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 Main {
	
	public static void main(String[] args) {
		Scanner cin = new  Scanner(System.in);
		int n = cin.nextInt(); int K = cin.nextInt();
		int [] a = new int[n];
		int last = n - K; int now = n, pre = 1;
		for (int i = 0; i < last; i++) a[i] = now--;
		for (int i = last; i < n; i += 2) a[i] = pre++;
		for (int i = last + 1; i < n; i += 2) a[i] = now--;
		for (int i = 0; i < n; i++) System.out.print(a[i] + " ");
		System.out.println();
	}
	
}
