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. 
if __name__ == '__main__':
    n, k = map(int, input().split())
    p, q = 1, n
    rest = list()
    for i in range(k):
        if i % 2 == 0:
            rest.append(p)
            p += 1
        else:
            rest.append(q)
            q -= 1
    if k % 2 == 0:
        for i in range(q, p - 1, -1):
            rest.append(i)
    else:
        for i in range(p, q + 1):
            rest.append(i)
    print(' '.join(map(str, rest)))
