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 A482 {

    public static void main(String[] args) {
        Scanner input = new Scanner(System.in);
        int N = input.nextInt();
        int K = input.nextInt();
        int down = 1;
        int up = N+1;
        boolean lastUp = false;
        StringBuilder output = new StringBuilder("1");
        for (int n=2; n<=N; n++) {
            int next;
            if (n <= K) {
                if (lastUp) {
                    next = ++down;
                } else {
                    next = --up;
                }
                lastUp = !lastUp;
            } else {
                if (lastUp) {
                    next = --up;
                } else {
                    next = ++down;
                }
            }
            output.append(' ');
            output.append(next);
        }
        System.out.println(output);
    }
    
}
