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 DiversePermutation {
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        
        int n = in.nextInt();
        int k = in.nextInt();
        
        int[] permutation = new int[n];
        for (int i = 0; i < n; i += 2) {
            permutation[i] = i / 2 + 1;
            if (i + 1 < n)
                permutation[i + 1] = n - i / 2;
        }
        if (k % 2 == 0) {
            for (int i = k, p = permutation[k - 1] - 1; i < n; i++, p--) {
                permutation[i] = p;
            }
        } else {
            for (int i = k, p = permutation[k - 1] + 1; i < n; i++, p++) {
                permutation[i] = p;
            }
        }
        for (int i = 0; i < n; i++) {
            if (i > 0) System.out.print(" ");
            System.out.print(permutation[i]);
        }
        System.out.println();
        
        in.close();
        System.exit(0);
    }
}