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.*;
import java.util.*;


public class SolutionC {
    public void solve() throws Exception{
        BufferedReader bf = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter out = new PrintWriter(System.out);
        String []s = bf.readLine().split(" ");
        int n = Integer.parseInt(s[0]);
        int k = Integer.parseInt(s[1]);
        int ar[] = new int[n];
        ar[0]=1;
        int j = k;
        for(int i = 1 ; i <= k; i++){
            if(i%2==1)
                ar[i] = ar[i-1] + j;
            else
                ar[i] = ar[i-1] - j;
            j--;
        }
        for(int i = k+1 ; i<n ; i++)
            ar[i] = i+1;
        
        for(int i : ar){
            out.print(i+" ");
        }
        out.println();
        out.flush();
    }
    public static void main(String args[]) throws Exception{
        new SolutionC().solve();
    }

}
