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 DiversePermutation {

    public static InputReader in;
    public static PrintWriter out;
    
    public static final int MOD = (int) (1e9 + 7);
    public static void main(String[] args) {
        in = new InputReader(System.in);
        out = new PrintWriter(System.out);
        
        int n = in.nextInt(),
                k = in.nextInt();
        ArrayList<Integer> a = new ArrayList<Integer>();
        if((k&1) == 0) {
            for(int i = 1; i <= (n-1)/2; i++) {
                a.add(i);
                a.add(n + 1 - i);
            }
            a.add((n+1)/2);
            if((n&1) == 0)  a.add(n/2 + 1);
            int i = n - 1;
            for (; i > 0; i--) {
                if(Math.abs(a.get(i) - a.get(i-1)) > k)
                    break;
            }
            i--;
            for (; i >= 0; i -= 2) {
                a.add(a.get(i));
                a.set(i, -1);
            }
       } else {
           for(int i = 1; i <= (n-1)/2; i++) {
               a.add(n + 1 - i);
               a.add(i);
           }
           if((n&1) == 0)  a.add(n/2 + 1);
           a.add((n+1)/2);
           
           int i = n - 1;
           for (; i > 0; i--) {
               if(Math.abs(a.get(i) - a.get(i-1)) > k)
                   break;
           }
           i--;
           for (; i >= 0; i -= 2) {
               a.add(a.get(i));
               a.set(i, -1);
           }
       }
       //int[] result = new int[n];
       for (Integer ii : a) {
           if(ii == -1) continue;
           out.print(ii + " ");
       }
       out.close();
    }
    
    static class Node implements Comparable<Node>{
        int next;
        long dist;
        
        public Node (int u, int v) {
            this.next = u;
            this.dist = v;
        }
        
        public void print() {
            out.println(next + " " + dist + " ");
        }
        
        public int compareTo(Node n) {
            return Integer.compare(-this.next, -n.next);
        }
    }
    
    static class InputReader {

        private InputStream stream;
        private byte[] buf = new byte[8192];
        private int curChar, snumChars;
        private SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int snext() {
            if (snumChars == -1)
                throw new InputMismatchException();
            if (curChar >= snumChars) {
                curChar = 0;
                try {
                    snumChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (snumChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        public int nextInt() {
            int c = snext();
            while (isSpaceChar(c))
                c = snext();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = snext();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = snext();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public long nextLong() {
            int c = snext();
            while (isSpaceChar(c))
                c = snext();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = snext();
            }
            long res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = snext();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public int[] nextIntArray(int n) {
            int a[] = new int[n];
            for (int i = 0; i < n; i++)
                a[i] = nextInt();
            return a;
        }

        public String readString() {
            int c = snext();
            while (isSpaceChar(c))
                c = snext();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = snext();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        public boolean isSpaceChar(int c) {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);
        }
    }
}