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. 
def get_ints():
    return map(int, raw_input().strip().split(' '))

n, k = get_ints()

ans = [0 for i in xrange(n)]
ans[0] = 1
dx = 1
s = n - 1
for i in xrange(1, n):
    if k == 1:
        ans[i] = ans[i - 1] + dx
    else:
        k -= 1
        ans[i] = ans[i - 1] + dx * s
        s -= 1
        dx *= -1
        
for i in xrange(n):
    print ans[i],
