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. 
from sys import stdin
lines = list(filter(None, stdin.read().split('\n')))

def parseline(line):
	return list(map(int, line.split()))

lines = list(map(parseline, lines))

n, k = lines[0]

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

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