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 Main {

	public static void main(String[] args) {
		Scanner sc=new Scanner(System.in);
		int n=sc.nextInt(),k=sc.nextInt();
		boolean[] vis=new boolean[n+1];
		
		int val=k,cur=1;
		vis[1]=true;
		System.out.print(cur);
		for(int i=1;i<n && val>0;++i){
			if(cur-val>0 && !vis[cur-val])cur-=val;
			else if(cur+val<=n && !vis[cur+val])cur+=val;
			System.out.print(" "+cur);
			vis[cur]=true;--val;
		}
		for(int i=1;i<=n;++i)if(!vis[i])System.out.print(" "+i);
		System.out.println();
		sc.close();
	}

}
