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. 
data = [int(g) for g in raw_input().split()]
n = data[0]
k = data[1]

answer=[]

if k==1:
	for i in range(n):
		answer.append(i+1)
else:	
	if k % 2 == 1:
		pairs = k//2
		for i in range(pairs):
			answer.append(i+1)
			answer.append(n-i)
		
		for j in range(pairs+1,n-i):
			answer.append(j)

	else:
		pairs = k//2
		for i in range(pairs):
			answer.append(i+1)
			answer.append(n-i)
		
		for j in range(pairs+1,n-i):
			answer.append(n-j+1)
			
print ' '.join(map(str, answer))
	
