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.*;
public class MyClass {
    public static void main(String args[]) {
        Scanner scan = new Scanner(System.in);
        Vector <Integer> v= new Vector();
        int n=scan.nextInt(),k=scan.nextInt(),i=0;
        for(;i<n;i++)v.add(i+1);
        for(i=0;i<k;i++){
            if(i==0)continue;
            else if(i==1){v.insertElementAt(v.get(v.size()-1) , 0);v.remove(v.size()-1);}
            else if(i==2){Collections.swap(v, 0, 1);}
            else{
                if(i%2==1)Collections.swap(v, v.size()-1, v.size()-2);
                else {
                    v.insertElementAt(v.get(v.size()-2) , i-1);
                    v.remove(v.size()-2);
                }
            }
        }
        for(int j:v)System.out.print(j+" ");
    }
}//