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. 
/*
    Problem: find an order of the permutation of digits < n
    of length n such that |p1-p2|, |p2-p3|, ... |pn-1 - pn|
    has exactly k distinct values.

    Solution: Greedy. First noteyou can create a successive
    string of 1s by going in ascending or descending order
    Then note you can get unique numbers, by switching from
    high to low.
    Combine these strategies to make k-1 unique, and n-k 1s

    ex: n = 10, k = 5
    1 10 2 9 8 7 6 5 4 3
     9  8 7 1 1 1 1 1 1
*/

import java.util.Scanner;
public class CF482A {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int k = sc.nextInt();
        sc.close();

        StringBuilder out = new StringBuilder();

        // Create k - 1 uniques diffs
        int low = 2;
        int high = n;
        out.append(1);
        int i = 0;
        boolean startlow = true;
        while (i != k-1) {
            if (i == k - 1) { break; }
            out.append(" "+high);
            high--;
            i++;
            startlow = !startlow;

            if (i == k - 1) { break; }
            out.append(" "+low);
            low++;
            i++;
            startlow = !startlow;
        }

        // Create n-k 1 diffs
        if (startlow) {
            for (int j = low; j <= high; j++) {
                out.append(" "+j);
            }
        } else {
            for (int j = high; j >= low; j--) {
                out.append(" "+j);
            }
        }

        System.out.println(out);
    }
}
