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.BufferedWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.util.Locale;
import java.util.StringTokenizer;


public class A {
	
	private static BufferedReader in;
	private static StringTokenizer st;
	private static PrintWriter out;

	public static void main(String[] args) throws Exception {
		Locale.setDefault(Locale.US);
		in = new BufferedReader(new InputStreamReader(System.in));
		st = new StringTokenizer("");
		out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
		int n = nextInt();
		int k = nextInt();
		int ans[] = new int [n+1];
		boolean used[] = new boolean [n+1];
		for (int i = 1; i <=k; i++) {
			if(i % 2 == 1){
				ans[i] = i/2 + 1;
			}else{
				ans[i] = n - ans[i-1] + 1;
			}
			used[ans[i]] = true;
		}
		int count = k;
		if(k % 2 ==0){
			for (int i = n; i >=1; i--) {
				if(!used[i]){
					ans[++count] = i;
				}
			}
		}else{
			for (int i = 1; i <=n; i++) {
				if(!used[i]){
					ans[++count] = i;
				}
			}
		}


		for (int i = 1; i <= n; i++) {
			out.print(ans[i]+" ");
		}
		out.close();
	}

	private static double nextDouble() throws Exception {
		return Double.parseDouble(next());
	}

	private static long nextLong() throws Exception {
		return Long.parseLong(next());
	}

	private static int nextInt() throws Exception {
		return Integer.parseInt(next());
	}
	
	private static String next() throws IOException {
		while(!st.hasMoreTokens())
			st = new StringTokenizer(in.readLine());
		return st.nextToken();
	}

}
