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.Scanner;


public class Diverse {
 public static void main(String[]args){
     Scanner in=new Scanner(System.in);
    
     int n = in.nextInt();
     int k = in.nextInt();
     int[] A = new int[n];
     A[0] = 1;
     int f = 1;
     int i;
     for (i = 1; i <= k; i++) {
         A[i] = A[i - 1] + f * (k - i + 1);
         f *= -1;
     }
     int current = k + 2;
     while (i < n)
         A[i++] = current++;
     for (int j = 0; j < n; j++)
         System.out.print(A[j] + " ");   
 
     
     }
 
 }
    
    
    

