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 itertools import permutations


def main():
    n, k = map(int, input().strip().split())
    a = b = k // 2 + 1
    delta = (k & 1) * 2 - 1
    res = []
    for _ in range(k // 2):
        res.append(a)
        a -= delta
        b += delta
        res.append(b)
    if k & 1:
        res.append(a)
    for a in range(k + 1, n + 1):
        res.append(a)
    print(*res)


main()