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. 
from functools import lru_cache

from sys import stderr

INF = 10 ** 18 + 3
EPS = 1e-10


def res_to_stderr(function):
    def wrapped(*args, **kwargs):
        res = function(*args, **kwargs)
        print(res, file=stderr)
        return res

    return wrapped


@res_to_stderr
def range_of_len(start, length, step=1):
    return range(start, start + length * step, step)


@lru_cache(10 ** 9)
def find_perm(length, n_different):
    if length == 0:
        return []

    if n_different != length - 1:
        return (list(range_of_len(length, length - n_different - 1, - 1))
                + find_perm(n_different + 1, n_different))

    curr = length
    go_down = True
    res = []
    for _ in range(n_different + 1):
        res.append(curr)
        curr = length - curr + go_down
        go_down ^= True

    return res


def main():
    n, k = map(int, input().split())
    print(*find_perm(n, k))


if __name__ == '__main__':
    main()
