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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Random;
import java.util.StringTokenizer;
import java.io.BufferedReader;
import java.io.InputStreamReader;

public class Two {

    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskA solver = new TaskA();
        solver.call(in,out);

        out.close();
    }

    static class TaskA {
        public void call(InputReader in, PrintWriter out) {
            int n ,k , a = 0 , b = 0;
            n = in.nextInt();
            k = in.nextInt();
            for (int i = 1; i <=n-k ; i++) {
                out.print(i+" ");
            }
            a = n-k;
            a++;
            b = n;
            for (int i = 0; i <k ;i++) {
                if(i%2==0) {
                    out.print(b+" ");
                    b--;
                }
                else{
                    out.print(a+" ");
                    a++;
                }
            }

        }
    }

    static final Random random=new Random();

    static void shuffleSort(int[] arr) {
        int n=arr.length;
        for (int i=0; i<n; i++) {
            int a=random.nextInt(n), temp=arr[a];
            arr[a]=arr[i];
            arr[i]=temp;
        }
        Arrays.sort(arr);
    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }
        public long nextLong(){
            return Long.parseLong(next());
        }

    }
}