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.*;
import java.util.*;

public class DiversePerm{
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
		long n,k;
		n=sc.nextLong();
		k=sc.nextLong();
		ArrayList<Long> al = new ArrayList<Long>();
		long j=1;
		if(k%2==1){
			for(long i=k+1;j<=(k+1)/2;i--,j++){
				al.add(j);
				al.add(i);
			}
		}
		else{
			long i=k+1;
			for(;j<=(k/2);j++,i--){
				al.add(j);
				al.add(i);
			}
			al.add(i);
		}
		for(long i=k+2;i<=n;i++){
			al.add(i);
		}
		for(long a : al){
			System.out.print(a+" ");
		}
		System.out.println();
	}
}