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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.*;

public class Main {

	public static void main(String[] args) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		Scanner sc = new Scanner(br);
		int n = sc.nextInt();
		int k = sc.nextInt();
		int lastRemoved = 0;
		LinkedList<Integer> list = new LinkedList<Integer>();
		for (int i = 1; i <= n; i++) {
			list.add(i);
		}
		for (int i = 0; i < (k == 1 ? 0 : k); i++) {
			if (i % 2 == 0) {
				lastRemoved = list.removeLast();
				System.out.print(lastRemoved + " ");
			} else {
				lastRemoved = list.removeFirst();
				System.out.print(lastRemoved + " ");
			}
		}
		if (list.size() > 0) {
			if (Math.abs(list.getFirst() - lastRemoved) == 1) {
				while (list.size() != 0) {
					System.out.print(list.removeFirst() + " ");
				}
			} else {
				while (list.size() != 0) {
				System.out.print(list.removeLast() + " ");
				}
			}
		}
	}
}
