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. 
# Description of the problem can be found at http://codeforces.com/problemset/problem/482/A

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

l_n = list()

h = n
l = 1
for i in range(n):
    if i < k:
        if i % 2 == 0:
            l_n.append(i // 2 + 1)
            l = i // 2 + 1
        else:
            l_n.append(n - i // 2)
            h = n - i // 2
    else:
        if i % 2 == 1:
            l_n.extend(l + x for x in range(1, n + 1 - i))
        if i % 2 == 0:
            l_n.extend(h - x for x in range(1, n + 1 - i))
        break
print(" ".join(str(x) for x in l_n))