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.*;
import java.io.*;
import java.net.URL;
import java.util.ArrayList;

public class C {
	FastScanner in;
	PrintWriter out;

	public void solve() throws IOException {
		int n = in.nextInt();
		int k = in.nextInt();
		int[] ans = new int[n];
		int d = 1;
		int u = n;
		for (int i = 0; i < k; i++) {
			if (i % 2 == 0) {
				ans[i] = d;
				d++;
			} else {
				ans[i] = u;
				u--;
			}
		}
		if (k % 2 == 1) {
		for (int i = k; i < n; i++) {
			ans[i] = d;
			d++;
		}
		} else {
			for (int i = k; i < n; i++) {
				ans[i] = u;
				u--;
			}
				
		}
		for (int i = 0; i < n; i++) {
			out.print(ans[i] + " ");
		}
		out.println();
	}

	public void run() {
		try {
			in = new FastScanner(System.in);
			out = new PrintWriter(System.out);

			solve();

			out.close();
		} catch (IOException e) {
			e.printStackTrace();
		}
	}

	class FastScanner {
		BufferedReader br;
		StringTokenizer st;

		FastScanner(InputStream f) {
			try {
				br = new BufferedReader(new InputStreamReader(f));
			} catch (Exception e) {
				e.printStackTrace();
			}
		}

		String next() {
			while (st == null || !st.hasMoreTokens()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}

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

		double nextDouble() {
			return Double.parseDouble(next());
		}

		String nextLine() {
			try {
				return br.readLine();
			} catch (Exception e) {
				return null;
			}
		}

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

	public static void main(String[] arg) {
		new C().run();
	}
}