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. 
'''
if the k max n-1
the difference are 1,2,..,n-1
n-1 is odd
    +2 -1 +3
n-1 is even
    +2 -1 +4 -3

the difference are 1, 2, n-2, let the repeated be 1
'''
n, k = [int(x) for x in input().split()]
repeated = n - k - 1
current = 1 + repeated
print(' '.join([str(x) for x in list(range(1,repeated+2))]),end=' ')
for i in range(1,k+1):
    current += ((-1)**(i+1))*(k-i+1)
    if i <k:
        print(current,end=' ')
    else:
        print(current)