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=input().split()
n=int(n)
k=int(k)-1
b=[]
s=(k+3)//2
b.append(s)
if k%2==0:
	i=1
else: i=-1
while k>-1:
	s=s+i
	b.append(s)
	if i>0:
		i=-1*i-1
	else: i=-1*i+1
	k-=1
while s<n:
	s+=1
	b.append(s)
for d in range(len(b)):
	print(b[d],end=' ')