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.lang.*;
    import java.io.*;
    import java.io.BufferedReader;
    import java.io.InputStreamReader;
    import java.math.BigInteger;
     
     
    public class Main {
   
    public static void main(String args[] ) throws Exception {
  
    BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    String line = br.readLine();
     
     String[] my; 
  my = line.split(" ");
  int n,k;
  n = Integer.parseInt(my[0]);
  k = Integer.parseInt(my[1]);
  int i,j;
  i = k;
  j=k-1;
  int fir = k+1;
  int sec = 1;
  int tu = 1;
  int a[] = new int[n];
  while(true)
  {
      if(i<0 && j<0)break;
      if(tu%2==1){
          a[i] = fir;
          i-=2;
          fir--;
      }
      else {
          a[j] = sec;
          j-=2;
          sec++;
      }
      tu++;
    
  }
  for(i=k+1;i<n;i++)
  a[i] = a[i-1] + 1;
  for(i=0;i<n;i++)
  System.out.print(a[i] + " ");
  
   
   
    }
    
    }
     

