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.ArrayList;
import java.util.List;
import java.util.Scanner;

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/**
 *
 * @author Rinat
 */
public class C275A {
    public static void main(String... args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int k = sc.nextInt();
        
        int arr[] = new int[n];
        
        for (int i = 0; i < n; i++) {
            arr[i] = (i + 1);
        }
        
        List ll = new ArrayList();
        int c = k;
        for (int i=0; i<k;i++) {
            ll.add(arr[i]);
            arr[i] = 0;
            ll.add(arr[i + c]);
            
            arr[i + c] = 0;
            c-=2;
            if (c <=0 ) break;            
        }
        for (int i : arr) {
            if (i != 0) {
                ll.add(i);
            }
        }
        
        for (Object object : ll) {
            System.out.print(object  + " ");
        }
    }
}
