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.Scanner;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.IOException;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 * @author mongsiry013
 */
public class Main {
	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		Scanner in = new Scanner(inputStream);
		PrintWriter out = new PrintWriter(outputStream);
		Task solver = new Task();
		solver.solve(1, in, out);
		out.close();
	}
}

class Task {
    public void solve(int testNumber, Scanner in, PrintWriter out) {
        int n, k;
        n = in.nextInt();
        k = in.nextInt();

        int ans[] = new int[n];

        ans[0] = 1;
        for(int i=0, j = k; j>0; ++i, j--){
            if(i % 2 == 0)
                ans[i+1] = ans[i] + j;
            else
                ans[i+1] = ans[i]-j;
        }
        for(int i=k+1; i<n; ++i){
            ans[i] = i+1;
        }
        for(int i : ans) out.printf(i + " ");
    }
}

