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.*;
public class a {

    public static void main(String[] args) {
        Scanner input = new Scanner(System.in);
        int n = input.nextInt(), k = input.nextInt();
        int[] res = new int[n];
        int lo = 0, hi = n-1;
        for(int i = 0; i<k; i++)
        {
            if(i%2 == 0) res[i] = lo++;
            else res[i] = hi--;
        }
        for(int i = k; i<n; i++)
        {
            if(k%2 == 1) res[i] = lo++;
            else res[i] = hi--;
        }
        for(int x: res) System.out.print((x+1)+" ");
    }

}
