A. Diverse Permutation
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output
Permutation p is an ordered set of integers p1, p2, ..., pn, consisting of n distinct positive integers not larger than n. We'll denote asn 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.
Sample test(s)
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.