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, raw_input().split())

r1 = [(i%2)*((i+1)/2)+(i%2==0)*(n-i/2) for i in range(k-1)]
r2 = range((k+1)/2, n-(k-(k+3)/2)) if k%2==0 else range(n-(k-(k+1)/2), (k-1)/2, -1)

print ' '.join(map(str, r1+r2))

