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. 
def arr_inp():
    return [int(x) for x in stdin.readline().split()]


from sys import stdin
from collections import *

n, k = arr_inp()
ans, mem, c = [], defaultdict(int), 0

for i in range(n - k):
    ans.append(i + 1)
    mem[i + 1] = 1

for i in range(k, 0, -1):
    ix = ans[-1]
    if c & 1:
        ix -= i
    else:
        ix += i
    if mem[ix] == 0:
        mem[ix] = 1
        ans.append(ix)
    c += 1

print(*ans)
