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. 
par = map(int, raw_input().split(" "))
n,k = par[0], par[1]#, par[2], par[3]

p1, p2, z = 1, n, n
while k > 0:
    if k % 2 == 0:
        print p2,
        p2 -= 1
    else:
        print p1,
        p1 += 1
    k -= 1
    z -= 1
for i in xrange(z):
    print p1,
    p1 += 1
    