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 sys
stdin = sys.stdin

while True:
    try:
        n, k = map(int, stdin.readline().strip().split())
    except:
        break

    re = [None] * n
    perm = range(1, n+1)
    for i in range(n):
        index = 2*i
        if index >= n:
            index = n-index-1
        re[index] = perm[i]

    last_part = re[-(n-k+1):]
    last_part.sort()
    if (k) % 2 == 0:
        last_part.reverse()
    re[-(n-k+1):] = last_part
    if k == 2:
        re = perm[1:] + [perm[0]]

    print ' '.join(map(str, re))
