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.*;
public class CF0482A
{
 public static void main(String[] helloWorld) throws IOException
 {
  BufferedReader sIn = new BufferedReader(new InputStreamReader(System.in));
  String cS = sIn.readLine();
  int space = cS.indexOf(32);
  int n = Integer.parseInt(cS.substring(0, space));
  int k = Integer.parseInt(cS.substring(space + 1));
  StringBuilder sB = new StringBuilder();
  int nmink = n - k + 1;
  for (int i = 1; i < nmink; i ++)
  {
   sB.append(' ');
   sB.append(i);
  }
  for (int rhombus = n, r = nmink % 2, i = nmink; i <= n; i ++)
  {
   sB.append(' ');
   sB.append((i % 2 == r) ? rhombus -- : nmink ++);
  }
  System.out.println(sB.substring(1));
 }
}