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. 
import sys

n,k = map(int,(sys.stdin.readline().split()))

l = [n]
t = k
bit = 0

while t >= 1:
    if bit == 0:
        l.append(l[-1]-t)
        bit = 1
    else:
        l.append(l[-1]+t)
        bit = 0
    t -= 1

r = n-k-1
while r > 0:
    l.append(r)
    r -= 1
for i in l:
    print i,
