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.Random;
import java.util.Scanner;

public class Main {
    public static void main(String args[]){
        Scanner s=new Scanner(System.in);
        int n=s.nextInt();
        int k=s.nextInt();
        int l=1;
        int r=n;
        while(k-->0){
            if(k%2==0){
                System.out.print((l++) +" ");
            }
            else{
                System.out.print((r--)+" ");
            }
        }
        for(int i=l;i<=r;i++){
            System.out.print(i+" ");
        }
    }
}
