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.util.Scanner;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.IOException;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 * @author bitver
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Scanner in = new Scanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskC solver = new TaskC();
        solver.solve(1, in, out);
        out.close();
    }
}

class TaskC {
    public void solve(int testNumber, Scanner in, PrintWriter out) {

        int n = in.nextInt();
        int k = in.nextInt();

        boolean[] used = new boolean[n+1];

        int current = 1;
        out.print(current);
        used[current] = true;
        while (k > 0){

            if (current - k > 0 && !used[current-k]){
                current = current-k;
            } else {
                current = current+k;
            }
            used[current] = true;
            out.print(" " + current);
            k--;
        }
        for (int i = 1; i < used.length; i++){
            if (!used[i]){
                out.print(" " + i);
            }
        }

    }
}

