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 sys
n, k = map(int, raw_input().split())
if k == 1:
	for i in range(n):
		print i + 1,
	sys.exit()

print 1,n,
Min, Max = 1, n 
last = 1
for i in range(k - 2):
	if i & 1:
		Max -= 1
		print Max,
		last = 1
	else:
		Min += 1
		print Min,
		last = 0
if last == 1:
	for i in range(Max - 1, Min, -1):
		print i,
else:
	for i in range(Min + 1, Max):
		print i,
