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.

Difficulty: EASY

Solutions:
from collections import Counter
import string
import math
import sys
from fractions import Fraction

def array_int():
	return [int(i) for i in sys.stdin.readline().split()]

def vary(arrber_of_variables):
	if arrber_of_variables == 1:
		return int(sys.stdin.readline())
	if arrber_of_variables >= 2:
		return map(int, sys.stdin.readline().split())

def makedict(var):
	return dict(Counter(var))
testcases = 1
for _ in range(testcases):
	(n, k) = vary(2)
	temp = k
	num = [i for i in range(1, n + 1)]
	j = 0
	for i in range(k + 1):
		if i % 2 == 0:
			print(num[j], end=' ')
			j += 1
		else:
			print(num[k], end=' ')
			k -= 1
	for i in range(temp + 1, n):
		print(num[i], end=' ')


([n, k], s) = (map(int, input().split()), [1])
for i in range(k, 0, -1):
	s.append(s[-1] + (-i if (k - i) % 2 else i))
print(*s + sorted(set(range(1, n + 1)) - set(s)))


(n, k) = map(int, list(input().split()))
for i in range(1, (k + 3) // 2):
	print(i, k + 2 - i, end=' ')
if k > 1 and k % 2 == 0:
	print(k // 2 + 1, end=' ')
for i in range(k + 2, n + 1):
	print(i, end=' ')


from sys import stdin, stdout
input = stdin.readline
(n, k) = map(int, input().split())

def f(n):
	n += 1
	l = []
	for i in range(1, 1 + n // 2):
		l.append(str(i))
		l.append(str(n - i + 1))
	if n % 2 == 1:
		l.append(str(n // 2 + 1))
	return l
ans = f(k)
for i in range(n - k - 1):
	ans.append(str(i + k + 2))
stdout.write(' '.join(ans))


(n, k) = map(int, input().split())
a = list(range(1, n + 1))
for i in range(1, k + 1):
	a[i] = a[i - 1] + (k - i + 1 if i & 1 else i - k - 1)
print(' '.join((repr(x) for x in a)))


__author__ = 'neki'
import sys
words = input().split()
n = int(words[0])
k = int(words[1])
perm = [1]
viz = [0 for x in range(n + 1)]
viz[1] = 1
dif = k
one = 1
while dif > 0:
	num = perm[len(perm) - 1] + one * dif
	perm.append(num)
	viz[num] = 1
	one *= -1
	dif -= 1
for i in range(1, n + 1):
	if viz[i] == 0:
		perm.append(i)
for i in range(n - 1):
	print(perm[i], end=' ')
print(perm[n - 1])


(n, k) = map(int, input().split())
L = []
for i in range(n + 1):
	L.append(i)
k1 = k
s = n * (n + 1) / 2 - 1
L[1] = 0
L[k + 1] = 0
print('1', k + 1, end=' ')
k = k - 1
b = k + 2
while s > 0:
	if k == 0:
		break
	if b - k > 0 and L[b - k] != 0:
		print(L[b - k], end=' ')
		L[b - k] = 0
		s -= b - k
		b = abs(b - k)
		k -= 1
	else:
		print(L[b + k], end=' ')
		L[b + k] = 0
		s -= b + k
		b = abs(b + k)
		k -= 1
for i in range(len(L)):
	if L[i] != 0:
		print(L[i], end=' ')