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.BufferedWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.Arrays;
import java.util.HashMap;
import java.util.Locale;
import java.util.Map;
import java.util.PriorityQueue;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.util.TreeSet;

public class C {
	static StringTokenizer st;
	static BufferedReader br;
	static PrintWriter pw;

	public static void main(String[] args) throws IOException {
		Locale.setDefault(Locale.US);
		br = new BufferedReader(new InputStreamReader(System.in));
		pw = new PrintWriter(new BufferedWriter(new OutputStreamWriter(
				System.out)));
		int n = nextInt(), k = nextInt(), t = 0, l = 1, r = n;
		int a[] = new int[n + 1];
		while (++t <= k) {
			if (t % 2 == 1) {
				a[t] = r--;
			} else {
				a[t] = l++;
			}
		}
		if (k % 2 == 0) {
			l = a[k] + 1;
			for (int i = k + 1; i <= n; i++) {
				a[i] = l++;
			}
		} else {
			r = a[k] - 1;
			for (int i = k + 1; i <= n; i++) {
				a[i] = r--;
			}
		}
		for (int i = 1; i <= n; i++) {
			pw.print(a[i] + " ");
		}
		pw.close();
		/*
		 * 6 2 6 1 2 3 4 5 6 3 6 1 5 4 3 2 6 4 6 1 5 2 3 4 6 5 6 1 5 2 4 3
		 */
	}

	private static int nextInt() throws IOException {
		return Integer.parseInt(next());
	}

	private static long nextLong() throws IOException {
		return Long.parseLong(next());
	}

	private static double nextDouble() throws IOException {
		return Double.parseDouble(next());
	}

	private static String next() throws IOException {
		while (st == null || !st.hasMoreTokens())
			st = new StringTokenizer(br.readLine());
		return st.nextToken();
	}
}
