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. 
from sys import stdout
def main():
    n, k = map(int, raw_input().split())
    if k == 1:
        a = range(1, n+1)
    elif k == 2:
        a = [n] + range(1, n)
    else:
        a = [0] * n
        b = (k+1) / 2
        for i in xrange(b):
            a[i*2] = i + 1
        for i in xrange(k-b):
            a[i*2+1] = n - i
        if k % 2 == 1:
            a[k:] = range(b+1, n-k+b+1)
        else:
            a[k:] = range(n-k+b, b, -1)
    stdout.write(' '.join(map(str, a)))
main()
