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.io.PrintWriter;
import java.util.Scanner;

public class T483C {

	public static void main(String[] args) {
		Scanner in=new Scanner(System.in);
		int i,j,n=in.nextInt(),k=in.nextInt();
		in.close();
		boolean[] f=new boolean[n+1];
		int[]ans=new int[n];

		ans[0]=1;
		f[ans[0]]=true;
		j=1;
		boolean b=false;
		while(k>0){
			if(!b&&!f[ans[j-1]+k]){
				ans[j]=ans[j-1]+k;
				b=true;
			}else if(b&&!f[ans[j-1]-k]){
				ans[j]=ans[j-1]-k;
				b=false;
			}
			f[ans[j]]=true;
			j++;
			k--;
		}
		
		for(i=1;i<=n;i++){
			if(!f[i])
				ans[j++]=i;
		}
		PrintWriter out=new PrintWriter(System.out);
		for(int e:ans)
			out.print(e+" ");
		out.flush();
	}

}
