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. 
def main():
    n, k = map(int, input().split())

    res = [1]
    visited = {1}
    j = 0
    for i in range(k, 0, -1):
        res.append(res[-1] + i if j % 2 == 0 else res[-1] - i)
        visited.add(res[-1])
        j += 1


    for i in range(1, n + 1):
        if i not in visited:
            res.append(i)

    print(*res)

if __name__ == '__main__':
    main()
