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. 
a, b = map(int, input().split(' '))
for i in range(1, a - b + 1):
    print(i)
curr = i

if b % 2 == 0:
    for i in range(b, 0, -1):
        if i % 2 == 0:
            curr = curr + i
        else:
            curr = curr - i
        print(curr)

else:
    for i in range(b, 0, -1):
        if i % 2 == 1:
            curr = curr + i
        else:
            curr = curr - i
        print(curr)
