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.*;

public class Solution {

    private static void solve(InputReader in, OutputWriter out) {
        int n, k;
        n = in.nextInt();
        k = in.nextInt();

        int left, right;
        left = 0;
        right = 2 + k;

        while (true) {
            left++;
            if (left == right)break;
            out.print(left + " ");

            right--;
            if (right == left) break;
            out.print(right + " ");
        }

        for (int i = 2 + k; i <= n; i++)
            out.print(i + " ");
    }

    public static void main(String[] args) {
        InputReader in = new InputReader(System.in);
        OutputWriter out = new OutputWriter(System.out);
        solve(in, out);
        in.close();
        out.close();
    }

    private static class InputReader {

        private BufferedReader br;
        private StringTokenizer st;

        InputReader(InputStream is) {
            br = new BufferedReader(new InputStreamReader(is));
            st = null;
        }

        String nextLine() {
            String line = null;

            try {
                line = br.readLine();

            } catch (IOException e) {
                e.printStackTrace();
            }

            return line;
        }

        String next() {
            while (st == null || !st.hasMoreTokens()) {
                String line = nextLine();

                if (line == null)
                    return null;

                st = new StringTokenizer(line);
            }

            return st.nextToken();
        }

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

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

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

        int[] nextIntArray(int n) {
            int[] a = new int[n];

            for (int i = 0; i < n; i++)
                a[i] = nextInt();

            return a;
        }

        long[] nextLongArray(int n) {
            long[] a = new long[n];

            for (int i = 0; i < n; i++)
                a[i] = nextLong();

            return a;
        }

        void close() {
            try {
                br.close();

            } catch (IOException e) {
                e.printStackTrace();
            }
        }
    }

    private static class OutputWriter {

        BufferedWriter bw;

        OutputWriter(OutputStream os) {
            bw = new BufferedWriter(new OutputStreamWriter(os));
        }

        void print(int i) {
            print(Integer.toString(i));
        }

        void println(int i) {
            print(i);
            print('\n');
        }

        void print(long l) {
            print(Long.toString(l));
        }

        void println(long l) {
            print(l);
            print('\n');
        }

        void print(double d) {
            print(Double.toString(d));
        }

        void println(double d) {
            print(d);
            print('\n');
        }

        void print(boolean b) {
            print(Boolean.toString(b));
        }

        void println(boolean b) {
            print(b);
            print('\n');
        }

        void print(char c) {
            try {
                bw.write(c);

            } catch (IOException e) {
                e.printStackTrace();
            }
        }

        void println(char c) {
            print(c);
            print('\n');
        }

        void print(String s) {
            try {
                bw.write(s);

            } catch (IOException e) {
                e.printStackTrace();
            }
        }

        void println(String s) {
            print(s);
            print('\n');
        }

        void close() {
            try {
                bw.close();

            } catch (IOException e) {
                e.printStackTrace();
            }
        }
    }
}
