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,m=map(int,input().split())
l=[1]
m=m-1
s=n
p=2
while m>0 :
    l.append(s)
    m=m-1
    s=s-1
    if m>0 :
        l.append(p)
        m=m-1
        p=p+1
if l[len(l)-1]-p==-1 :
    z=p
    c=1
else :
    z=s
    c=2
while len(l)!=n :
    if c==1 :
        l.append(z)
        z=z+1
    else :
        l.append(z)
        z=z-1
print(*l)
    
    
