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.util.*;
import java.io.*;

/**
 *
 * @author umang
 */

public class C483 {
    
    public static int mod = 1000000007;
    
    public static void main(String[] args) {
 
        InputReader in = new InputReader(System.in);
        PrintWriter w = new PrintWriter(System.out);
                    
        int n = in.nextInt();
        int k = in.nextInt();
        HashSet<Integer> set = new HashSet<>();
        ArrayList<Integer> list = new ArrayList<>();
        for(int i=1;i<=n;i++) set.add(i);        
        list.add(1);

        int dif=k;
        int ele = 1;
        set.remove(1);
        int f=0;
        for(int i=k;i>0;i--,dif--){
            if(f==0){
                if(!set.contains(ele+dif)){
                    ele-=dif;
                }
                else{
                    ele +=dif;
                    f=1;
                }
            }
            else{
                if(!set.contains(ele-dif)){
                    ele+=dif;
                }
                else{
                    ele-=dif;
                    f=0;
                }
            }
            list.add(ele);
            set.remove(ele);
        }
        
        for(int i=0;i<list.size();i++) w.print(list.get(i)+" ");
        for(int i=k+2;i<=n;i++) w.print(i+" ");
        w.close();
    }
    
    static class Pair{
        int c;
        int x;
        
        public Pair(int x,int c){
            this.x=x;
            this.c=c;
        }
        
    }
    
    static class CompareCost implements Comparator{

        @Override
        public int compare(Object t, Object t1) {
            Pair p1 = (Pair)t;
            Pair p2 = (Pair)t1;
            
            if(p1.c<p2.c){
                return -1;
            }
            else if(p1.c>p2.c){
                return 1;
            }
            else return 0;
        }
        
    }
    
    static class InputReader {

		private final InputStream stream;
		private final 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);
		}
	}
}    

