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.OutputStreamWriter;
import java.io.PrintWriter;
import java.util.StringTokenizer;


public class C {
	static BufferedReader in;
	static PrintWriter out;
	static StringTokenizer tok;

	public static void main(String[] args) throws IOException {
		in = new BufferedReader(new InputStreamReader(System.in));
		out = new PrintWriter(new OutputStreamWriter(System.out));
		tok = new StringTokenizer("");
		new C().solve();
		out.flush();
		out.close();
	}
	
	String nextTok() throws IOException {
		if (!tok.hasMoreTokens()) {
			tok = new StringTokenizer(in.readLine());
		}
		return tok.nextToken();
	}
	
	int nextInt() throws IOException {
		return Integer.parseInt(nextTok());
	}
	
	double nextDouble() throws IOException {
		return Double.parseDouble(nextTok());
	}
	
	void solve() throws IOException {
		int n = nextInt();
		int k = nextInt();
		boolean used[] = new  boolean[n+1];
		int[] ans = new int[n+1];
		//out.print(1+" ");
		used[1] = true;
		int ind = 2;
		ans[1] = 1;
		boolean pl = true;
		while (true) {
			if (k != 0) {
				if (pl) {
					pl = false;
					used[ans[ind-1]+k] = true;
					ans[ind] = ans[ind-1]+k;
					ind++;
					--k;
				} else {
					pl = true;
					used[ans[ind-1]-k] = true;
					ans[ind] = ans[ind-1]-k;
					ind++;
					--k;
				}
				
			} else break;
		}
		for (int i = 1; i < used.length; i++) {
			if (!used[i]) {
				ans[ind] = i;
				ind++;
			}
		}
		for (int i = 1; i < ans.length; i++) {
			out.print(ans[i]+" ");
		}
	}

}
