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 G on 11/1/14.
 */
public class CF482A {

    public static void main(String[] args){

        Scanner sin = new Scanner(System.in);

        int n = sin.nextInt();
        int k = sin.nextInt();

        int i = 1;
        int last = 1;
        System.out.print("1 ");

        while (i <= k){
            int dif = k - i + 1;
            if (i % 2 == 0){
                dif *= -1;
            }

            last = last + dif;
            System.out.print(last + " ");
            ++i;
        }

        while(i < n){
            System.out.print(++i + " ");
        }
    }
}
