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.Arrays;
import java.util.StringTokenizer;

/*
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/**
 *
 * @author Alex
 */
public class Main {
   static int [] permut;
    public static void main(String[] args)throws IOException {
        BufferedReader bff = new BufferedReader(new InputStreamReader(System.in));    
            StringTokenizer st = new StringTokenizer(bff.readLine());
            int n = Integer.parseInt(st.nextToken());
            int k =Integer.parseInt(st.nextToken());
            permut = new int[n+1];
            int cont =0;
            int res = n-k;
            int menor =1;
            int mayor =n;
            for(int j=0;j<res;j++){
                 permut[j]=menor;
                 menor++;
            }
            for(int i=res;i<n;i+=2){
                    permut[i]=mayor;
                    permut[i+1]=menor;
                menor++;
                mayor--;
            }
            StringBuilder sb = new StringBuilder();
            for (int i = 0; i <n; i++) {
                sb.append(permut[i]+" ");
             }
            sb.deleteCharAt(sb.length()-1);
           System.out.println(sb);
    }

}
