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 First {
    private static final Scanner sc = new Scanner(System.in);
    private static final PrintWriter pw = new PrintWriter(System.out);
    private static StringBuffer ans = new StringBuffer();

    public static void main(String[] args) throws Exception {
        int n = sc.nextInt(), k = sc.nextInt();
        ArrayDeque<Integer> a = new ArrayDeque<>();
        for (int i = 0; i < n; i++) a.addLast(i + 1);
        for (int i = 0; i < k; i++) {
            ans.append(a.pollFirst() + " ");
            i++;
            if (i == k) {
                while (!a.isEmpty()) ans.append(a.pollFirst() + " ");
                break;
            }
            else ans.append(a.pollLast() + " ");
        }
        while (!a.isEmpty()) ans.append(a.pollLast() + " ");
        pw.print(ans);
        sc.close();
        pw.close();
    }
}
class Scanner {
    private final BufferedReader br;
    private StringTokenizer st;
    public Scanner(InputStream in) {
        br = new BufferedReader(new InputStreamReader(in));
        st = new StringTokenizer("");
    }
    public String next() throws IOException {
        if (!st.hasMoreTokens())
            st = new StringTokenizer(br.readLine());
        return st.nextToken();
    }
    public int nextInt() throws IOException {
        return Integer.parseInt(next());
    }
    public void close() throws IOException {
        br.close();
    }
}
class PrintWriter {
    private final BufferedOutputStream pw;
    public PrintWriter(OutputStream out) {
        pw = new BufferedOutputStream(out);
    }
    public void print(Object o) throws IOException {
        pw.write(o.toString().trim().getBytes());
        pw.flush();
    }
    public void close() throws IOException {
        pw.close();
    }
}