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. 
s = input()
arr = s.split()
n = int(arr[0])
k = int(arr[1])

print(1,end='')
i = 2
while i in range(2,k+1):
	if i % 2 == 0:
		print('',n - i//2 + 1,end='')
	else:
		print('',(i+1)//2,end='')
	i = i + 1

if k % 2 == 0:
	x = n - k//2
	i = k
	while i in range(k,n):
		print('',x,end='')
		x = x - 1
		i = i + 1
else:
	x = (k + 1)//2 + 1
	i = k
	while i in range(k,n):
		print('',x,end='')
		x = x + 1
		i = i + 1
print()
