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. 
/**
 * Created by Phillip on 10/27/2014.
 */
import java.io.*;
import java.util.*;
public class Main {
    public static void main(String[] args) throws IOException{
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer(in.readLine());
        int n = Integer.parseInt(st.nextToken());
        int k = Integer.parseInt(st.nextToken());
        boolean[] covered = new boolean[n+1];
        int index=0;
        int numberof = 1;
        if(k%2==0){
            System.out.print(n+" ");
            covered[n] = true;
            System.out.print("1");
            k--;
            index++;
            numberof++;
        }
        else{
            System.out.print("1");
        }
        for(int i=2;i<=n;i++){
            if(numberof<k){
                System.out.print(" "+(n-index));
                covered[n-index] = true;
                numberof += 2;
                index++;
            }
            if(!covered[i]) System.out.print(" "+i);
        }
        in.close();
        System.exit(0);
    }
}
