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.FileNotFoundException;
import java.io.InputStreamReader;
import java.io.IOException;
import java.io.FileReader;
import java.io.BufferedReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.io.InputStream;

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

class TaskC {
    public void solve(int testNumber, FastScanner in, PrintWriter out) {
        int n = in.nextInt();
        int k = in.nextInt();

        int[] data = new int[n];
        for (int i = 0; i < n; ++i) {
            data[i] = i+1;
        }

        for (int i = n; i >= k+2; --i) {
            out.write(i + " ");
        }

        int s = 1;
        int e = k+1;

        while(s <= e) {
            if(s == e)
                out.write(s + " ");
            else
                out.write(e + " " + s + " ");
            s++;
            e--;
        }
    }
}

class FastScanner {
    BufferedReader br;
    StringTokenizer st;

    public FastScanner(InputStream stream) {
        br = new BufferedReader(new InputStreamReader(stream));
    }

    public String nextToken() {
        while (st == null || !st.hasMoreElements()) {
            try {
                st = new StringTokenizer(br.readLine());
            } catch (IOException e) {
                e.printStackTrace();
            }
        }
        return st.nextToken();
    }

    public int nextInt() {
        return Integer.parseInt(nextToken());
    }

}

