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.io.PrintWriter;



public class Main {
	public static void main(String[] args) throws IOException {
		BufferedReader in = new BufferedReader(new InputStreamReader(
				System.in));
		PrintWriter out = new PrintWriter(System.out);
		
		String[] t = in.readLine().split(" ");
		int n = Integer.parseInt(t[0]);
		int k = Integer.parseInt(t[1]);

		out.print("1 ");
		int jump = n-1;
		int dir = 1;
		int pi = 1;
		int left = n-1;
		for (int i=1;i<k;i++) {
			pi = pi + (dir)*jump;
			dir = dir*-1;
			jump--;
			left--;
			out.print(pi + " ");
		}
		while (left>0) {
			pi = pi + dir;
			out.print(pi+ " ");
			left--;
		}

		out.close();
	}
}
