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. 
import fileinput

def str_to_int(s):
	return([ int(x) for x in s.split() ])

# args = [ 'line 1', 'line 2', ... ]
def proc_input(args):
	return(str_to_int(args[0]))

def solve(args, verbose=False):
	(n, k) = proc_input(args)
	perm = [ 1 ] * n
	mult = 1
	ind = 1
	while ind != k + 1:
		perm[ind] = perm[ind - 1] + mult * (k - ind + 1)
		mult *= -1
		ind += 1

	for i in xrange(ind, n):
		perm[i] = i + 1

	if verbose:
		print ' '.join([ str(x) for x in perm ])
	return(perm)

def test():
	assert(str_to_int('1 2 3') == [ 1, 2, 3 ])
	assert(solve([ '3 2' ]) == [ 1, 3, 2 ])
	assert(solve([ '5 2' ]) == [ 1, 3, 2, 4, 5 ])
	assert(solve([ '3 1' ]) == [ 1, 2, 3 ])

if __name__ == '__main__':
	from sys import argv
	if argv.pop() == 'test':
		test()
	else:
		solve(list(fileinput.input()), verbose=True)
