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

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

i, j = n, n - k + 1
for t in range(n - len(a)):
    if t % 2 == 0:
        a.append(i)
        i -= 1
    else:
        a.append(j)
        j += 1
print(' '.join(map(str, a)))
