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. 
s = input().split()
n, k = int(s[0]), int(s[1])
x = 1
c = k
r = 0
for i in range(n):
    print(x, end=" ")
    x += (2 * ((i + 1) % 2) - 1) * c
    c -= 1
    if c < 0:
        r = n - (i + 1)
        break
for i in range(r):
    print((k + 1 + i) % n + 1, end=" ")