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.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;
/**
 *
 * @author Sourav Kumar Paul
 */
public class C483 {
    public static void main(String[] args) throws IOException{
        BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
    
        StringTokenizer st = new StringTokenizer(reader.readLine());
        int n = Integer.parseInt(st.nextToken());
        int k = Integer.parseInt(st.nextToken());
         int low = 1, high =n;
         int i;
        for( i=0;i<k; i++)
        {
            if(i%2==0)
                System.out.print((low++)+ " ");
            else
                System.out.print((high--)+" ");
        }
        if(i%2==1)
        for( i=low; i<=high; i++)
            System.out.print(i+" ");
        else
            for(i =high; i>=low; i--)
                System.out.print(i+" ");
    }
}
