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. 
x=raw_input()
n,k=x.split(" ")
n=int(n)
k=int(k)
l=1
r=0
if k==1:
    for i in xrange(1,n+1):
        print i,
else:
   
    r=k+1
    while l<r:
        print l,r,
        l=l+1
        r=r-1
    if(l==r):
        print l,
    if(l>=r):
        if k+1!=n:
            for i in xrange(k+2,n+1):
                print i,