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 P(n):
    return n * (n - 1) // 2

n, k = map(int, raw_input().split())
p=[i//2+1 if i%2==0 else n-i//2 for i in range(n) ]
a=p[:k]
if a[k-1]<p[k]:
    a+=sorted(p[k:])
else:
    a+=sorted(p[k:],reverse=True)
    
for i in a:
    print i,


    
