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 _482A_Diverse_Permutation {
    public static void main(String[] args) {
	Scanner in = new Scanner(System.in);
	int n = in.nextInt();
	int k = in.nextInt();
	int MAX = 100005;
	boolean[] a = new boolean[MAX];
	int l = 1;
	boolean inc = true;
	a[1] = true;
	System.out.print(1 + " ");
	for (int i = k; i > 0; i--) {
	    if (inc) {
		l = l + i;
	    } else {
		l = l - i;
	    }
	    inc = !inc;
	    a[l] = true;
	    System.out.print(l + " ");
	}
	for (int i = 1; i <= n; i++) {
	    if (!a[i])
		System.out.print(i + " ");
	}
    }
}