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;

public class DiversePermutation {
    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];
        int high = n;
        int low = 1;
        for (int i = 0; i < k; i++) {
            if (i % 2 == 0) {
                arr[i] = low++;
            } else {
                arr[i] = high--;
            }
        }
        if (k % 2 == 0) {
            for (int i = k; i < n; i++) {
                arr[i] = high--;
            }

        } else {
            for (int i = k; i < n; i++) {
                arr[i] = low++;
            }
        }

        for (int i = 0; i < n; i++) {
            System.out.print(arr[i] + " ");
        }
    }
}
