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.*;
public class Main{
  /*
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  some constants
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  */
  static int i=0,j=0,k=0,l=0;
  static int arr[]=new int[100000+1];
  static boolean visited[]=new boolean[100000+1];
  static int a=-1;
  /*
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  if any
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  */
  public static void main(String[] args) throws IOException{
		/*
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		*/
    i=j=k=l=0;
    int n=ni();
    int k=ni();
    boolean flag=true;
    push(1);
    int temp=1;
    int count=1;
    while(k>0){
      if(flag){
        temp += k;
        push(temp);
        k--;
        flag=false;
      }
      else{
        temp -= k;
        push(temp);
        k--;
        flag=true;
      }
      count++;
    }
    i=1;
    while(count<n){
      while(visited[i]){
        i++;
      }
      push(i);
      count++;
      i++;
    }
    for(i=1;i<=n;i++){
      System.out.print(arr[i-1]+" ");
    }
    /*
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		*/
	}
	/*
	temporary functions
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	.
	*/
  static void push(int data){
    a++;
    arr[a]=data;
    visited[data]=true;
  }
	/*
	fuctions
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	abcdefghijklmnopqrstuvwxyz
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	*/
	static int modulo(int j,int m){
		if(j<0)
			return m+j;
		  if(j>=m)
			return j-m;

			return j;
	}
	static final int mod=1000000007;
	static final double eps=1e-8;
	static final long inf=100000000000000000L;
	static final boolean debug=true;
	static Reader in=new Reader();
	static StringBuilder ans=new StringBuilder();
	static long powm(long a,long b,long m){
		long an=1;
		long c=a;
		while(b>0){
			if(b%2==1)
				an=(an*c)%m;
			c=(c*c)%m;
			b>>=1;
		}
		return an;
	}
	static Random rn=new Random();
	static void sop(Object a){System.out.println(a);}
	static int ni(){return in.nextInt();}
	static int[] nia(int n){int a[]=new int[n];for(int i=0;i<n;i++)a[i]=ni();return a;}
	static long nl(){return in.nextLong();}
	static long[] nla(int n){long a[]=new long[n];for(int i=0; i<n; i++)a[i]=nl();return a;}
	static String ns(){return in.next();}
	static String[] nsa(int n){String a[]=new String[n];for(int i=0; i<n; i++)a[i]=ns();return a;}
	static double nd(){return in.nextDouble();}
	static double[] nda(int n){double a[]=new double[n];for(int i=0;i<n;i++)a[i]=nd();return a;}
	static class Reader{
		public BufferedReader reader;
		public StringTokenizer tokenizer;
		public Reader(){
			reader=new BufferedReader(new InputStreamReader(System.in),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());
		}
		public double nextDouble(){
			return Double.parseDouble(next());
		}
	}
}
