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(' '))
lst = [1]
vis = [0 for i in range(0, k+2)]
for i in range(k, 0, -1):
    tmp = lst[-1] + i
    if tmp <= k+1 and vis[tmp] == 0:
        lst.append(tmp)
        vis[tmp] = 1
    else:
        tmp = lst[-1] - i if lst[-1] - i > 0 else i - lst[-1]
        if vis[tmp] == 0:
            vis[tmp] = 1
            lst.append(tmp)
if len(lst) != n:
    lst.extend([i for i in range(k+2, n+1)])
print ' '.join([str(i) for i in lst])
