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():
    from sys import stdin, stdout
    (n, k) = map(int, stdin.readline().strip().split(' '))
    p = []
    for i in range(n - k):
        p.append(i + 1)
    l = n - k + 1
    o = n
    x = False
    for i in range(n - k + 1, n + 1):
        if x:
            p.append(l)
            l += 1
        else:
            p.append(o)
            o -= 1
        x ^= True
    #se = set()
    #for i in range(len(p) - 1):
        #se.add(abs(p[i] - p[i + 1]))
    #print(len(se))
    stdout.write(' '.join(list(map(str, p))) + '\n')
main()
