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())
i,j,c = 1,n,0
while c < k:
    c += 1
    if c % 2 == 1:
        print i,
        i += 1
    else:
        print j,
        j -= 1
if c % 2 == 0:
    for x in xrange(j,j-(n-k),-1):
        print x,
else:
    for x in xrange(i,i+(n-k)):
        print x,