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.PrintWriter;
import java.util.Scanner;


public class CF_5 {
    
    public static void main(String[] args){
        PrintWriter pw = new PrintWriter(System.out, true);
        Scanner sc = new Scanner(System.in);
        int n, k, a ,c,d;
        n = sc.nextInt();
        k = sc.nextInt();
        int[] ans = new int[n+1];
        boolean[] v = new boolean[n+1];
        a = n-k;
        
        for(int i=1;i<=a;i++){
            ans[i] = i;
            v[i] = true;
        }
        
        for(int i=a+1, b = k;i<=n;i++, b--){
            c = ans[i-1]+b;
            d = ans[i-1]-b;
            
            if(c <= n  && !v[c]){
                v[c] = true;
                ans[i] = c;
            }else if(d > 0){
                v[d] = true;
                ans[i] = d;
            }
        }
        
        for(int i=1;i<=n-1;i++){
            pw.print(ans[i]+" ");
        }
        pw.println(ans[n]);
        pw.close();
        sc.close();
    }
}
