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 Solution {

    public static void main(String[] args){
        Scanner scanner = new Scanner(System.in);

        long n = scanner.nextLong();
        long k = scanner.nextLong();

        if (k == 1){
            for (int i=1; i<=n; i++){
                System.out.print(i + " ");
            }

            return;
        }

        long small = 1;
        long big = n;

        int i = 0;

        while (k > 1){

            if (i % 2 == 0){
                System.out.print(big + " ");
                big--;
            } else {
                System.out.print(small + " ");
                small++;
            }

            k--;
            i++;
        }

        if (i % 2 == 0){
            for (long j = big; j>= small; j--){
                System.out.print(j + " ");
            }
        } else {
            for (long j = small; j<=big; j++){
                System.out.print(j + " ");
            }
        }
    }

}
