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 = list(map(int, input().split()))

ar = [i + 1 for i in range(n)]

if k == 1:
    print(' '.join(map(str, ar)))
else:
    shuffle = ar[:k+1]

    r = len(shuffle)-1
    l = 0

    ans = []
    t = 'r'
    while l != r:
        if t == 'r':
            ans.append(shuffle[r])
            r -= 1
            t = 'l'
        else:
            ans.append(shuffle[l])
            t = 'r'
            l += 1

    ans.append(shuffle[l])
    ans = ans + ar[k+1:]
    print(' '.join(map(str, ans)))