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 = map(int,input().split())

b = ''

i = 1
j = n
c = 0
p = 0

while(p < n):
	if(c < k):
		if(p % 2 == 0):
			b += str(i) + ' '
			i += 1
			c += 1
		else:
			b += str(j) + ' '
			j -= 1
			c += 1
	else:
		if(p % 2 == 1):
			for q in range(i,j+1):
				b += str(q) + ' '
			print(b)
			exit(0)
		else:
			for q in range(j,i-1,-1):
				b += str(q) + ' '
			print(b)
			exit(0)
	p += 1

print(b)