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. 
[n, k] = map(int, raw_input().split())
res = []
res.append(1)
res.append(k + 1)
i = 2
delta = k
while i < k + 1:
    delta -= 1
    if i & 1 == 1:
        res.append(res[i - 1] + delta)
    else:
        res.append(res[i - 1] - delta)
    i += 1
i = k + 1
while i < n:
    res.append(i + 1)
    i += 1
print ' '.join(map(str,res))