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 = [x + 1 for x in range(n)]

l = 0
r = n - 1
p = 0

for i in range(k - 1):
    if p:
        print(a[r], end = ' ')
        r -= 1
        p = not p
    else:
        print(a[l], end = ' ')
        l += 1
        p = not p
        
p = not p

if p:
    for i in range(l, r + 1):
        print(a[i], end = ' ')
else:
    for i in range(r, l - 1, -1):
        print(a[i], end = ' ')
