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 main(data):
    n, k = map(int, data.split())
    result = [0]
    n -= 1
    k -= 1
    cur_delta = 0
    while k < n and n > 0:
        result.append(result[-1] + 1)
        n -= 1
        cur_delta += 1
    while n > 0:
        if cur_delta > 0:
            cur_delta = -(cur_delta + 1)
        else:
            cur_delta = -(cur_delta - 1)
        result.append(result[-1] + cur_delta)
        n -= 1
    m = min(result)
    for r in result:
        print (r-m)+1,

import sys
main(sys.stdin.readline())
