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.*;

/**
 *
 * @author al26n
 */
public class C {

        void solution() throws Exception {
                int n = in.nextInt();
                int k = in.nextInt() - 1;
                int l = 2, r = n;
                ArrayList<Integer> ans = new ArrayList<>();
                ans.add(1);
                boolean inc = true;
                while (k > 0) {
                        if (inc) {
                                ans.add(r);
                                r--;
                                inc = false;
                        } else {
                                ans.add(l);
                                l++;
                                inc = true;
                        }
                        k--;
                }
                if (inc) {
                        for (int i = l; i <= r; i++) {
                                ans.add(i);
                        }
                } else {
                        for (int i = r; i >= l; i--) {
                                ans.add(i);
                        }
                }
                for (int p : ans) {
                        out.print(p + " ");
                }
                out.println();
        }

        public static void main(String args[]) throws Exception {
                new C().init();
        }

        Scanner in;
        PrintWriter out;

        public void init() throws Exception {
                in = new Scanner(System.in);
                out = new PrintWriter(System.out);

                solution();

                out.flush();
                out.close();
        }

        class Scanner {

                private final BufferedReader reader;
                private StringTokenizer tokenizer;

                public Scanner(InputStream inputStream) {
                        reader = new BufferedReader(new InputStreamReader(inputStream));
                }

                public String next() throws Exception {
                        while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                                tokenizer = new StringTokenizer(reader.readLine());
                        }
                        return tokenizer.nextToken();
                }

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

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

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