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 solve(n, k):
    result = [x for x in xrange(1, n+1)]

    m = k+1

    for x in xrange(1, (m+1)/2 + 1):
        result[2*x-2] = x

    for x in xrange((m+1)/2+1, m+1):
        result[(m-x)*2+1] = x

    return result


def main():
    inputs = raw_input().split()
    n, k = int(inputs[0]), int(inputs[1])

    print ' '.join([str(x) for x in solve(n, k)])

if __name__ == '__main__':
    main()