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.util.StringTokenizer;

public class asdf {
	public static int[][] freqC = { { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 },
			{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }, { 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 },
			{ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 }, { 0, 0, 2, 1, 0, 0, 0, 0, 0, 0 },
			{ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 }, { 0, 0, 0, 1, 0, 1, 0, 0, 0, 0 },
			{ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 }, { 0, 0, 3, 0, 0, 0, 0, 1, 0, 0 },
			{ 0, 0, 1, 2, 0, 0, 0, 1, 0, 0 } };

	public static void main(String[] Args) throws IOException {
		FastScanner sc = new FastScanner(System.in);
		int n = sc.nextInt();
		int k = sc.nextInt();
		for (int j = 0; j <= k;j++){
			if (j!=0)
				System.out.print(" ");
			if (j%2==0)
				System.out.print(j/2+1);
			else
				System.out.print(1 + k-j/2);
		}
		for (int j = k + 1; j < n; j++){
			System.out.print(" ");
			System.out.print(j+1);
		}
	}

	private static long f(long l) {
		return (l * (l - 1)) / 2;
	}

	public static class Pair implements Comparable<Pair> {
		int sort;
		int val;

		Pair(int a, int b) {
			sort = a;
			val = b;
		}

		public int compareTo(Pair o) {
			return sort - o.sort;
		}
	}

	public static char g(char o) {
		if (o >= '5')
			return (char) ('0' + 9 - o + '0');
		return o;
	}

	public static class FastScanner {
		StringTokenizer st;
		BufferedReader br;

		FastScanner(InputStream in) throws IOException {
			br = new BufferedReader(new InputStreamReader(in));
			st = new StringTokenizer(br.readLine());
		}

		String next() throws IOException {
			if (st.hasMoreTokens()) {
				return st.nextToken();
			}
			st = new StringTokenizer(br.readLine());
			return next();
		}

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