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, f = map(int, raw_input().split())

a = range(1, n + 1)
res = []

i = 0
k = f
n -= k
while k:
    res.append(a.pop(i * (-1)))
    i = 1 - i
    k -= 1

while n:
    if f % 2:
        res.append(res[-1] + 1)
    else:
        res.append(res[-1] - 1)
    n -= 1

print ' '.join(map(str, res))