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. 
#In the name of Allah

from sys import stdin, stdout
input = stdin.readline

n, k = map(int, input().split())

def f(n):
        n += 1
        l = []
        for i in range(1, 1 + n // 2):
                l.append(str(i))
                l.append(str(n - i + 1))
        if n % 2 == 1:
                l.append(str(n // 2 + 1))
        return l

ans = f(k)

for i in range(n - k - 1):
        ans.append(str(i + k + 2))

stdout.write(" ".join(ans))
