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 __future__ import nested_scopes, generators, division, absolute_import, with_statement, print_function, unicode_literals
import sys, os, time
input = raw_input
range = xrange

import itertools

def rv(): return map(int, input().split())
def rl(n): return [list(map(int, input().split())) for _ in range(n)]
if os.path.exists("test.txt"): sys.stdin = open("test.txt")
# sys.stdout = open(pass, 'w')

def works(perm, k):
    return len(set(    [abs(perm[i + 1] - perm[i]) for i in range(len(perm) - 1)]     )) == k

def solve(n, k):
    l = [i for i in range(1, n + 1)]
    # for perm in itertools.permutations(l):
    #     if works(perm, k) and perm[0] == 1 and perm[1] == 1 + k:
    #         pass
            # print(perm)
            # print(" ".join(map(str, [perm[i + 1] - perm[i] for i in range(n - 1)])))
    res = [1]
    up = 1
    for i in range(k, 0, -1):
        res.append(res[-1] + i * up)
        up *= -1
    there = set(res)
    for i in range(1, n + 1):
        if i not in there:
            res.append(i)
    # if not works(res, k):
    #     print(n, k, res)
    print(" ".join(map(str, res)))


# for n in range(1, 100):
#     for k in range(1, n):
#         solve(n, k)
n,k, = rv()
solve(n, k)