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. 
i = str.split(input(), " ")
n = int(i[0])
k = int(i[1])
maxx = n
minn = 1

res = ""
for x in range(n-k):
    res += str(maxx) + " "
    maxx -= 1
for z in range(k):
    if z%2 == 0:
        res += str(minn) + " "
        minn += 1
    else:
        res += str(maxx) + " "
        maxx -= 1 
res = res[:-1]
print(res)
