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 Codeforces {
	public static void main(String args[]) {
		Scanner input = new Scanner(System.in);
		//int test = input.nextInt();
		//while(test-->0) {
			int n = input.nextInt();
			int m = input.nextInt();

			int count = m;
			int arr[] = new int[n+1];
			for(int i =1;i<=n;i++)arr[i] = i;
			int l = 1;
			int r = n;
			ArrayList<Integer>list = new ArrayList<>();
			while(l<r) {
				list.add(arr[l]);
				l++;
				count--;
				if(count == 0)break;
			    list.add(arr[r]);
				r--;
				count--;
				if(count == 0)break;
			}
			if(m%2 == 1) {
				for(int it:list)System.out.print(it+" ");
				for(int i =l;i<=r;i++) {
					System.out.print(i+" ");	
				}
				System.out.println();
			}else {
				for(int it:list)System.out.print(it+" ");
				for(int i = r;i>=l;i--)System.out.print(i+" ");
				System.out.println();
			}
		//}
			
			
	}
	
	public  static void sort(int arr[]) {
		ArrayList<Integer>list = new ArrayList<Integer>();
		for(int it:arr)list.add(it);
		Collections.sort(list);
		for(int i=0;i<arr.length;i++)arr[i] = list.get(i);
		
	}
}


class Pair{
	int a, b;
	public Pair(int a,int b) {
		this.a = a;
		this.b = b;
	}
}
