            } catch (IOException e) {

            }
            out.close();
        }
    }
    StringTokenizer st;
    String nextToken() {
        while (st == null || !st.hasMoreTokens())
            try {
                st = new StringTokenizer(in.readLine());
            } catch (IOException e) {

            }
        return st.nextToken();
    }

    int nextInt() {
        return Integer.valueOf(nextToken());
    }
    long nextLong() {
        return Long.valueOf(nextToken());
    }

    public void solve() {
        int n = nextInt();
        int k = nextInt();
        boolean[] a = new boolean[n+1];
        a[k+1] = true;
        a[1] = true;
        out.print(1 + " " + (1+k) + " ");
        int t = k-1;
        if (t == 0) t = 1;
        int lf = k+1;
        int i = 1;
        while(i <= n) {
            if (lf - t >= 1 && !a[lf - t]) {
                a[lf - t] = true;
                out.print(lf - t + " ");
                lf -= t;
                if (t > 1)
                    t--;
            } else if (lf + t <= n && !a[lf + t]) {
                a[lf + t] = true;
                out.print(lf + t + " ");
                lf += t;
                if (t > 1)
                    t--;
            }
            i++;
        }
        for (int j = 1; j <= n; j++) {
            if (!a[j])
                out.print(j + " ");
        }
    }

    public static void main(String[] args) {
        new SolveProblem();
    }
}