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.BufferedReader;
import java.io.InputStreamReader;
import java.util.HashSet;
import java.util.StringTokenizer;

/**
 * Created by chinh on 7/19/14.
 */
public class R275D2C {
    public static void main(String[] args) throws Exception {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer(br.readLine());
        int n = Integer.parseInt(st.nextToken());
        int k = Integer.parseInt(st.nextToken());
        int cur = n;
        int count=1;
        System.out.print(cur+" ");
        for(int i=k; i>0; i--){
            cur += (k-i)%2==0 ? -i : i;
            count++;
            if(count==n) System.out.println(cur); else System.out.print(cur+" ");
        }
        for(int i=n-k-1; i>0; i--){
            count++;
            if(count==n) System.out.println(i); else System.out.print(i+" ");
        }
    }
}
