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 void main(String[] args) throws IOException
    {
        Reader in = new Reader();
        StringBuilder out = new StringBuilder();
        int n, k, c, t;
        int[] check;
        
        for (int i = 0; i < 1; i++) 
        {
            n = in.nextInt();
            k = in.nextInt();
            check = new int[n+1];
            for (int j = 1; j <= n; j++) 
                check[j]=j;
            if(k==1)
                for (int j = 1; j <= n; j++) 
                    out.append(j+" ");
            else
            {
                out.append(n+" ");
                check[n]=-1;
                t = n;
                for (int j = k; j >= 1; j--) {
                    if(j<t )
                    {
                        if(t+j <= n && check[t+j]!=-1)
                            t = t+j;
                        else
                            t = t-j;
                        out.append(t+" ");
                        check[t]=-1;
                    }
                    else
                    {
                        t = t+j;
                        out.append(t+" ");
                        check[t]=-1;
                    } 
                }
                if(k+1 != n)
                    for (int j = n; j > 0; j--) 
                        if(check[j]!=-1)
                            out.append(check[j]+" ");
                    
            }
            out.deleteCharAt(out.length()-1).append("\n");
             
        }
        System.out.print(out);
    }
    static class  Reader 
    {
        BufferedReader br;
        StringTokenizer st;
        Reader() { // To read from the standard input
            br = new BufferedReader(new InputStreamReader(System.in));
        }
        Reader(int i) throws IOException { // To read from a file
            br = new BufferedReader(new FileReader("Sample Input.txt"));
        }
       String next() throws IOException {
          while (st == null || !st.hasMoreTokens())
             st = new StringTokenizer(br.readLine());
          return st.nextToken();
       }
       int nextInt() throws IOException { return Integer.parseInt(next()); }
       long nextLong() throws IOException { return Long.parseLong(next()); }
       double nextDouble() throws IOException { return Double.parseDouble(next()); }
       String nextLine() throws IOException { return br.readLine(); }
    }

}