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.*;


public class bucky{




public static void main (String args[]) {

Scanner input=new Scanner(System.in);

HashMap<Long, Integer> map1= new HashMap<Long, Integer>();
HashMap<Integer, Integer> map2= new HashMap<Integer, Integer>();
HashMap<Integer, Integer> linieleft= new HashMap<Integer, Integer>();
HashMap<Integer, Integer> linieright= new HashMap<Integer, Integer>();

	
	
			
		//	String str=input.next();
			
			
			int n=input.nextInt();
			int k=input.nextInt();
			
	int a=1; System.out.print(a+" ");
	int contor=1; int x=a;
	
	for(int j=k;j>=1;j--){
	
		if(contor%2==1) a+=j; 
		
		else a-=j;
		
		if(contor==1) x=a;
		
		contor++;
		System.out.print(a+" ");
	
	}
//	System.out.println("x="+x);
	
	for(int l=x+1;l<=n;l++)
	System.out.print(l+" ");
		
		
		}
		
		}
		
		
		
		
	