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.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashSet;
import java.util.StringTokenizer;

public class ProblemC {

	static Scanner sc = new Scanner(System.in);
	static PrintWriter pw = new PrintWriter(System.out);

	public static void main(String[] args) throws IOException {
		int n = sc.nextInt(), k = sc.nextInt();
		if ((k - 1) % 2 == 0) {
			int last = n;
			for (int i = 0, j = 1, x = (k - 1) / 2; i < n; j++, x--) {
				if (x <= 0) {
					pw.print(j + " ");
					i++;
				} else {
					pw.print(j + " " + last-- + " ");
					i += 2;
				}
			}
		} else {
			int last = n - 1;
			pw.print(n + " ");
			for (int i = 0, j = 1, x = (k - 1) / 2; i < n - 1; j++, x--) {
				if (x <= 0) {
					pw.print(j + " ");
					i++;
				} else {
					pw.print(j + " " + last-- + " ");
					i += 2;
				}
			}
		}
		pw.flush();
	}

	static class Scanner {
		StringTokenizer st;
		BufferedReader br;

		public Scanner(InputStream s) {
			br = new BufferedReader(new InputStreamReader(s));
		}

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

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

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