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 = [int(g) for g in input().split()]
num = list(range(n+1))
del num[0]

#print(num)
s = ""
for i in range(n-k):
	s+=str(num[i])
	s+=" "
#print(s)
f = n-k
r = n-1
i = 0
while r >=f :
	if i % 2 == 0:
		s+=str(num[r])
		s+=" "	
		r-=1
	if i % 2 != 0:
		s+=str(num[f])
		s+=" "	
		f+=1
	i+=1
print(s)