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.Scanner;

public final class DiversePermutationCF {
    public static void main(String[] args) {
        Scanner sc=new Scanner(System.in);
        int n=sc.nextInt();
        int k=sc.nextInt();
        int ans[]=new int[n];
        int left=1,right=1+k;
        int start=0;
        boolean ok=true;
        while(left<=right){
            if(ok){
                ans[start]=left++;
                ok=false;
            }else{
                ans[start]=right--;
                ok=true;
            }
            start++;
        }
        for(int i=k+2;i<=n;i++){
            ans[start]=i;
            start++;
        }
        for(int ele:ans)
            System.out.print(ele+" ");
        System.out.println();
    }
}
