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. 
__author__ = 'neki'

import sys

#sys.stdin = open("permutation.in", "r")
#sys.stdout = open("file.out", "w")

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])
