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 = [int(i) for i in raw_input().split()]
increase_seq = xrange(1,(k+1)/2+1)
decrease_seq = [n-i for i in xrange(0,(k+1)/2)]
combine_seq = []
for i in xrange((k+1)/2):
    combine_seq.append(increase_seq[i])
    combine_seq.append(decrease_seq[i])
combine_seq = combine_seq[:k]
if k%2==0:
    for i in xrange(n-k):
        combine_seq.append(combine_seq[-1]-1)
else:
    for i in xrange(n-k):
        combine_seq.append(combine_seq[-1]+1)
for i in combine_seq:
    print i,





