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.Arrays;
import java.util.StringTokenizer;

public class Solution_A {
    private static BufferedReader in;
    private static StringTokenizer st;
    private static PrintWriter out;

    private static final boolean IS_JUDGE = true;

    public static void main(String[] args) throws IOException {
        if (IS_JUDGE) {
            in = new BufferedReader(new InputStreamReader(System.in));
            out = new PrintWriter(new OutputStreamWriter(System.out));
        } else {
            in = new BufferedReader(new FileReader(new File("input.txt")));
            out = new PrintWriter(new FileWriter(new File("output.txt")));
        }

        new Solution_A().solve();
        out.close();
    }

    private void solve() throws IOException {
        int n = nextInt();
        int k = nextInt();


        int[] a = new int[n];

        int l = 1;
        int r = n;

        for (int i = 0; i < k; i++) {
            if (i % 2 == 0) {
                a[i] = r;
                --r;
            } else {
                a[i] = l;
                ++l;
            }
        }

        if (k % 2 == 0) {
            for (int i = k; i < n; i++) {
                a[i] = l++;
            }
        } else {
            for (int i = k; i < n; i++) {
                a[i] = r--;
            }
        }

        for (int i = 0; i < a.length; i++) {
            out.print(a[i]);
            out.print(" ");
        }
    }

    public String next() throws IOException {
        while (st == null || !st.hasMoreTokens()) {
            st = new StringTokenizer(in.readLine());
        }
        return st.nextToken();
    }

    public int nextInt() throws IOException {
        return Integer.parseInt(next());
    }

    public long nextLong() throws IOException {
        return Long.parseLong(next());
    }

    public double nextDouble() throws IOException {
        return Double.parseDouble(next());
    }
}