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;

/**
 * Created by Константин on 24.10.2014.
 */
public class C {
    public static void main(String[] args) {
        Scanner scanner  = new Scanner(System.in);
        int first = scanner.nextInt();
        int k = scanner.nextInt();
        int[] array = new int[first];
        int i;
        for (i = 0; i < first; i++) {
            array[i] = i+1;
        }
        if(k!= 1){
            i = 1;
            while (k > 0){
                if(i%2 == 0){
                    array[i] = array[i - 1] - k;
                }else {
                    array[i] = array[i - 1] + k;
                }
                k--;
                i++;
            }

        }

        for (int j = 0; j < array.length; j++) {
            System.out.print(array[j] + " ");
        }
    }
}