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 math

n, k = [int(x)for x in raw_input().split(' ')]

init = range(1, n + 1)
r = []
#init[0] = -1
for i in xrange(n - k):
    r.append(i + 1)
    init[i] = -1

start = r[-1]

for i in xrange(k):
    h = r[-1] + (1 - 2 * (i % 2)) * (n - start - i)
    r.append(h)
    #print init, h
    init[h - 1] = -1
    #print r


'''

for i in xrange(k, 1, -1): #xrange(1, k + 1):
    h = i + r[-1]
    if h <= n and h not in r:
        r.append(h)
    else:
        h = r[-1] - i
        r.append(h)
    init[h - 1] = -1

#print r

for e in init:
    if e is not -1:
        r.append(e)
'''
print ' '.join([str(x) for x in r])