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 = []
k += 1
one = 0
two = 0
f = False
for i in range(1, n + 1):
    if i % 2 != 0:
        i -= one
        a.append(i)
        one += 1
    else:
        i -= two
        a.append(n + 2 - i)
        two += 1
    k -= 1
    if k == 1:
        f = True
        d = set(a)
        if len(a) % 2 == 0:
            for j in range(n -  1, 0, -1):
                if j not in d:
                    a.append(j)
        else:
            for j in range(1, n + 1):
                if j not in d:
                    a.append(j)
    if f:
        break
print(*a)