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, input().split())

ans = [1]
L = [i for i in range(k, 0, -1)]
adds = set([1])
rems = set([i for i in range(2, n + 1)])
flg = True
for l in L:
    if flg:
        tmp = ans[-1] + l
    else:
        tmp = ans[-1] - l
    """
    if tmp in rems:
        ans.append(tmp)
        adds.add(tmp)
        rems.remove(tmp)
    else:
        tmp = ans[-1] - l
        ans.append(tmp)
        adds.add(tmp)
        rems.remove(tmp)
    """
    ans.append(tmp)
    rems.remove(tmp)
    flg = not flg
rems = list(rems)
rems.sort()
for rem in rems:
    ans.append(rem)
print(" ".join(map(str, ans)))
