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_Permutation {

    public static void main(String[] args) {
        // TODO Auto-generated method stub
        Scanner x = new Scanner(System.in);
        int n = x.nextInt();
        int k = x.nextInt();
        int tempk = k+1;
        int temp = 1;
        int [] lis = new int [k+2];
        
        for (int i = 1; i <= k+1; i+=2) {
            lis[i] = temp;
            temp++;
            
        }
        for (int i = 2; i <=k+1; i+=2) {
            lis[i] = tempk;
            tempk--;
        }
        for (int i = 1; i <= k+1; i++) {
            System.out.print(lis[i]+ " ");
        }
        for(int i = k+2 ;i<=n;i++)
        {
            System.out.print(i + " ");
        }

    }

}