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;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;
import java.util.StringTokenizer;

public class kvati {
    private String[] s;
    public static void main(String[] args) throws IOException {
        BufferedReader rd = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter pw = new PrintWriter(System.out, true);
        new kvati().run(rd, pw);
    }
    
    public void run(BufferedReader rd, PrintWriter pw) throws IOException {
        StringTokenizer st = new StringTokenizer(rd.readLine());
        int n = Integer.parseInt(st.nextToken());
        int k = Integer.parseInt(st.nextToken());
        
        for (int i = 1; i <= n - k - 1; i ++)
            pw.print(i + " ");
        for (int i = 0; i <= k / 2; i ++)
            pw.print(n - k + i + " " + ((k % 2 == 0 && i == k / 2)? "": (n - i) + " "));
        pw.flush();
    }   

}
