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.math.*;;

public class Solution
{
	public static void main(String[] args)
	{
		Scanner s=new Scanner(System.in);
		int n=s.nextInt();
		int t=s.nextInt();
		int[] arr=new int[n+1];
		Arrays.fill(arr, 0);
		arr[0]=1;
		System.out.println(1);
		arr[1]=1;
		int d=1,sign=1;
		int f=t;
		for(int i=0;i<f;i++)
		{
			d+=(sign*t);
			arr[d]=1;
			t--;
			sign*=-1;
			System.out.println(d);
		}
		for(int i=2;i<n+1;i++)
			if(arr[i]==0)
				System.out.println(i);
		
		
	}
}

